Seminarium Zakładowe - Archiwum

We analyze the correlation between the energy, pressure and spatial entanglement produced by two luminal jets in the massive Schwinger model. Using tensor network methods, we show that for m/g>1/pi, in the vicinity of the strong to weak coupling transition, a nearly perfect and chargeless effective fluid behavior appears around the mid-rapidity region with a universal energy-pressure relationship. The evolution of energy and pressure for this range of masses is strongly correlated with the rise of the spatial entanglement entropy, indicating a key role of quantum dynamics - in contrast to the behaviour for small masses.

Tensor networks have been enormously successful at studying the quantum many body problem. By exploiting the structure of entanglement in a many-body quantum lattice system, a tensor network ansatz can accurately represent quantum state vectors with exponentially fewer parameters. While well known tensor network algorithms such as DMRG and TDVP are primarily used for the study of one-dimensional, closed systems, this presentation describes some state-of-the-art methods that can be applied to two-dimensional quantum systems evolving according to the Lindblad equation. Some new developments enabling the study of models with long-range interactions are also presented.

The Atomic Clock Ensemble in Space (ACES), launched on April 21st from ESA's Kourou spaceport in French Guiana, will bring a new generation of ultra-precise atomic clocks to the microgravity environment of the International Space Station (ISS). Using an advanced microwave link, ACES will enable direct time comparisons with a global network of ground-based clocks. At the core of its scientific objectives, ACES will test Einstein’s theory of General Relativity through an absolute measurement of gravitational redshift. Additionally, it will search for temporal variations of fundamental constants, probe for local dark matter structures near Earth, and explore extensions of the Standard Model. This talk will provide an overview of the instrument, its primary scientific goals, and the fundamental physics tests it will conduct.

Michele Armano is a senior scientist at the European Space Agency (ESA) with a Ph.D. in physics and a background in quantum field theory and general relativity. He specializes in gravitational physics and precision measurement in space, with past key roles in ACES (Atomic Clock Ensemble in Space) and LISA Pathfinder as an expert in instrumentation and data analysis. He now serves in the Scientific Performance Team of the LISA project. Armano teaches aerospace engineering at Universidad Europea in Madrid and is a visiting professor at AGH’s Space Technology Center & Faculty in Krakow, where he teaches orbital mechanics and general relativity in the newly-established Master's Program.

Perception of physical phenomena was a crucial part of survival techniques, which eventually resulted in formulation of physics. Together with the relativity theory, quantum mechanics became a crack on our consistent understanding of the Universe by the means of deterministic classical mechanics. Numerous interpretations have been proposed, prioritizing a special role of the agent (observer), attachement to classical physics concepts, time-reversal symmetry, or even neglecting the physical background alltogether. In this work I attempt to revise the status of these interpretations starting with possibly light luggage of philosophical points of view. If we assume frugality (minimalism in defining new beings), the Copernican principle (that physical laws govern systems irrespective of human role) and physicality (that our observations correspond to reality), we end up with conclusion similar to Everett’s, but not ivalidating main aspects of some other viewpoints. One can now propose a model for a wide variety of quantum measurement devices, define the precise moment of a measurement and provide some answers to both measurement problems of Itamar Pitovski. Wigner’s friend gedankenexperiment shall also be revised in this framework.
This work is a lead article in the “Quantum Measurement” special issue of “Entropy”.

We formulate the criterion for a lossless transfer of information across a many-body system and show that a single qubit can play the role of an antenna that gathers vast amounts of information from a complex system. We derive the condition under which the antenna, far apart from the source and embedded in a many-body interacting medium, can still collect the complete information. A striking feature of this setup is that a single-qubit antenna can accommodate even the full signal amplified by the entanglement of the source. In consequence, the retrieval of this information can be performed with simple one-qubit operations on the antenna (which we fully characterize) rather than multi-qubit measurements of the source. Finally, we discuss the control over the system parameters that is necessary for lossless signal propagation. A method discussed here could improve the precision of quantum devices and simplify the metrological protocols.

We theoretically derive the probability densities of the entanglement measures of a pure non-ergodic many-body state, represented in a bipartite product basis and with its reduced density matrix described by a generalized, multi-parametric Wishart ensemble with unit trace. Our results indicate significant fluctuations of the measures around their average behavior (specifically for the states away from separability and maximum entanglement limits). The information is rel- evant not only for hierarchical arrangement of entangled states (e.g., revealing the flaws in their characterization based on average behavior) but also for phase transition studies of many body systems.

We analyze the correlation between the energy, pressure and spatial entanglement produced by two luminal jets in the massive Schwinger model. Using tensor network methods, we show that for m/g>1/pi, in the vicinity of the strong to weak coupling transition, a nearly perfect and chargeless effective fluid behavior appears around the mid-rapidity region with a universal energy-pressure relationship. The evolution of energy and pressure for this range of masses is strongly correlated with the rise of the spatial entanglement entropy, indicating a key role of quantum dynamics - in contrast to the behaviour for small masses.

Spin-squeezing and Bell non-locality are consequences of quantum correlations among particles, the latter conveniently identified using inequalities. Spin chains are especially suitable for studying the fundamental aspects of these correlations. Vacancies or multiple spins per site are usually omitted from theoretical investigations in the literature. However, they may play an important role in spin squeezing and Bell correlations. We provide a microscopic study of occupation defects on the dynamical generation of spin squeezing when different t-J models effectively govern dynamics. We also propose a Bell inequality tailored for such a scenario expressed in collective measurements. Our results bound the filling factors which generate non-trivial quantum correlations in the system.

[1] https://doi.org/10.1103/PhysRevB.109.214310
[2] https://doi.org/10.1103/PhysRevA.111.023312

Identifying the optimal quantum metrological protocols in presence of realistic noise may be challenging. Brute force methods usually do not allow to study models in the regimes interesting from practical point of view. In this talk I will present the state-of-the-art (and even a bit beyond..) tools that allow for an efficient search of the optimal protocols even in asymptotic regime of infinite available resources (particles, time, etc..) as well as methods to derive fundamental bounds that can certify their optimality.

When a Rydberg atom and a ground state perturber atom encounter one another, they interact via an oscillatory potential mediated by the scattering of the Rydberg electron off of the perturber. The wells in this potential can trap the perturber, binding the two atoms together into a molecule. This same mechanism can also cause trimers, tetramers, and larger clusters to form. As the number of perturbers increases, it becomes impractical to describe this Rydberg composite within the framework of molecular physics, as its properties start to mirror those of a solid-state system. A clear example of this is the modified spectrum of the Rydberg electron in the presence of a dense environment of immobile perturbers. Because this spectrum of an isolated Rydberg atom is highly degenerate due to its SO(4) symmetry, an exact mapping exists between the perturbed Rydberg states and the states of a particle in a tight-binding lattice. Using this mapping, we demonstrate how to realize a thermodynamic limit in the Rydberg electron. This thermodynamic limit and the control over the properties of the tight-binding lattice through the arrangement of the perturbers allow us to prove that the Rydberg electron can undergo Anderson localization in a disordered perturber landscape. The confluence of the infinite-ranged Coulomb potential and the zero-range electron-atom potentials leads to a plethora of possible lattice parameters, ranging from nearest-neighbor hopping to all-to-all coupling between sites.

Solutions of the wave equations for time-independent disordered media can exhibit Anderson localization where instead of wave propagation we observe their localization around different points in space. Photonic time crystals are spatially homogeneous media in which the refractive index changes periodically in time, leading to the formation of bands in the wave number domain. By analogy to Anderson localization in space, one might expect that the presence of temporal disorder in photonic time crystals would lead to Anderson localization in the time domain. Here, we show that indeed periodic modulations of the refractive index with the addition of temporal disorder lead to Anderson localization in time, where an electromagnetic field can emerge from the temporally modulated medium at a certain moment in time and then decay exponentially over time. Thus, we are dealing with a situation where, in a fluctuating three-dimensional medium, the birth and death of waves can occur, and the mechanism of this phenomenon corresponds to Anderson localization.

We provide insights into how isolated quantum systems approach eigenstate transitions by analysing low-ω offdiagonal matrix elements and fidelity susceptibilities. We put forward a minimal model that focuses on integrals of motion and how they acquire finite relaxation times. It captures two limiting cases: one with narrowly distributed relaxation times, leading to fading ergodicity and maximal divergence of fidelity susceptibilities, and another with broadly distributed relaxation times, resulting in a slowdown of autocorrelation functions and sub-maximal scaling of fidelity susceptibilities. We test this minimal model in the 3D Anderson system, examining transitions from quasimomentum-space localization to quantum chaos and from quantum chaos to position-space localization. We observe peaks in fidelity susceptibilities near both transitions, with maximal divergence emerging only near the first one. Finally, we relate the sub-maximal scaling of the second peak to the polynomial decay of the survival probability.

With the rapid development of various concepts in quantum information and metrology, there is a continuous need to verify emerging ideas. Unfortunately, many studies can only be conducted using complex and costly setups that trap ultracold atomic gases or ions. Our approach aims to utilize a simpler and more accessible platform for testing quantum protocols, which is especially important from the perspective of quantum metrology. This seminar introduces an alternative approach focused on collective quantum states formed within a macroscopic cloud of approximately 109 atoms in room-temperature alkali-metal vapors.

In this talk, I will present the current state of development of our experimental research platform for quantum information studies. I will begin by introducing our method for quantum state tomography (QST), highlighting new techniques that enhance its stability. Next, I will discuss a newly developed approach for generating nonlin- earity within our system, which plays a crucial role in expanding the range of accessible quantum phenomena by providing new possibilities for quantum state control. Additionally, I will introduce our progress in quantum pro- cess tomography, demonstrating its feasibility within our platform. Finally, I will showcase a practical application of our system in the study of a new class of metrological states—Perfect Quantum Protractors (PQP).

Levitated nanoparticles provide a controllable and isolated platform for probing fundamental quantum phenomena at the macroscopic scale due to their large mass. After a successful experimental preparation of a motional ground state of a nanoparticle via optical control techniques, one of the pursued directions to expand the quantum control toolbox is to take advantage of potentially less decoherence-prone electric potentials in a hybrid optical-nonoptical setup. Due to the large masses of nanoparticles, such potentials are wide---their characteristic length scales are much larger than the zero-point motion of optically trapped particles. This discrepancy of scales leads to complicated, phase-space multiscale, and nonlinear dynamics that is particularly challenging to model. We provide two methods that enable tackling such scenarios. The first one is based on physically informed dynamical frame transformation and numerically exact solutions [1], while the second one involves semiclassical approximations of the system’s time-evolved state [2].
Based on those methods, we present an experimental proposal [3] for the rapid preparation of the center of mass of a levitated particle in a macroscopic quantum state, that is a state delocalized over a length scale much larger than its zero-point motion and that has no classical analog. This state is prepared by letting the particle evolve in a static double-well potential after a sudden switchoff of the harmonic trap, following initial ground-state cooling.
Beyond such a double-well protocol, we introduce an optimization method to determine optimal static potentials for the generation of largely delocalized and non-Gaussian quantum states [4]. Our optimization strategy accounts for position-dependent noise sources originating from the fluctuations of the potential. We provide key figures of merit that allow for fast computation and capture relevant features of the dynamics, mitigating the computational demands associated with the multiscale simulation of this system.
Finally, we explore the time-dependent shaping of a wide nonharmonic potential with quantum optimal control techniques [5]. Specifically, we show that optimal potential modulation alongside nonharmonicity enhancement due to motional delocalization can be utilized to prepare a variety of quantum non-Gaussian states, including Fock or cat states, in a resource-optimal way.

[1] Roda-Llordes et al., Numerical simulation of large-scale nonlinear open quantum mechanics, Phys. Rev. Res. 6, 013262 (2024).
[2] Riera-Campeny et al., Wigner Analysis of Particle Dynamics and Decoherence in Wide Nonharmonic Potentials, Quantum 8, 1393 (2024).
[3] Roda-Llordes et al., Macroscopic quantum superpositions via dynamics in a wide double-well potential, Phys Rev. Lett. 132, 023601 (2024).
[4] Casulleras et al., Optimization of Static Potentials for Large Delocalization and Non-Gaussian Quantum Dynamics of Levitated Nanoparticles Under Decoherence, Phys. Rev. A 110, 033511 (2024)
[5] Grochowski et al., Quantum control of continuous systems via nonharmonic potential modulation, arXiv:2311.16819.

I will present an overview of recent results on the relation between thermodynamics and information- theoretic correlations in nonequilibrium open quantum systems coupled to a thermal environment. First, I will demonstrate that the entropy production - a key quantity characterizing the irreversibility of thermodynamic processes - can be linked to the generation of correlations between the degrees of freedom within the environment [1]. Next, I will discuss how such correlations can be decomposed into classical and quantum components [2]. For fermionic systems, classical correlations are shown to always dominate, whereas bosonic systems exhibit a quantum-to-classical transition, with classical correlations prevailing in the high-temperature regime.
Furthermore, I will show that in fermionic systems, quantum entanglement between the system and the environment can emerge under relatively mild nonequilibrium conditions, even when the system's dynamics can be effectively described classically [3]. Finally, I will explain how the delocalized state of a single fermion can, to some extent, be classified as an entangled state, as it enables certain open quantum thermodynamic processes that are classically forbidden [4].

[1] K. Ptaszyński, M. Esposito, Phys. Rev. Lett. 123, 200603 (2019)
[2] K. Ptaszyński, M. Esposito, PRX Quantum 4, 020353 (2023)
[3] K. Ptaszyński, M. Esposito, Phys. Rev. B 109, 115408 (2024)
[4] K. Ptaszyński, M. Esposito, Phys. Rev. Lett. 130, 150201 (2023)

I will introduce the topic of scalar field dark matter, quite relevant for lovers of Bose quantum gases and classical wave fields, and then tell a bit about our preliminary investigations with collaborators at Newcastle University into the nonequilibrium dynamics of a nonequilibrium dark matter halo. So far simplified to include only radial excitations.

Recently, high harmonic spectroscopy has emerged as a useful tool for probing condensed matter systems with the potential to identify unconventional phases. In this talk, the basics of the interaction between an intense laser field and crystalline materials beyond the linear response theory will be presented. It will also be shown that the analysis of high harmonic spectra can be used to characterize some nontrivial phases and transitions between them. Examples include the metal-insulator transition, states with non-trivial topology, or with multifractal wave functions. The application of high harmonic spectroscopy to the study of strongly correlated systems will also be discussed.

The impurity embedded in a medium acquires effective mass and can often be described as a quasiparticle. For strong interactions the problem becomes difficult to study, as one can no longer separate the lengthscales corresponding to few- and many-body phenomena. I will describe simple theoretical approaches which include the long-range nature of the potential at the cost of making other approximations, applicable both to Fermi and Bose gases.

Our theoretical research focuses on quasi-one-dimensional systems. The one-dimensional (1D) confinement gives rise to effects ranging from classical-like solitons to genuinely many-body phenomena, such as the 'fermionization' of bosons and the super-Tonks-Girardeau effect -- where a gas remains unexpectedly stable after the interaction is tuned to attractive. These effects can be combined to impmelent 'topological' pumping, as demonstrated with Dysprosium atoms in the experiments by Ben Lev's group [1].

Building on this foundation, I will explore the emergence of self-bound states, precursors of 1D quantum droplets, driven by non-local attractions [2], extending to the strongly interacting regime [3], and present novel 1D effects specific to dipolar systems. Within a dipolar quantum droplet, one can generate a dark solitary wave with a controllable width, which can become infinitely broad in certain regimes [4]. Intriguingly, when a one-dimensional dipolar droplet undergoes a change in van der Waals interactions from repulsive to attractive, it displays unexpected many-body behavior. Contrary to intuitive expectations of either collapse (due to purely attractive forces) or enhanced stability (as seen in the super-Tonks-Girardeau effect), the droplet instead evaporates [5].

Finally, I will present three-dimensional results to discuss the feasibility of creating these quasi-one-dimensional objects within real three-dimensional systems.

[1] W. Kao, et al. Science 371 ,296 (2021)
[2] D. Edler, C. Mishra, F. Wachtler, R. Nath, S. Sinha, L. Santos, Phys. Rev. Lett. 119, 050403 (2017), B. Tüzemen, M. Marciniak, K. Pawłowski, arxiv 2410.03513
[3] R. Ołdziejewski, W. Gorecki, K. Pawłowski, K. Rzazewski, Phys. Rev. Lett. 124, 090401 (2020)
[4] J. Kopycinski, M. Łebek, W. Górecki, K. Pawłowski, Phys. Rev. Lett. 130, 043401 (2023)
[5] M. Marciniak, M. Łebek, J. Kopycinski, W. Górecki, R. Ołdziejewski, K. Pawłowski, Phys. Rev. A 108, 043304 (2023)

Time crystalline structures can be created in periodically driven systems. They are temporal lattices which can reveal different condensed matter behaviours ranging from Anderson localization in time to temporal analogues of many-body localization or topological insulators. However, the potential practical applications of time crystalline structures have yet to be explored. We pave the way for time-tronics where temporal lattices are like printed circuit boards for realization of a broad range of quantum devices. The elements of these devices can correspond to structures of dimensions higher than three and can be arbitrarily connected and reconfigured at any moment. Moreover, our approach allows for the construction of a quantum computer, enabling quantum gate operations for all possible pairs of qubits. This research indicates that the limitations faced in building devices using conventional spatial crystals can be overcome by adopting crystalline structures in time.

Several high-precision experiments at the Antiproton Decelerator complex at CERN aim to look for any significant differences between matter and antimatter. One of these experiments is AEgIS, whose primary goal is to test the weak equivalence principle for antimatter by measuring (with atomic accuracy) the free fall of a neutral antihydrogen atom in the Earth's gravitational field. The experimental setup can also be used to produce on-demand antiprotonic atoms in which one of the electrons is substituted by an almost 2,000 times heavier antiproton. I will present how this research could potentially become yet another opportunity for precise testing of fundamental theories.

We drive a spin resonance by two nearly degenerate microwave fields and observe magnetic resonance structures with two components of different widths. One component undergoes regular power-broadening, whereas the linewidth of the other one becomes power-independent and undergoes field-induced stabilization. We show that the observed width stabilization is a general phenomenon that occurs in open systems.

Periodic driving of systems of particles can create crystalline structures in time. Such systems can be used to study solid-state physics phenomena in the time domain. In addition, it is possible to engineer the wave-number band structure of optical systems and to realize photonic time crystals by periodic temporal modulation of the material properties of the electromagnetic wave propagation medium. We introduce here a versatile averaged-permittivity approach which empowers emulating various condensed matter phases in the time dimension in a traveling wave resonator. This is achieved by utilizing temporal modulation of permittivity within a small segment of the resonator and the spatial shape of the segment. The required frequency and depth of the modulation are experimentally achievable, opening a pathway for research into the practical realisation of crystalline structures in time utilising microwave and optical systems.

The concept of indistinguishability constitutes the fundamental principle for quantum many-particle systems, from which other equally important concepts such as the Pauli exclusion or appearance of Bose-Einstein condensation bear their origin. We show that for strongly correlated fermions very heavy and spin dependent effective masses of quasiparticles appear naturally and in this way a unique opportunity of testing this principle opens up. A transmutation of indistinguishable particles into their distinguishable correspondents (and back) is discussed in detail as a function of the system with spin polarization. An explicit example of the statistics transmutation appriopriate to this situation is also demonstrated.
*The research supported by the Narodowe Centrum Nauki through the grant OPUS

Intensity modulation/direct detection optical key distribution (IM/DD OKD) is a technique to generate a cryptographic key over an optical communication link that is secure against passive eavesdropping. The key security is guaranteed by the shot noise inherent to the photodetection process and can be ensured even when the fraction of the signal captured by an eavesdropper is larger than that received by the legitimate recipient. This talk will review the physical principle of IM/DD OKD, present a proof-of-principle demonstration, and discuss estimates for attainable key rates in space-to-ground communication scenarios.remotehowtojoin=

We study a mixture of a dipolar condensate and a degenerate Fermi gas in a quasi-one-dimensional geometry. We demonstrate that the presence of fermions can drastically change the behavior of a dipolar condensate. For strong enough boson-fermion attraction a dipolar Bose-Fermi droplet appears in the mixture and a roton excitation develops in the Bogoliubov spectrum. As shown analytically and by solving numerically the coupled set of extended Gross-Pitaevski and Hartree- Fock equations for bosonic and fermionic components, respectively, the roton instability mechanism leads to the formation of a supersolid phase in a Bose-Einstein condensate. Scaling arguments show that, although the dysprosium atoms are considered to demonstrate the appearance of the supersolid phase, such a phase can be observed with less magnetic atoms.remotehowtojoin=

Many-body localization (MBL) hinders the thermalization of quantum many-body systems in strong disorder, resulting in numerous experimental and numerical studies. Although the status of MBL as a dynamical phase of matter is to be addressed, this does not diminish the importance of the regime of (nearly) arrested dynamics at strong disorder strengths. Typical studies on MBL consider the presence of on-site disorder; the phenomenological properties in the MBL regime can then be described within the framework of local integrals of motions (LIOMs) identified as dressed single-site operators. This seminar will focus on a bond-disordered Hamiltonian, a model relevant for experiments in Rydberg atom platforms, which shows nonparadigmatic features in the MBL regime that are not captured within a standard LIOM description. Instead, a simple renormalization group-based scheme will be used to elucidate the eigenstate properties and reveal appropriate probes for experiments. It will also illustrate how to extend this scheme to more generic Hamiltonians.

We demonstrate that searching for local integrals of motion in lattice quantum systems is equivalent to a data compression problem. We use this equivalence for the studies of tilled systems which exhibit several unusual phenomena, including the Hilbert space fragmentation. It is an ergodicity breaking phenomenon, in which Hamiltonian shatters into exponentially many dynamically disconnected sectors. We show that one of paradigmatic models which exhibit the Hilbert space fragmentation, hosts also local integrals of motion (LIOMs), which correspond to frozen density modes with long wavelengths. Finally, we make a connection with a Stark chain. Contrary to the dipole-conserving effective models, the Stark chain is shown to support either Hamiltonian or dipole moment as an LIOM.

Spin-squeezing in systems with single-particle control is a well-established resource of modern quantum technology. Applied in an optical lattice clock can reduce the statistical uncertainty of spectroscopic measurements. During the seminar, I will discuss my journey in exploring the dynamical generation of spin squeezing with ultra-cold, both bosonic and fermionic species. I will show different scenarios leading to squeezing generation via spin-orbit coupling, anisotropy or rising lattice depth. I will also discuss the effect of non-uniform filling caused by hole doping, non-zero temperature and external confinement which we studied recently at a microscopic level demonstrating their limiting role in the dynamics and scaling of spin squeezing.

In this talk I will apply the hydrodynamic paradigm to construct a low energy theory for Fractonic systems at finite temperature including dissipative effects. Fractons are excitation that are not allowed to move, however, they can travel in tandem. In fact, their kinematic constraints can be understood in term of the so-called multipole symmetry group.
After a brief introduction to fractons and the multipole symmetry group, I will construct the most general hydrodynamic theory compatible with a translational invariant systems that conserves charge and dipole moment. I will conclude with a comparison of the predicted hydrodynamic modes with those of ordinary hydrodynamics.

In the initial part of the talk an extended overview will be presented on individual and collective spins, the states of the collective spin, squeezing the collective spin states. We will also talk on different spin squeezing mechanism including one axis twisting (OAT) and two axis countertwisting (TACT) spin squeezing models. Subsequently we discuss possibilities to produce spin squeezing for spinful atomic fermions in optical lattices It is shown that by applying laser radiation one can simulate not only OAT but also TACT spin squeezing models, the latter TACT model providing better squeezing. The spin squeezing generated in this way is mediated by spin waves playing a role of the intermediate states facilitating the squeezing process. The spin squeezing can be used for increasing sensitivity of atomic clocks.
More about this work:
Phys. Rev. Lett. 129, 090403 (2022)
Phys. Rev. B 108, 104301 (2023)

The multitime probability distributions that describe the sequential measurements of a quantum observable generally violate Kolmogorov's consistency property. Therefore, one cannot interpret such distributions as the result of the sampling of a single trajectory representing the observable. We show that, nonetheless, they do result from the sampling of one pair of trajectories. In this sense, rather than give up on trajectories, quantum mechanics requires to double down on them. To this purpose, we prove a generalization of the Kolmogorov extension theorem that applies to families of complex-valued bi-probability distributions (that is, defined on pairs of elements of the original sample spaces), and we employ this result in the quantum mechanical scenario [1].

[1] D. Lonigro, F. Sakuldee, Ł. Cywiński, D. Chruściński, P. Szańkowski arXiv: 2402.01218 [quant-ph]

The experimental realization of an ultracold mixture with a single impurity immersed in several fermions in a one-dimensional harmonic trap motivated theoretical studies of this system. Unfortunately, for strong inter-component interactions, typical numerical methods require tremendous computational resources, what limit the analysis to very small mixtures. In my seminar, I will present an alternative, numerically exact approach in which the problem is simplified using an appropriately tailored canonical transformation. The method is especially effective in the case of heavy impurity, where the problem is reduced to a weakly interacting system.

The monochromatic eigenstates of the free electromagnetic (EM) field Hamiltonian are a common and natural choice for expressing the state of a normalised, single-photon wave packet. The orthogonality and dynamics of these states help to both simplify calculations and provide natural interpretations of different effects. A complementary but equally useful approach would be to represent photon wave packets in terms of point-like localised excitations. A local description of the EM field, however, is prohibited due to violations of strict causality in the standard quantisation and the non-orthogonality of the local EM field observables. In this talk I shall explore a description of localised photon states that overcomes previous difficulties by extending the Hilbert space of the EM field. By modelling light in terms of causally-propagating local photons, I shall re-derive two results that are traditionally associated with the frequency representation of the EM field; namely the Casimir force between two flat conducting plates and the relativistic Doppler shift of single photons.

The well-known interference pattern of bright and dark fringes was first observed for light beams back in 1801 by Thomas Young. The maximum visibility fringes occur when the irradiance of the two beams is equal, and as the ratio of the beam intensities deviates from unity, fringe visibility decreases. An interesting outcome that might not be entirely intuitive, however, is that the wavefront of such unequal amplitude beams' superposition will be “wavy”. We experimentally observed the backflow phenomenon within this wavy wavefront [1]. Backflow appears in both optics (retro- propagating light) and in quantum mechanics (QM), where a local phase gradient is not present within the spectrum of the system [2]. In a follow-up experiment, we examined the interference of classical light carrying only negative orbital angular momenta, and in the dark fringes of such an interference, we detected positive local orbital angular momentum [3]. In the last part of the talk, I will discuss a different aspect of two-beam interference. We demonstrated that even when the lowest order interference fringes cannot be detected due to phase fluctuations, fringes appearing in intensity correlations enable the recovery of spatial phase profiles [4].

[1] A. Daniel, B. Ghosh, B. Gorzkowski, and R. Lapkiewicz, “Demonstrating backflow in classical two beams’ interference” New. J. Phys. 24, 123011(2022).
[2] M. V. Berry, “Quantum backflow, negative kinetic energy and optical retro-propagation” J. Phys. A: Math. Theor. 43, 415302 (2010).
[3] B. Ghosh, A. Daniel, B. Gorzkowski, and R. Lapkiewicz, “Azimuthal backflow in light carrying orbital angular momentum” Optica 10 (9), 2334-2536 (2023).
[4] J. Szuniewicz, S. Kurdziałek, S. Kundu, W. Zwoliński, R. Chrapkiewicz, M. Lahiri, R. Lapkiewicz, “Noise-resistant phase imaging with intensity correlation” Sci. Adv.9,eadh5396 (2023).

The idea of causal order of events is rooted in our natural understanding of the world. Nevertheless, quantum mechanics shows that our intuition may fail and order of some events may be indefinite. Basing on the formalism of the process matrices, in this talk, we would investigate to what extend the causal order can be correctly deduced. To do so, we propose N-player communication task in which players try to maximize the probability of successful discrimination of the hidden causal order.

Research, initiated and fully developed at the Institute of Physics of the Polish Academy of Sciences, demonstrated that quantum graphs can be experimentally simulated by microwave networks. This technique and methodology has become an universal experimental tool, now used globally in studying properties of linear and nonlinear quantum graphs.

One-dimensional wave simulators of quantum graphs have been used, e.g., to demonstrate that Mark Kac’s famous question, 'Can one hear the shape of a drum?' can be extended to one-dimensional scattering systems, to prove that there exist non-Weyl graphs which do not obey a standard Weyl’s law.

In my talk I will also discuss an experimental study of missing-level statistics of chaotic microwave networks and the application of two types of Euler characteristics of graphs.

A pendulum clock has been the primary instrument for measuring time for several centuries, and yet there are still some aspects of its dynamics that are not fully understood. In the current era of atomic clocks, what can be still learned from studying mechanical devices? How the 1722 design of John Harrison achieved an error of under 1 second in 100 days of operation, and despite that has been mostly overlooked until recently? What is the connection between time measurement and increase of entropy - seemingly the only physical phenomenon that indicates the direction of the flow of time? I'll provide the answers to these and other questions in my presentation, spanning multiple topics in classical mechanics, termodynamics, chaos theory and.. Lego bricks.

During the talk, I will tackle some generally known 'facts' about overpopulation, disastrous effects of CO2 on life, and weather changes over the last 70 years using available data for Poland and the world.

Quantum phase transitions manifest themselves in various forms, each with their own features. In particular, criticality is known to be a resource for quantum enhanced sensitivity. In this talk, we investigate various forms of criticality in both closed and open quantum systems to find out what features in these phase transitions are responsible for achieving quantum enhanced sensitivity. In particular, we explore Stark localization [1], symmetry protected topological systems [2], Floquet systems for both DC [3] and AC [4] and boundary time crystals [5]. While phase transition in these systems may have different origins, there is one common feature among all of them: gap closing. This suggests that gap closing is the main feature in phase transitions which is responsible for quantum enhanced sensitivity.

References:
[1] X. He, R. Yousefjani, A. Bayat, Phys. Rev. Lett. 131, 010801(2023)
[2] S. Sarkar, C. Mukhopadhyay, A. Alase, A. Bayat, Phys. Rev. Lett. 129, 090503 (2022)
[3] U. Mishra, A. Bayat, Phys. Rev. Lett. 127, 080504 (2021)
[4] U. Mishra, A. Bayat, Scientific Reports 12, 14760 (2022)
[5] V. Montenegro, M. G. Genoni, A. Bayat, M. G. A. Paris, Commun. Phys. 6, 304 (2023)

The escalating demand for energy is directly correlated with the global increase in population and advancements in living standards. To meet this demand sustainably, various sources of renewable energy are being harnessed amidst the backdrop of a growing climate crisis. One promising avenue is the utilization of the thermoelectric (TE) effect, which involves the conversion of thermal energy into electrical energy (and vice versa) through the use of solid-state materials. This presents a viable option for renewable energy, offering advantages such as the absence of moving parts, compact device designs with minimal maintenance requirements, low levels of vibration and noise, and the ability to tap into waste heat energy produced by other machines. Despite these benefits, the widespread application of thermoelectric technology has been hampered by the relatively low efficiency of available TE materials. Consequently, scientists from diverse fields such as physics, chemistry, and engineering are investing substantial theoretical and experimental efforts to enhance the TE efficiency of existing materials or discover new materials with superior efficiency and other desirable properties. In this pursuit, half-Heusler (HH) compounds have emerged as focal points for research. In 2019, the theoretical prediction of the existence of HH compounds, including TaFeSb, MOsSb, and NRuAs (with M = Ta, Nb; N = Ta, Nb, V), opened new possibilities. TaFeSb, in particular, was synthesized and demonstrated an exceptionally high thermoelectric efficiency, surpassing that of other well-known p-type HH compounds. Building upon this significant advancement, further theoretical investigations were undertaken to comprehend the impact of carrier concentration on the thermoelectric properties of HH compounds. Notably, previous studies have overlooked the volumetric changes resulting from chemical pressure while assessing the effects of varying carrier concentration on the thermoelectric properties of these HH compounds. Addressing this gap, we aims to explore how volume compression and expansion influence the electronic and thermoelectric properties of HH compounds. This investigation leverages a combination of density-functional theory (DFT) and Boltzmann transport theory for a comprehensive understanding of the intricate interplay between volume changes and thermoelectric characteristics. In this talk, we will first provide an overview of DFT and Boltzmann theories, elucidating their relevance to our study. Subsequently, we will delve into the electronic characteristics of our focal materials, shedding light on parameters like density of states and band structure. Following this, we'll pivot to thermoelectric properties, encompassing the Seebeck coefficient, electrical and thermal conductivity, power factor, and overall thermoelectric efficiency. Furthermore, we will underscore the role of volume variations on these pivotal parameters and especially thermoelectric efficiency.

1. W. Ren, Y. Sun, D. Zhao, A. Aili, S. Zhang, C. Shi, J. Zhang, H. Geng, J. Zhang, L. Zhang, J. Xiao, and R. Yang, Sci. Adv. 7, eabe0586 (2021).
2. H. Zhu, J. Mao, Y. Li, J. Sun, Y. Wang, Q. Zhu, G. Li, Q. Song, J. Zhou, Y. Fu, R. He, T. Tong, Z. Liu, W. Ren, L. You, Z. Wang, J. Luo, A. Sotnikov, J. Bao, K. Nielsch, G. Chen, D. J. Singh, and Z. Ren, Nat. Commun. 10, 270 (2019).
3. P. S. Mahapatra, B. Ghawri, M. Garg, S. Mandal, K. Watanabe, T. Taniguchi, M. Jain, S. Mukerjee, and A. Ghosh, Phys. Rev. Lett. 125, 226802 (2020).
4. M. Yazdani-Kachoei, S. Li, W. Sun, S. Mehdi Vaez Allaei, and I. Di Marco Phys. Rev. Materials 7, 104602 (2023).

During the last decade, a new paradigm has emerged where the quantum-chaotic aspects of both realistic and toy-like models of quantum gravity play a fundamental role. In the case of our 3+1 dimensional universe, a celebrated aspect of this new paradigm is the consistent idea of black holes as fast, in fact the fastest, scramblers.

Research on the quantum signatures of chaos in gravitational models got then a very strong input from the study of solvable models in low (1+1) dimensions, specially after the celebrated paper of Saad, Shenker and Stanford in 2019 where Jackiw-Teitelboim (a particularly simple model of two-dimensional quantum gravity) was shown to be dual to a matrix theory in the precise sense that the genus expansions of their spectral correlators can be shown to be identical. In particular SSS shows that JT gravity possess an universal limit of its spectral correlators given by Random Matrix Theory: JT gravity displays quantum chaos.

This remarkable result opens the door to ask whether quantum gravitational degrees of freedom can be interpreted as having a classical chaotic limit, where techniques and ideas from semiclassical analysis, in particular Gutzwiller trace formula and its versions, can be invoked to explain the emergence of universal spectral fluctuations. In this direction, a first step is to establish a semiclassical mechanism for the emergence of genus expansions of semiclassically-calculated spectral correlators.

In this talk, I present an introduction to the main ideas behind the JT/RMT duality from the quantum chaos perspective, and then I will explain the efforts currently undergoing in our group in Regensburg to connect the corresponding results from suitable defined semiclassical correlators of an underlying classical theory displaying classical chaos. I will make special emphasis on the several open questions and possible directions to pursue within the general moto of quantum gravitational chaos as signature of classical chaos.

While much research has been dedicated to the exploration of quantum state entanglement, the investigation of entangled measurements has not received commensurate attention, despite its pivotal role in comprehending non-locality, as well as its central significance in quantum networks and computation. In this study, we systematically examine entangled measurements and offer a comprehensive classification of all equivalence classes of iso-entangled bases applicable to joint von Neumann measurements on two qubits. Application of this classification to the triangular network reveals that, among various measurements, the Elegant Joint Measurement under white noise and a subset of the Elegant family, stand out as the only measurements leading to output permutation invariant probability distributions when nodes are linked by maximally entangled Bell states. The exploration extends to higher dimensions, concluding with a discussion of partial results.

In this talk I will comment some of our recent works on dipolar quantum gases. In the first part of the talk, I will comment on dipolar supersolids, and most specifically in the case of dipolar mixtures, focusing on double supersolidity and supersolid catalyzation [1], and on self-bound crystals of anti-aligned dipoles [2]. I will then move to our recent works on dipolar spin models. I will first discuss how dipolar interactions induce correlated creation of spin excitations in a bilayer lattices, resulting in the formation of non-trivial spatial spin correlations [3]. I will then discuss the case of ladder geometries, where the spin dynamics and the long-term equilibration (or its absence) presents an unexpected dependence with the dipole orientation and the inter-leg distance [4].

[1] D. Scheiermann, L. A. Peña Ardila, T. Bland, R. N. Bisset, and L. Santos, Phys. Rev. A 107, L021302 (2023).
[2] M. Arazo, A. Gallemi, M. Guilleumas, R. Mayol, and L. Santos, Phys. Rev. Res. 5, 043038 (2023).
[3] T. Bilitewski, G. A. Dominguez-Castro, D. Wellnitz, A. M. Rey, and L. Santos, Phys. Rev. A 108, 013313 (2023).
[4] G. A. Dominguez-Castro, T. Bilitewski, D. Wellnitz, A. M. Rey, and L. Santos, arXiv:2311.18091.

To begin, I will provide a short introduction to massive photon electrodynamics. Then, I will discuss the charge operator in such a theory and the certain class of quantum states in which the mean electric field has the periodically oscillating Coulomb component. Finally, I will discuss the propagation of a shock wave in such states and the empty hose paradox pertaining to the periodic “charge” oscillations.

Spin anticoherent states recently acquired a lot of attention as the most 'quantum' states. Some coherent and anticoherent spin states are known as optimal quantum rotosensors. In this talk we introduce a measure of quantumness for orthonormal bases of spin states, determined by the average anticoherence of individual vectors and the Wehrl entropy. This method allows us to identify the most spin-coherent (classical) and most quantum states, which lead to orthogonal measurements of extreme quantumness. Their symmetries can be revealed using the Majorana stellar representation, which provides an intuitive geometrical representation of a pure state by points on a sphere. The obtained results lead to maximally (minimally) entangled bases in the symmetric subspace of the space of states of multipartite systems composed of 2j qubits. Some bases that we have found are isocoherent as they consist of all states of the same degree of spin-coherence. Based on:
[1] M. Rudziński, A. Burchardt, and K. Życzkowski, Orthonormal bases of extreme spin coherence, arxiv:2306.00532

We present a projected Krylov approach for efficient computation of real-frequency spectra on top of ground state (GS) matrix product states (MPS) obtained from the Density Matrix Renormalization Group (DMRG). Our method relies on projecting resolvents to the tangent space of the GS-MPS, where they can be efficiently represented using Krylov space techniques. This allows for a direct computation of spectral weights and their corresponding position on the real-frequency axis. We demonstrate the accuracy and efficiency of the projected Krylov method by showcasing spectral data for various models. These include the Haldane-Shastry model on a ring and free fermions on cylinders as benchmarks, as well as interacting fermionic models on cylinders as challenging and physically interesting applications.

The notion of convolution of two probability vectors can be extended to operations determined by multistochastic tensors, to describe Markov chains of a higher order. On the other hand, the idea of convolution lies in the centre of machine learning algorithms for image processing: Convolutional Neural Networks. In my talk, I will first present the characterization of the probability eigenvectors of multi-stochastic tensors, corresponding to fixed points of generalized Markov chains. Similar results will be also obtained in the quantum case for multi-stochastic channels acting on mixed quantum states. Next, I propose a quantum analogue of the convolution, based on coherifications of tristochastic tensors, defined for two arbitrary density matrices of the same size. Finally, I will discuss possible applications of this notion to construct schemes of error mitigation or as building blocks in quantum Convolutional Neural Networks.

In the talk I will present our experimental setup which allows for cooling 87Rb atoms into Bose - Einstein condensate. I will describe the techniques employed - laser cooling in a magneto-optical trap and evaporative cooling in an optical dipole trap. I will briefly present our plans for further work with the condensate.

Quantum sun model is an interacting spin-1/2 model that was originally introduced as a toy model to describe the mechanism of quantum avalanches [1,2]. Later work has shown that the model has signatures of ergodicity breaking transition [3], making it interesting to study as a standalone model. We show [4] that the U(1) symmetry can be introduced to the model, making it realistic to realize it experimentally, e.g. on cold atomic platforms. Moreover, we demonstrate that both variants of the model, original and U(1) symmetric, exhibit the many-body mobility edge phenomenon.

[1] De Roeck, W., & Huveneers, F. (2017). Stability and instability towards delocalization in many-body localization systems. Physical Review B, 95(15), 155129.
[2] Luitz, D. J., Huveneers, F., & De Roeck, W. (2017). How a small quantum bath can thermalize long localized chains. Physical review letters, 119(15), 150602.
[3] Šuntajs, J., & Vidmar, L. (2022). Ergodicity breaking transition in zero dimensions. Physical Review Letters, 129(6), 060602.
[4] Pawlik, K., Sierant, P., Vidmar, L., & Zakrzewski, J. (2023). Many-Body Mobility Edge in Quantum Sun models. arXiv preprint arXiv:2308.01073.

The Hubbard model in all its variations plays a central role in the description of strongly correlated many-body systems. Despite its simple form, the solution of the model remains a challenge for analytical and numerical methods. Quantum simulation has been established as an alternative solution method in the last 20 years. My talk takes a comprehensive look at this development and introduces both atomic and electronic many-body systems suitable for quantum simulation of Hubbard models. In particular, the focus is on various extensions of the model, such as electron-phonon interaction, long-range interactions, two-layer geometry, which play an important role for superconductivity or superfluidity, as well as for exotic phases with broken lattice symmetries.

Higher-order tensor renormalization group (HOTRG) is a precision tool for simulation of the low-lying spectrum of large periodic spin systems. In particular, it allows for precise determination of the phase transition points as well as good quantitative conformal field theory description of the system at criticality. We successfully apply HOTRG in order to determine quantitatively the phase diagram of the non-integrable spin-1/2 XXZ model in a staggered magnetic field, and show that the system resembles the Luttinger liquid in its gapless phase. Also we investigate consistently the antiferromagnetic area of the non-integrable bilinear-biquadratic spin-1 Heisenberg model, in particular, we determine quantitatively the spectral gap and the spin wave velocity. We detect additional symmetry that governs the gapless Takhtajan-Babujian point in addition to SU(2) Wess-Zumino-Witten theory, and determine quantitatively the higher critical dimensions in the gapless phase.

Particle fluctuations of a number of condensed atoms is one of fundamental problems of quantum gases physics. In the last five years it is not only a theoretical, but also the experimental problem. I will review over a quarter of the century of our own efforts. I will explain our new method of the Fock states sampling in application to the condensate statistics.

We identified new schemes to generate lattice Hamiltonian models that produce dispersionless (flat) energy bands and support extreme localization even without the disorder. We analyze the nonperturbative effect of interaction and external fields on such systems.

I will discuss measurement-induced phase transitions that arise when many-body unitary dynamics is interspersed with repeated measurements. I will focus on the so-called post-selection problem which hinders the possibilities of experimental observation of measurement-induced phase transition and I will discuss our recent attempt [1] to circumvent this problem. Employing feedback-control operations that steer the dynamics toward an absorbing state, we study the entanglement entropy behavior at the absorbing state phase transition. For short-range control operations, we observe a transition between phases with distinct subextensive scalings of entanglement entropy. In contrast, the system undergoes a transition between volume-law and area-law phases for long-range feedback operations. The fluctuations of entanglement entropy and of the order parameter of the absorbing state transition are fully coupled for sufficiently strongly entangling feedback operations. In that case, entanglement entropy inherits the universal dynamics of the absorbing state transition. This is, however, not the case for arbitrary control operations, and the two transitions are generally distinct. We quantitatively support our results by introducing a framework based on stabilizer circuits with classical flag labels. Our results shed new light on the problem of observability of measurement-induced phase transitions.

[1] P. Sierant, X. Turkeshi, Phys. Rev. Lett. 130, 120402 (2023)

Spatial-mode demultiplexing was predicted to provide a significant advantage, in discriminating between different types of light sources, when compared to standard measurement techniques. We study source discrimination with imperfect spatial-mode demultiplexer and with unbalance in sources' intensities, proposing alternative decision strategies that allow to preserve the performance advantage of spatial mode-demultiplexing even in imperfect settings.

Central spin models, where a single spinful particle interacts with a spin environment, find wide application in quantum information technology and can be used to model e.g. the decoherence of a qubit in a disordered environment. We propose a method of realizing an ultracold quantum simulator for the central spin model. The proposed system consists of a single Rydberg atom (central spin) and polar molecules (environment spins), coupled via dipole-dipole interactions. By mapping internal particle states to spin states, spin-exchanging interactions can be simulated. Precise control over the model can be exerted by directly manipulating the placement of environment spins. As an example, we consider a ring-shaped arrangement of environment spins, and show how the system's time evolution is affected by the tilt angle of the ring.

The interplay between interactions and disorder in quantum many-body systems is a field of current interest in condensed matter physics. In this context, ultracold bosonic atoms in optical lattices represent an extremely powerful tool for engineering quantum systems with a broad tunability of parameters, thus serving as quantum simulators [1]. It is now well established that random on site (i.e., diagonal) disorder can destroy the direct superfluid to Mott insulator transition via the so-called Bose glass phase [2]. While the effects of diagonal disorder have been widely recognized, studies of random hopping amplitudes, belonging to the “off-diagonal” category, are scarce. The importance of this kind of disorder in bosonic systems lies in the fact that it allows one to make contact with interesting and unexplored features from the realm of spin glasses [3]. In this talk I report the recent study of disordered interacting bosons described by the Bose- Hubbard model with Gaussian-distributed random tunneling amplitudes [4]. It is shown that the off-diagonal disorder induces a spin-glass-like ground state, characterized by randomly frozen quantum-mechanical U(1) phases of bosons. I will introduce the relevant theoretical framework based on the “n-replica trick,” as in the spin-glass theory, and the Trotter-Suzuki method for decomposition of the statistical density operator, along with numerical calculations. The interplay between disorder, quantum, and thermal fluctuations leads to phase diagrams exhibiting a glassy state of bosons, which are studied as a function of model parameters. The considered system may be relevant for quantum simulators of optical lattice bosons, where the randomness can be introduced in a controlled way. The latter is supported by a proposition of experimental realization of the system in question.

[1] M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A.Sen(De), and U. Sen, Adv. Phys. 56, 243 (2007).
[2] M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S.Fisher, Phys. Rev. B 40, 546 (1989).
[3] C. De Dominicis and I. Giardina, Random Fields and Spin Glasses: A Field Theory Approach (Cambridge University Press, Cambridge, England, 2006).
[4] A. M. Piekarska and T. K. Kopeć, Phys. Rev. Lett. 120, 160401 (2018).

Deep learning models have provided huge interpretation power for image-like data. Specifically, convolutional neural networks (CNNs) have demonstrated incredible acuity for tasks such as feature extraction or parameter estimation. Here we test CNNs on strong-field ionization photoelectron spectra, training on theoretical data sets to `invert' experimental data. Pulse characterization is used as a `testing ground', specifically we retrieve the laser intensity, where `traditional' measurements typically lead to 20% uncertainty. We report on crucial data augmentation techniques required to successfully train on theoretical data and return consistent results from experiments, including accounting for detector saturation. The same procedure can be repeated to apply CNNs in a range of scenarios for strong-field ionization. Using a predictive uncertainty estimation, reliable laser intensity uncertainties of a few percent can be extracted, which are consistently lower than those given by traditional techniques. Using interpretability methods can reveal parts of the distribution that are most sensitive to laser intensity, which can be directly associated to holographic interferences. The CNNs employed provide an accurate and convenient way to extract parameters, and represent a novel interpretational tool for strong-field ionization spectra.

Experimental progress in strongly coupling quantum gases into quantized electromagnetic fields of quantum cavities has opened a new avenue in many-body physics --- referred to commonly as many-body cavity quantum electrodynamics (QED) --- where the dynamics of both quantum matter and electromagnetic fields play equally essential roles. In this talk, after a short review of state of the art in many-body cavity QED I will present our recent joint theory-experiment work on many-body fermionic cavity QED [1]. In particular, I will talk about the interplay between the density-wave ordering and the Cooper paring in a highly interacting Fermi gas inside a cavity.

1. V Helson, T Zwettler, F Mivehvar, E Colella, K Roux, H Konishi, H Ritsch, JP Brantut, “Density-wave ordering in a unitary Fermi gas with photon-mediated interactions”, arXiv preprint: arXiv:2212.04402

Quantum simulators made of magnetic atoms allow to investigate intriguing topological states of matter. In the case of bosonic atoms we show that the combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. In particular, we reveal the presence of two distinct topological quantum critical points with localized edge states and gapless bulk excitations. Our results demonstrate that the topological critical points always separate two phases, one topologically protected and the other topologically trivial, both characterized by a long-range ordered string correlation function. In the case of fermionic dipolar quantum simulators, we uncover a topological sector which remained elusive in previous finite-size numerical studies due to boundary effects. We first show that, for an infinite system, the bond order wave regime is characterized by two degenerate bulk states corresponding to the trivial and topological sectors. At the same time, for finite size systems, we show that the topological sector can be stabilized by imposing a suitable border potential. Finally I will discuss how all such topological orders can be detected with a quantum gas microscope.

Neutron stars are fascinating remnants of stars that offer a glimpse into some of the most extreme conditions in the universe. These objects typically rotate in less than a second, and their description relies heavily on superfluidity. As a consequence, quantum vortices are essential building blocks for modeling neutron stars and understanding their physics.

In this talk, I will present recent findings on the properties and structure of neutron matter vortices. Our research employs cutting-edge numerical techniques based on density functional theory, utilizing a functional specifically designed for astrophysical problems. We systematically investigate how the length scales change in various layers of the neutron star's crust as a function of temperature. Furthermore, I will discuss the nonequilibrium dynamics of vortex ring creation, shedding new light on the physics of these exotic objects.

Purely ballistic transport is a rare feature even for integrable models. By numerically studying the Heisenberg chain with the power-law exchange, \mbox{$J\propto1/r^\alpha$}, where $r$ is a distance, we show that for spin anisotropy $\Delta \simeq \exp(-\alpha+2)$ the system exhibits a quasiballistic spin transport and the presence of fermionic excitation which do not decay up to extremely long times $\sim10^3/J$. This conclusion is reached on the base of the dynamics of spin domains, the dynamical spin conductivity, inspecting the matrix elements of the spin-current operator, and by the analysis of most conserved operators. Our results smoothly connects two models where fully ballistic transport is present: free particles with nearest-neighbor hopping and the isotropic Haldane-Shastry model.

n this study, we explore the behavior of a rotating molecular impurity in a two-dimensional Bose-Einstein condensate. Using a Gross-Pitaevskii-type equation, we investigate how the impurity-bath interaction and size of the condensate affect the angular momentum distribution, density deformation, and density currents in the system. In line with experimental results and angulon theory, we show that the impurity's effective moment of inertia is modified by its interaction with the quantum solvent, leading to a slowing down of its rotation for low angular momentum states. Additionally, we observe the emergence of collective excitations such as solitons and vortices in the system after rapid rotation of the impurity. Our model provides insight into the behavior of impurities in two-dimensional quantum gases and can be seen as an effective description of a rotating molecule on the surface of a superfluid helium droplet.

The concept of Markovianity, which asks whether a given channel can be realised through a memoryless interaction with the environment, has been a long-standing question in both classical and quantum physics. Over the years, various applications of Markovian maps have been introduced separately for classical and quantum systems. Recently, the novel concept of quantum embeddability has been discovered which constructs a bridge between the quantum Markovian world and the classical realm. A stochastic matrix is said to be quantum embeddable if it is the classical action of a Markovian quantum channel. This allows the benefits of memoryless quantum evolution to be applied to classical systems that typically require memory to be simulated. In this talk, we elaborate on classical transitions that can be advantageously simulated quantumly without memory, as well as those that still require memory.

I will review our recent studies concerning a chain of interacting fermions with random disorder that was intensively studied in the context of many-body localization. We have shown that only a small fraction of the two-body interaction represents a true local perturbation to the Anderson insulator [1]. While this true perturbation is nonzero at any finite disorder strength W, it decreases with increasing W. This establishes a view that the strongly disordered system should be viewed as a weakly perturbed integrable model, i.e., a weakly perturbed Anderson insulator. As a consequence, the latter can hardly be distinguished from a strictly integrable system in finite-size calculations at large W. We then introduced a rescaled model in which the true perturbation is of the same order of magnitude as the other terms of the Hamiltonian, and showed that the system remains ergodic at arbitrary large disorder.
We have also studied a quench dynamics of interacting spinless fermions on a disordered, two-dimensional lattice [2]. First, we demonstrated that the semiclassical description provides the upper bound for the relaxation rates. We obtained this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one dimensional chains. Next, we showed that strongly disordered two-dimensional systems exhibit a transient, logarithmic-in- time relaxation which is well established for one-dimensional disordered chains. Finally, we have discussed a relation between the diffusion constant and the energy-level structure, which leads to the Thouless localization criterion. The latter explains the linear (or sublinear )drift of the crossover/transition to the localized regime with increasing system size [3].

[1] B. Krajewski, L. Vidmar, J. Bonča, M. Mierzejewski, Phys. Rev. Lett. 129, 260601 (2022)
[2] Ł. Iwanek, M. Mierzejewski, A. Polkovnikov, D. Sels, A. S. Sajna, Phys. Rev. B107, 064202 (2023)
[3] P. Prelovšek, J. Herbrych, M. Mierzejewski, arXiv:2302.1456.

The second law of thermodynamics imposes a fundamental asymmetry in the flow of events. The so-called thermodynamic arrow of time introduces an ordering that divides the system's state space into past, future and incomparable regions. In this work, we analyse the structure of the resulting thermal cones, i.e., sets of states that a given state can thermodynamically evolve to (the future thermal cone) or evolve from (the past thermal cone). Specifically, for a d-dimensional classical state of a system interacting with a heat bath, we find explicit construction of the past thermal cone and the incomparable region. Moreover, we provide a detailed analysis of their behaviour based on thermodynamic monotones given by the volumes of thermal cones.

The second law of thermodynamics imposes a fundamental asymmetry in the flow of events. The so-called thermodynamic arrow of time introduces an ordering that divides the system's state space into past, future and incomparable regions. In this work, we analyse the structure of the resulting thermal cones, i.e., sets of states that a given state can thermodynamically evolve to (the future thermal cone) or evolve from (the past thermal cone). Specifically, for a d-dimensional classical state of a system interacting with a heat bath, we find explicit construction of the past thermal cone and the incomparable region. Moreover, we provide a detailed analysis of their behaviour based on thermodynamic monotones given by the volumes of thermal cones.

Numerical simulations are an important ingredient of modern research. In the field of Bose-Einstein condensates, the Gross–Pitaevskii equation (GPE) is a workhorse that facilitates the interpretation of experimental data for various setups. The counterpart of GPE for superfluid fermions are mean-field Bogoliubov-de Gennes (BdG) equations. Formally, their applicability is limited to weak couplings, while the experiments typically operate for strong couplings (around the unitary limit). The density functional theory (DFT) can be a remedy for this disparity. It is a versatile method describing with very good accuracy the static, dynamic, and thermodynamic properties of many-body Fermi systems in a unified framework, while keeping the numerical cost at the same level as the mean- field approach. I will summarize developments of the DFT dedicated to ultracold atomic gases across BCS-BEC crossover, together with its numerical implementation. Selected applications of the method to various experimental setups will be presented. Finally, I will discuss opportunities offered by the DFT method in the context of the modeling systems that are not directly accessible, like neutron stars.

I'll present a deterministic classical algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible configurations. Using approximate tensor-network contractions, we can efficiently map the low-energy spectrum of some quasi-two-dimensional Hamiltonians. Exploiting the local nature of the problems allows computing spin-glass droplets geometries, which provides a new form of compression of the low-energy spectrum. This naturally encompasses sampling, which otherwise, for exact contraction, is $\#P$ hard in general.

I'll discuss the performance of that approach in the context of existing and upcoming quantum annealing devices. I'll also show that inhomogeneous quantum annealing that employs information about the droplets may allow one to reach higher diversity of solutions than the standard homogeneous quantum annealing schedules.

Based on: [1] M. M. Rams, M. Mohseni, D. Eppens, K. Jałowiecki, B. Gardas, Phys. Rev. E 104, 025308 (2021).
[2] M. Mohseni, M. M. Rams, et. al., arXiv:2110.10560
[3] A. Dziubyna, T. Śmierzchalski, B. Gardas, M. M. Rams, et. al., in prep.

Spontaneous time-translation symmetry breaking had not attracted much attention until Wilczek [1] introduced the concept of time crystals. Despite this particular realization being prohibited by the ,,no-go'' theorem [2], the idea inspired a new version of time crystals, i.e. the discrete time crystals (DTCs) [3]. In general, a DTC is a periodically driven quantum many-body system that spontaneously breaks the discrete time-translational symmetry of the Hamiltonian due to particle interactions and starts evolving with a period s-times longer than the period of the external driving.
In our previous works, we developed a theoretical basis for the realization of DTCs in the ultra-cold atom platform, i.e. a Bose-Einstein condensate (BEC) of weakly interacting bosonic atoms bouncing resonantly on a periodically driven atom mirror in a 1D space [3-5]. In our present work we take that idea further, and consider a collection of BECs.
In my talk I will present the first stage of our analysis. It constitutes a classical basis for quantum research of novel time crystal and condensed matter phenomena in the time domain. We consider the dynamics of N impenetrable particles (hard balls) of equal masses stacked above each other in a 1D space. The particles bounce on an oscillating mirror in the presence of gravitational field. We identify the manifolds the particles move on and derive the effective secular Hamiltonian for the resonant motion of the particles. The effective Hamiltonian can be interpreted as describing a fictitious particle in an N-dimensional effective potential (N-dimensional particle) [6].
[1] F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012).
[2] H. Watanabe, and M. Oshikawa, Phys. Rev. Lett. 114, 251603 (2015).
[3] K. Sacha, Phys. Rev. A 91, 033617 (2015).
[4] A. Kuros et al., New J. Phys. 22, 095001 (2020).
[5] K. Giergiel et al., New J. Phys. 22, 085004 (2020).
[6] W. Golletz et al., New J. Phys. 24 093002 (2022)

Discrete-time quantum walks have proven to be a powerful tool for simulating a wide variety of quantum phenomena and designing quantum algorithms. In this talk, we explore the dynamics of a three-state quantum walk that exhibits a form of intrinsic localization. First we shall lay out some transport properties of the walker and show how essential quantities such as the participation ratio and the survival probability satisfies universal dynamical scaling laws around a detrapping point. The participation ratio is found to grow linearly in time with a logarithmic correction, which explains previous reports of sublinear behavior [1]. In the second part of the talk, we discuss a nonlinear version of the same quantum walk model. We focus on the response of localized component against a tunable nonlinear operator. In this case it reaches an unstable regime and starts to radiate through the lattice, with its survival probability decaying asymptotically in time following a specific power law that is independent of the parameters of the system [2].
[1] Phys. Rev. E 104, 054106 (2021)
[2] Phys. Rev. A 106, 042202 (2022)

Fractons are excitations with mobility constraints. They exhibit constrained dynamics, being either unable to move in isolation, or able to move only in certain directions. Imprints of fractons have been identified in the context of ultracold atoms in tilted optical lattices, quantum error correction, elasticity and quantum Hall effect. Low energy dynamics of fracton theories presents itself with many exotic features and challenges that resemble glasses. I will explain the symmetry principles and conservation laws of dipole conserving fracton theories that exhibit subdiffusive glassy evolution seen in optical lattice experiments. Next I will focus on connections to elasticity that map theories of elasticity to tensor gauge theories sourced by fractons. Finally I will introduce a model of fractons that will be studied by means of the renormalization group approach. I will present a Berezinskii-Kosterlitz-Thouless transition of the fracton type that goes beyond known universality classes.

The interplay of disorder and interactions leads to many-body localization (MBL) which provides the only known generic mechanism for strong breakdown of thermalization in a closed quantum system. This phenomenon can protect exotic quantum order (in space and time) even at infinite temperature, leading to emergent nonergodic phases of matters with no equilibrium counterpart. In this talk, I will show that nonergodic dynamics, and the resulting localization protected order, can be found in minimal models dropping the essential ingredients needed for the existence of MBL. As a first example, I identify the absence of thermalization in a family of disorder-free, self-correcting quantum memories whose elementary excitations are associated with Abelian anyons. Our analysis reveals that mutual braiding statistics between anyons is suffice to intrinsically suppress the diffusion of anyons for an exponentially long time. The self-localization of anyons can impede logical errors, which in turn paves the way for identifying stable, low-dimensional quantum memories. I then turn to investigating a clean Floquet model whose quasi-energy spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline dynamics in the absence of disorder or fine-tuning. We related such behavior to a measure zero set of non-thermal Floquet eigenstates with long-range spatial correlations, which coexist with otherwise thermal states at infinite temperature and resemble the notion of "Floquet scars". We dubbed such a homogeneous time crystal formed in partially nonergodic systems, scarred discrete time crystal, which is distinct by nature from those stabilized by either many-body localization or prethermalization mechanism.

Entanglement is an important resource in protocols for quantum communication, computation and sensing. To make those protocols operational, we need increasingly more complex entangled states - of more particles, or of larger objects.Experimental generation of such states presents both technical and fundamental challenges. I will discuss experiments involving atomic and optomechanical systems, and their applications to quantum communication and sensing. Via those two experiments, I will also highlight the two typical entantled scenarios, i.e. Bell states [1,2,3], or continuous-variable EPR-type states [4,5].
[1] M. Lipka, M. Mazelanik, A. Leszczyński, W. Wasilewski, M. Parinak, Communications Physics 4, 46 (2021)
[2] M. Mazelanik, A. Leszczyński, M. Lipka, W. Wasilewski, M. Parniak, Quantum 5, 493 (2021)
[3] M. Lipka, M. Mazelanik, M. Parniak, New Journal of Physics 23, 053012 (2021)
[4] R. A. Thomas, M. Parniak, C. Østfeldt, C. B. Møller, et al., Nature Physics 17, 228 (2021)
[5] I. Galinskiy, Y. Tsaturyan, M. Parniak, E. S. Polzik, Optica 7, 718 (2020)

Ultracold atoms are extremely controllable quantum systems and thereby allow quantum simulation of many-body dynamics. Using this platform, we study the dynamics of atomic Josephson junctions and map out their characteristic regimes, which helped to realize an ideal atomic Josephson junction [1]. This also demonstrates that the working of a Josephson junction is governed by the phenomenon of quantum tunneling. Furthermore, we study the critical dynamics of two-dimensional Bose gases and condensates arranged in a triangular lattice by quenching them out of equilibrium [2,3].

1. Luick, Sobirey, Bohlen, Singh, Mathey, Lompe, Moritz Science 369, 89 (2020); Singh, Luick, Sobirey, Mathey PRR 2, 033298 (2020).
2. Sunami, Singh, Garrick, Beregi, Barker, Luksch, Bentine, Mathey, Foot arXiv:2209.13587.
3. Zahn, Singh, Kosch, Asteria, Freystatzky, Sengstock, Mathey, Weitenberg Phys. Rev. X 12, 021014 (2022).

Usually in the last part of the standard course of classical electrodynamics the problem of self-interaction of electron is discussed. One finds that Lorentz force is not enough to provide energy and momentum conservation in the system of classical electromagnetic field interacting with electron. The need o a force (called self-force) that the accelerating electron acts on itself arrises. Well known candidate for this force - Lorentz-Abraham-Dirac force is known to provide non-causal solutions - the electron starts to move before the external electromagnetic pulse touches it. No causal candidates for the needed force are known. In my talk I will shown that the causal self-force does not exists and as a consequence the causal classical Maxwell electrodynamics with point charged particles (electrons) does not exists.

In my talk I will summarise recent results obtained with my group, in which we combine quantum description of continuously monitored atomic sensors with efficient techniques of Bayesian statistical inference in order to track fluctuating signals in atomic magnetometry. I will start by discussing a linear-classical model in which it is sufficient to use Kalman Filtering (KF) methods to optimally estimate signals encoded in the light pumping the atomic ensemble. However, I will demonstrate how this scenario may be directly generalised with use of the Extended Kalman Filter (EKF) to track magnetic fields, i.e. the Larmor frequency, instead. Importantly, I will afterwards move onto the nonlinear-quantum setting in which, thanks to the phenomena of measurement back-action and continuous spin-squeezing, the classical limits imposed on precision may be spectacularly breached. On one hand, I will show how to determine then the correct ultimate noise-induced limits by employing tools of quantum information theory. On the other, I will demonstrate how to achieve such quantum-enhanced resolutions by resorting to the effective quantum stochastic description of the dynamics involving measurement-based feedback and the EKF.

Experimental demonstrations and control of strong coupling of light and matter has lead to various applications for lasers, quantum sensing, and quantum information processing since 1980s. In my talk, I will review [1] recent theoretical and experimental progress in the ultrastrong coupling (USC) and deep-strong coupling (DSC) regimes of light and matter, which are characterized by the coupling strengths comparable to their transition frequencies. In the last few years, the USC regime has been experimentally achieved in a wide range of different systems with very different spectral ranges. These systems include: superconducting quantum circuits, intersubband polaritons, Landau polaritons, organic molecules, magnetic systems, nano-plasmonics, and optomechanical systems. Emerging applications of the USC and DSC regimes are focused on quantum technologies and quantum information processing.

The ground state of light-matter systems in the DSC regime is a Schroedinger-cat state, where virtual photons are entangled with virtual excitations of the matter. A recent experimental demonstration of the cat state can be considered as the discovery of a new stable molecular state in which light and matter are hybridized [2]. The USC and DSC regimes can be effectively reached by squeezing a cavity field as proposed in [3] and experimentally demonstrated in [4]. This type of light squeezing can also be used to increase spin squeezing [5], which is of paramount importance for quantum metrology. The USC and DSC regimes enable also generating giant Schrodinger cat states of real photons and atomic real excitations by applying squeezing [6,7]. The USC methods have inspired developing a promising technique to beat the 3 dB limit for intracavity squeezing and, thus, to effectively apply it for nondemolition qubit experiments [8].

[1] A. F. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori: Ultrastrong coupling between light and matter, Nat. Rev. Phys. 1, 19 (2019).

[2] F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime, Nat. Phys. 13, 44 (2017).

[3] W. Qin, A. Miranowicz, P.-B. Li, X.-Y. Lu, J.-Q. You, and F. Nori: Exponentially Enhanced Light-Matter Interaction, Cooperativities, and Steady-State Entanglement Using Parametric Amplification, Phys. Rev. Lett. 120, 093601 (2018).

[4] S. C. Burd, R. Srinivas, H. M. Knaack, W. Ge, A. C. Wilson, D. J. Wineland, D. Leibfried, J. J. Bollinger, D. T. C. Allcock, and D. H. Slichter, Quantum amplification of boson-mediated interactions, Nat. Phys. 17, 898 (2021).

[5] W. Qin, Y.-H. Chen, X. Wang, A. Miranowicz, and F. Nori: Strong Spin Squeezing Induced by Weak Squeezing of Light inside a Cavity, Nanophotonics 9, 4853 (2020).

[6] W. Qin, A. Miranowicz, H. Jing, and F. Nori: Generating long-lived macroscopically distinct superposition states in atomic ensembles, Phys. Rev. Lett. 127, 093602 (2021).

[7] Y.-H. Chen, W. Qin, X. Wang, A. Miranowicz, F. Nori: Shortcuts to Adiabaticity for the Quantum Rabi Model: Efficient Generation of Giant Entangled Cat States via Parametric Amplification, Phys. Rev. Lett. 126, 023602 (2021).

[8] W. Qin, A. Miranowicz, and F. Nori: Beating the 3 dB Limit for Intracavity Squeezing and Its Application to Nondemolition Qubit Readout, Phys. Rev. Lett. 129, 123602 (2022).

We study the production of spin-squeezed states with ultra-cold atomic fermions described by the Fermi-Hubbard model in the Mott insulating phase. We show the activation of two twisting mechanisms by a position-dependent laser coupling between internal degrees of freedom of atoms. A single laser coupling simulates the one-axis twisting model with the orientation of the twisting axis determined by the coupling phase. Adding a second laser beam with a properly chosen phase paves the way to simulate the two-axis counter-twisting model, approaching the Heisenberg-limited level of squeezing.

The Hubbard model is a long-standing problem in the theory of strongly correlated electrons and a very active one in experiments with ultracold fermionic atoms. Motivated by current and prospective quantum simulations, we apply a two-dimensional tensor network, an infinite projected entangled pair state, evolved in imaginary time by the neighborhood tensor update algorithm working directly in the thermodynamic limit. With bond dimensions up to 29, we generate thermal states down to the temperature of 0.17 times the hopping rate. We obtain results for spin and charge correlators, unaffected by boundary effects. The spin correlators, measurable in prospective ultracold atoms experiments attempting to approach the thermodynamic limit, provide evidence of disruption of antiferromagnetic background with mobile holes in a slightly doped Hubbard model. The charge correlators reveal the presence of hole-doublon pairs near half-filling and signatures of hole-hole repulsion on doping. We also obtain specific heat in the slightly doped regime.

Quantum materials hold the promise for groundbreaking technologies making use of strongly correlated many-body states of matter. However, harnessing their potential is a challenging task. Ultracold atomic systems offer the possibility to design a quantum system with well-known microscopic properties, and are highly controllable. Hybrid systems involving multiple species are considerably more complex, which can increase the variety of simulable systems but introduces additional challenges. I will discuss two systems which are especially promising: ion-atom and Rydberg-ground state mixtures, highlighting their ability to access polaron physics in the regime of strong and long-ranged interactions.

In this talk we will provide an introduction to (deep) reinforcement learning (RL). Next, we will discuss how RL can be utilized in quantum technologies. As an example we will focus on quantum feedback control and quantum circuits optimization.

Special seminar (in polish only).

This talk concerns the problem of multipartite entanglement and its relation to combinatorial designs. We explain how the classical concepts in combinatorics can be extended into the quantum realm. The classical problem of 36 officers of Euler yields no solution as there are no two orthogonal Latin squares of order six. We show that the equivalent problem can be solved in the quantum domain by constructing a pair of six-dimensional quantum orthogonal Latin squares. As a consequence, we find an example of the Absolutely Maximally Entangled state AME(4, 6) of four subsystems with six levels each. The analytic form of a special unitary matrix of size 36 representing this state is the unexpected solution of the problem in Quantum Information Theory. This is the joint work with Suhail Ahmad Rather, Adam Burchardt, Grzegorz Rajchel-Mieldzioć, Arul Lakshminarayan and Karol Życzkowski. It is based on Phys. Rev. Lett. 128, 080507 (2022) and its follow up arXiv:2204.06800.

The weak ergodicity breaking induced by quantum many-body scars (QMBS) represents an intriguing concept that has recently received significant attention due to its relation to unusual non-equilibrium behavior. With the advent of a new generation of cold-atom quantum simulators, the weak ergodicity breaking manifested by QMBS has been experimentally detected in constrained spin and bosonic models. Crucially, both realizations can be viewed as lattice gauge theories (LGTs) where the energy constraints are induced by the Gauss law fixing the relation between gauge and charge variables. Here we reveal that this phenomenon can occur in a previously unexplored regime of a lattice gauge theory, where QMBS emerges due to the presence of an extensive number of local constraints. In particular, by analyzing the gauged Kitaev model, we provide an example where QMBS appears in a regime where charges are deconfined. By means of both numerical and analytical approaches, we find a variety of scarred states far away from the regime where the model is integrable. The presence of these states is revealed both by tracing them directly from the analytically reachable limit and by quantum quenches showing persistent oscillations for specific initial states.

Highly excited eigenstates of quantum many-body systems are typically featureless thermal states. Some systems, however, possess a small number of special, low-entanglement eigenstates known as quantum scars. We introduce a quantum-inspired machine learning platform based on a Quantum Variational Autoencoder (QVAE) that detects families of scar states in spectra of many-body systems. Unlike a classical autoencoder, QVAE performs a parametrized unitary operation, allowing us to compress a single eigenstate into a smaller number of qubits. We demonstrate that the autoencoder trained on a scar state is able to detect the whole family of related scar states sharing common features with the input state. We identify families of quantum many-body scars in the PXP model beyond the presently known ones and find dynamically decoupled subspaces in the Hilbert space of disordered, interacting spin ladder. The possibility of an automatic detection of subspaces of scar states opens new pathways in studies of models with a weak breakdown of ergodicity and fragmented Hilbert spaces.

In this talk, I will introduce the general theory of phase space crystals that aims to study condensed matter phenomena in the phase space of dynamical systems [1,2]. The relationship and difference between phase space crystals and time crystals will also be discussed. The vibrational modes of phase space crystals can realise topological chiral transport with preserved time-reversal symmetry which is impossible in the real-space scenario [3]. In the end, I will discuss the potential application of phase space crystal theory to design bosonic codes that can help building hardware-efficient fault-tolerant quantum computer. [1] L. Guo, M. Marthaler, and G. Schön, Phys. Rev. Lett. 111, 205303 (2013), Editors' Suggestion. [2] L. Guo, Phase Space Crystals: Condensed matter in dynamical systems, IOP Publishing 2021. [3] L. Guo, V. Peano, and F. Marquardt, Phys. Rev. B 105, 094301 (2022), Editors' Suggestion.

In this talk I will argue that the strongest quantum correlation, manifested by a many-body nonlocality, is a resource for ultra-precise metrology. I will show that the sensitivity of a quantum sensor can be expressed in terms of many-body correlation functions (such that witness the nonlocality) of all orders. I will illustrate this general result with some prominent examples, such as a collection of spins forming an Ising chain or a gas of ultra-cold bosons in any two-mode configuration.

It is common knowledge that atoms can form molecules if they attract each other. Here we show that it is possible to create molecules where bound states of atoms are not the result of the attractive interactions but have the topological origin. That is, bound states of atoms correspond to topologically protected edge states of a topological model. Such topological molecules can be realized if the interaction strength between ultra-cold atoms is properly modulated in time. Similar mechanism allows one to realize topologically protected localization of an electron on a classical orbit if a Rydberg atom is perturbed by a properly modulated microwave field.
Ref:
[1] https://arxiv.org/abs/2201.10246

We study the driven-dissipative dynamics of cavity arrays working as broadband quantum amplifiers [1-4]. We provide a theory to identify the conditions under which the steady-state of these photonic lattices enters a topological phase in which external signals are unidirectionally amplified [4]. Our theory also characterizes the quantum optical properties of such a device, showing that the topological amplification can be near quantum-limited with a gain growing exponentially with system size N, and it is moreover resilient to local disorder. Topological amplifiers are therefore very promising for improving single-photon detection, especially in the microwave domain, where quantum signals are typically very weak to be detected directly [5]. Finally, we discuss two ways of experimentally implementing these ideas using either Floquet engineering or 4-wave mixing [6]. In both cases, we show how to engineer synthetic gauge fields and non-local pumping terms in the photonic lattice, which are required to manifest the topological amplification.

References:
[1] V. Peano et al., PRX 6, 041026 (2016).
[2] D. Porras et al., PRL 122, 143901 (2019).
[3] C. Wanjura et al., Nat. Comm. 11, 3149 (2020).
[4] T. Ramos, et al., PRA 103, 033513 (2021).
[5] M. Esposito et al., APL 119 120501 (2021).
[6] T. Ramos, et al., to be submitted

We investigate the dynamics driven by various quantum quenches imposed on the Anderson impurity attached to superconductor. Under stationary conditions the proximity effect induces the electron pairing that competes with the Coulomb repulsion. In consequence, the ground state of impurity is either singly occupied (spinful) or has the BCS-type (spinless) configuration. We inspect evolution upon traversing this phase boundary, using the time-dependent numerical renormalization group calculations. Our results reveal the dynamical transition evidenced by nonanalytic features in the Loschmidt echo. We propose empirical means for their detection by the tunneling spectroscopy.

I will present our results on the properties and nonequilibrium dynamics of few-body quantum systems based on ultracold polar molecules, Rydberg atoms, or their mixtures. On the one hand, we investigated interacting ultracold molecules in a one-dimensional harmonic trap as a fundamental building block of molecular quantum simulators, where we observed an interesting interplay of intermolecular interactions, external fields, and trapping potentials. On the other hand, we studied the nonequilibrium properties of a Rydberg electron interacting with a gas of spin-1/2 fermionic atoms and found the dynamical emergence of the Kondo screening cloud. Finally, we explored quantum simulation of the central spin model with a Rydberg atom surrounded by polar molecules in optical tweezers.

Quantum systems are generally extremely hard to isolate from their environment, even more so if we want to exert control or perform measurements. It is therefore important to understand the effect of the coupling to the environment which gives rise to dissipation. I will discuss several examples of generic dissipation effects in quantum many-body systems, leading to an emergent dissipative hierarchy of relaxation timescales and potentially the existence of metastable states in the case of markovian dissipation.

Single fluorescent emitters in biological samples are probably the most common sources of quantum light. Nevertheless, their quantum optical properties are rarely exploited. I will discuss how fluorescence microscopy can benefit from measurements of quantum correlations. Such measurements allowed counting emitters within a diffraction-limited spot [1] and enhancing the resolution of classical super-resolution methods further beyond the diffraction limit, as in the case of recently introduced Quantum Image Scanning Microscopy (QISM) [2].
We found that the classical analog of QISM relying on classical light correlations offers a higher SNR at short measurement times and is less demanding experimentally. This method, termed Super-resolution optical fluctuation image scanning microscopy (SOFISM) [3], exploits fluorescent emitter blinking as its image contrast. SOFISM offers a robust path to achieve high-resolution images with a slightly modified confocal microscope, using standard fluorescent labels and reasonable acquisition times.
[1] Y. Israel, et al., Quantum correlation enhanced super-resolution localization microscopy enabled by a fibre bundle camera. Nat.Comm. 8, 14786 (2017).
[2] R. Tenne, et al., Super-resolution enhancement by quantum image scanning microscopy, Nat. Phot., 13, 116–122 (2019).
[3] A. Sroda, et al., SOFISM: Super-resolution optical fluctuation image scanning microscopy, SOFISM: Super-resolution optical fluctuation image scanning microscopy, Optica 7, 1308-1316 (2020).

Thermalization is a generic property of macroscopic systems and may be avoided onlyin integrable models and , possibly, also in strongly disordered systems which are many-body localized. However, only in latter case, nonergodicity does not require fine-tuning of models parameters. Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition.For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders. It suggests that many-body localized systems are similar to nearly integrable models.

The competition between unitary evolution that spreads information throughout the many-body system, and the monitoring action of an environment gives rise to dynamical phases separated by measurement-induced phase transitions. The first part of the talk will be devoted to numerical investigations of the structure of many-body wave functions of 1D random quantum circuits with local measurements across a measurement-induced transition between phases with volume-law and area-law scaling of entanglement entropy. The many-body wave functions are investigated by means of the participation entropies. The leading term in system size dependence of participation entropies indicates a multifractal scaling of the wavefunctions at any non-zero measurement rate. The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being non-zero in the volume-law phase and vanishing in the area-law phase. We provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D. The second part of the talk will concern the structure of many-body wave functions in systems that undergo localization transitions – both in presence and in absence of interactions. I will briefly introduce a polynomially filtered exact diagonalization method (POLFED) of computing eigenvectors of large sparse matrices at arbitrary energies and discuss its utility in studies of many-body localization transition as well as other problems of non-equilibrium many-body physics. The measures of localization ensuing from the analysis of structure of many-body wave functions alongside with the more conventional quantities will be used to discuss the problem of pin-pointing of many-body localization transition in spin-1⁄2 chains, and in particular in the Kicked Ising model.

Spectroscopy with visible light is generally insensitive to the structure of materials - for structural studies techniques using either shorter (X-ray) or longer (infrared) electromagnetic waves are methods of choice. Nevertheless techniques based on visible light have a great advantage other X-ray or infrared based methods, because excellent sources and detectors of visible light are readily available. I will briefly discuss how the process of stimulated emission can be utilized to make spectroscopy with visible light sensitive to the structure of materials at the molecular level. The idea is based on strong excitation of fluorophores in the studied material and creation of population inversion. Then, amplified stimulated emission or laser emission can be detected. In such a case the spectrum and intensity of the detected light depend on paths of photons in the material, and consequently – on its structure. The method has been successfully applied to study aggregation of peptides in biomaterials.

In this talk I will present a theoretical analysis of the phase diagram of ultracold bosons in a lattice and interacting with long-range forces decaying with the inter-particle distance. Those long-range interactions can be due to Rydberg interactions or to the atoms permanent dipoles. The theoretical model is an extended Bose-Hubbard model and describes the dynamics of ultracold atoms in optical lattices realised in present experimental platforms. We determine the ground state in one- and two-dimensions using mean-field treatments. In one dimension we complement our studies using numerical programs based on tensor networks. We focus in particular on parameters for which quantum fluctuations compete with the interaction-induced correlated hopping between lattice sites. We analyse the superfluid phases emerging from the competition of these two mechanisms, and identify the parameters where correlated hopping and quantum fluctuations destructively interfere. This quantum interference leads to insulating phases at relatively large kinetic energies, where one would otherwise expect superfluidity.

In this talk, I will discuss recent advances in the field of ultra-cold atoms trapped in optical lattices, which have allowed for proof-of-principle quantum simulations of lattice gauge theories in reduced spacetime dimensions. I will introduce a toolbox based on the idea of a Hubbard-dependent photon-assisted tunneling, and discuss recent experiments where this technique has been used to realize the minimal instance of Z2 gauge-invariant tunneling with ultra-cold atoms in a double well. Motivated by these advances, I will discuss one of the simplest generalizations where one could explore deconfinement in the lab: a Z2 gauge theory with fermionic matter in a cross-link ladder. This specific lattice regularization allows for an interesting interplay between symmetry-protected topological phases and topological order in the matter and gauge sectors.

There is no consistent classical theory for macroscopic fields (electromagnetic, acoustic, gravitational, etc.) interacting with environment. In particular, incoherent, thermal sources and sources moving faster than critical velocity and creating shock waves are poorly understood in classical terms. The reduced quantum description in terms of 'reduced state of the field' (RSF) containing the averaged field and the single (quasi) particle density matrix is discussed. Exact irreversible dynamics for RSF is proposed and illustrated by various examples of shock waves including sonic booms, heating of stellar atmosphere by Alfven waves and gravity waves amplification by rotating black holes. The extension of this approach to fermions can explain triboelectric phenomena.

References:
R. Alicki, 'Quantum features of macroscopic fields. Entropy and dynamics', Entropy 19, 1-13 (2019)
R. Alicki and A. Jenkins, 'Interaction of a quantum field with a rotating heat bath', Ann. Phys. (NY) 395, 69 (2018)
R. Alicki and A. Jenkins, 'Quantum thermodynamics of coronal heating', arXiv:2103.08746
R. Alicki and A. Jenkins, 'Quantum theory of triboelectricity', PRL 125, 186101 (2020)

Current plans for the construction of a fusion reactor assumes using a tokamak machine with tungsten plasma facing components. Tungsten impurities in the plasma deteriorate the energy confinement due to increased radiation and should be controlled to avoid plasma cooling. To achieve this, computational tools for plasma simulations are constantly developed and improved to provide reliable results.

One of the issues that needs refinement is the calculation of energy losses due to inelastic collisions of fast free electrons with non-fully ionized impurities. Such collisions lead to the excitation of ions, which then emit a photon while returning to a lower energy state. Such a photon typically leaves the plasma and, as a radiation emitted outside the plasma, contribute to lower energy confinement. To include such events into the Fokker-Planck equation solver, a modified collision frequency based on Bethe-Bloch theory is calculated. This approach requires at first to calculate the mean excitation energy for all the ion species in the plasma.

The upcoming seminar will present work carried out at the Institute of Nuclear Physics PAN on the calculation of the mean excitation energy. A first approach based on the Local Plasma Approximation (LPA) will be discussed together with further ideas to replace it with more detailed computation.

Spontaneous symmetry breaking is a fundamental concept in many areas of physics. The space crystals, superconductors and ferromagnets are respective examples of continuous space translation, gauge and rotational invariance breaking. Despite its popularity, the idea of breaking the continuous time translation symmetry and the discrete time-translation symmetry (DTTS) has received attention only very recently and manifested in the form of discrete time crystals [1-3].

It was shown that isolated periodically driven ultracold atoms [2] are able to spontaneously self-reorganise their motion leading to DTTS breaking. Here we focus on these kinds of systems bouncing resonantly on an oscillating atom mirror with the interaction between atoms greater than a critical value. Such a driven cloud of ultracold atoms moves with a period n-times longer than that of the mirror due to DTTS breaking, and the so-called n-tupling discrete time crystal (nDTC) is formed.

These systems are promising for experimental realisation [4]. As the experimental conditions are never perfect, we analyse the robustness of nDTC against small perturbations of the initial state by determining the phase diagrams. Moreover, we investigate the quantum many-body fluctuations of nDTCs resulting from interactions between atoms within the Bogoliubov theory and demonstrate that DTCs are resistant to quantum many-body effects [5].

1. F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012)
3. D. Else et al., Phys. Rev. Lett 117, 090402 (2016)
4. K. Giergiel et al., New J. Phys. 22, 085004 (2020)
5. A. Kuroś et al., New J. Phys. 22, 095001 (2020)

The quantum dynamics of large systems is obviously a well known difficult problem because the quantum configuration space grows exponentially with system size. However, it turns out that under the right conditions it can be mastered using appropriately noisy trajectories of a random sample of nonorthogonal quantum states.

We demonstrate the positive-P method known otherwise from quantum optics can treat the full quantum dynamics of the dissipative Bose-Hubbard model in a scalable way across a wide range of parameters. This model is important for a number of platforms such as polariton condensates, nanopillars, photonic lattices, or transmon qubits. As an example, full quantum dynamics of a nonuniform 256x256 lattice of sites is demonstrated. In the accessible regime numerical effort scales linearly with the number of sites, quadratically with the precision, and does not care about symmetry or its lack. We also find that the regions of applicability of the positive-P, and truncated Wigner approaches are mutually complementary. Together these approaches cover the majority of parameter space in the dissipative Bose-Hubbard model [1]. The positive-P approach also provides a simple and physically intuitive way to calculate many unequal time correlations, allowing their investigation in a non-perturbative and scalable way [2].
[1] P. Deuar, A. Ferrier, M. Matuszewski, G. Orso, M. H. Szymanska, PRX Quantum 2, 010319 (2021).
[2] P. Deuar, Quantum 5, 455 (2021).

Identifying phase transitions is one of the key problems in quantum many-body physics. The challenge is the exponential growth of the complexity of quantum systems’ description with the number of studied particles, which quickly renders exact numerical analysis impossible. A promising alternative is to harness the power of machine learning (ML) methods designed to deal with large datasets [1]. However, ML models, and especially neural networks (NNs), are known for their black-box construction, i.e., they usually hinder any insight into the reasoning behind their predictions. As a result, if we apply ML to novel problems, neither we can fully trust their predictions (lack of reliability) nor learn what the ML model learned (lack of interpretability). I will present a set of Hessian-based methods opening the black box of ML models, increasing their interpretability and reliability. We demonstrate how these methods can guide physicists in understanding patterns responsible for the phase transition. We also show that influence functions allow checking that the NN, trained to recognize known quantum phases, can predict new unknown ones. We present this power both for the numerically simulated data from the one-dimensional extended spinless Fermi-Hubbard model [2] and experimental topological data [3]. We also show how we can generate error bars for the NN’s predictions and check whether the NN predicts using extrapolation instead of extracting information from the training data [4]. The presented toolbox is entirely independent of the ML model’s architecture and is thus applicable to various physical problems.

[1] J. Carrasquilla. (2020). Machine learning for quantum matter, Advances in Physics: X, 5:1.
[2] A. Dawid et al. (2020). Phase detection with neural networks: interpreting the black box. New J. Phys. 22, 115001.
[3] N. Kaming, A. Dawid, K. Kottmann et al. (2021). Unsupervised machine learning of topological phase transitions from experimental data. Mach. Learn.: Sci. Technol. 2, 035037.
[4] A. Dawid et al. (2021). Hessian-based toolbox for interpretable and reliable machine learning in physics. arXiv:2108.02154.

I will discuss a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. I will specifically focus on the excitation spectrum properties. The droplet properties are governed by a single control parameter proportional to the particle number. For large values of this parameter the solution features the flat-top, droplet-like shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk. With decreasing control parameter these modes move to the continuum, sequentially crossing the particle-emission threshold. A notable exception is the breathing mode which is found to be always bound. As the control parameter tends to minus infinity, this ratio tends to one and the droplet transforms into the soliton solution of the integrable cubic GPE. For reference, see: Phys. Rev. A 101, 051601(R) (2020).

Non-equilibrium dynamics of slow quenches across continuous phase transitions have been understood very successfully under the unifying theory of the Kibble-Zurek mechanism. However, relatively less attention has been paid to the understanding of dynamics across first-order quantum phase transitions (FOQPT). In an attempt to mitigate this, here we will talk about the consequences of a slow dynamical ramp across the FOQPT transition line present in the Ising model with both transverse and longitudinal fields. The existence of a potential barrier, quintessential to the FOQPTs, gives rise to metastability in the dynamical state. We find that in the considered model, such metastability wear off by nucleating bubbles of the true ground state driven by quantum fluctuations. Specifically, we identify special resonant regions in the longitudinal field, where the metastable state can easily tunnel to nucleate bubbles of specific sizes (quantized). Further, we will describe our attempt to explain the entire non-adiabatic process under the unifying umbrella of Landau-Zener theories.

The quantum coherence effect in the light-matter system is the focus in the development of quantum optics, and it has brought new vitality in the quantum information area. The typical atomic coherence effects including the stimulated Raman adiabatic passage (STIRAP) and electromagnetically induced transparency (EIT) have been widely applied in quantum information area. It is possible to implement the efficient population transfer, quantum entanglement, quantum gate, photonic crystal and light storage utilizing the atomic coherence effects. Rydberg atoms have exaggerated properties which are quite different from ordinary neutral atoms as they have high principal quantum numbers. For instance, Rydberg atoms have large orbit radiuses, long lifetimes and huge dipole moments. The dipole-dipole interaction is typically enhanced by 12 orders of magnitude compared to two ground state atoms as the dipole moments of Rydberg atoms are very large. Based on these novel properties, the quantum coherence effect in Rydberg atomic ensemble will be different from that in common cold atomic ensemble, so we mainly focus on the quantum coherence effect and quantum coherence manipulation in ultra-cold Rydberg atomic ensemble. Our research includes the STIRAP and the light storage process in Rydberg atomic ensemble.

The difference between the energy of a ground state of a given Hamiltonian and the energy of the first excited state, called spectral gap, yields a key parameter of the system, useful for applications in adiabatic quantum computing and studies of quantum phase transitions in the model. We present a novel way to determine the upper bound for the energy gap based on properties of the set of expectation values of auxiliary observables. This formalism can be applied to obtain a new criterion of gaplessness, which we illustrate by a study of the XY model - an exemplary physical system with vanishing energy gap.

Traditionally, optical lattices are created by interfering two or more light beams, so that atoms are trapped at minima or maxima of the emerging interference pattern depending on the sign of the atomic polarizability [1]. Optical lattices are highly tunable and play an essential role in manipulation of ultracold atoms [2-3]. The characteristic distances over which optical lattice potentials change are limited by diffraction and thus cannot be smaller than half of the optical wavelength $\lambda$. Yet the diffraction limit does not necessarily apply to optical lattices [4-7] relying on coherent coupling between atomic internal states. It was demonstrated theoretically [4,5] and experimentally [6] that a periodic array of sub-wavelength barriers can be formed for atoms populating a long lived dark state of the $\Lambda$-type atom-light coupling scheme. The $\Lambda$ scheme has a single dark state, so no spin (or quasi-spin) degree of freedom is involved for the atomic motion in the dark state manifold affected by the sub-wavelength barriers.

In the present talk we will discuss various ways of producing subwavelength optical lattices [4-9]. In particular, we demonstrate that a tripod atom light coupling scheme can be used to create a lattice with spin-dependent sub-wavelength barriers [8,9]. The tripod scheme is characterized by two dark states playing the role of quasi-spin states. Inclusion of the spinor degree of freedom provides new possibilities for controlling the spectral and kinetic properties of atoms in the lattice. The tripod lattice can be realized using current experimental techniques.

[1] I. Bloch, Nature Physics 1(1), 23 (2005).
[2] M. Lewenstein et al., Advances in Physics 56(2), 243 (2007).
[3] I. Bloch, J. Dalibard and W. Zwerger, Rev. Mod. Phys 80, 885 (2008).
[4] M. Łącki et al., Phys. Rev. Lett. 117, 2330 (2016).
[5] F. Jendrzejewski et al., Phys. Rev. A 94, 063422 (2016).
[6] Y. Wang et al, Phys. Rev. Lett. 120, 083601 (2018).
[7] R. P. Anderson et al, Physical Review Research 2, 013149 (2020).
[8] E. Gvozdiovas, P. Rackauskas, G. Juzeliunas, https://arxiv.org/abs/2105.15148.
[9] P. Kubala, J. Zakrzewski and M. Łącki, https://arxiv.org/abs/2106.04709.

Many-body localization (MBL) is a robust manifestation of ergodicity breaking in interacting many-body systems. MBL behavior is analyzed in an extended Bose-Hubbard model with quasiperiodic infinite-range interactions being the only source of disorder. The analysis of the level statistics and of the eigenstates entanglement entropy shows that a significant fraction of eigenstates becomes localized as the strength of the global interactions is increased. This behavior scales differently depending on the choice of the thermodynamic limit. The system is asymptotically ergodic in a standard thermodynamic limit, namely by scaling the interaction strength so as to keep the energy extensive. On the other hand, the MBL regime seems to be stable if one allows for a non-standard thermodynamic limit with super-extensive scaling of the energy. In the latter one the mobility edge is observed. We argue that our findings can be experimentally verified in many-body cavity quantum electrodynamics setups by means of the so-called 'quench spectroscopy'

Quenched random disorders have been studied extensively and have been proposed to show Many-Body Localization (MBL) for large enough disorders. While much less theoretical attention has been paid to quasi-periodic spin chains. Quasi-periodic systems are interesting both as an experimentally more amenable system and also stemming from the recent work that shows it to be in a different universality class from quenched random disorders. In this talk, we will try to look at the scaling of observables and have a peek at whether MBL persists in the thermodynamic limit for quasi-periodic spin chains.

Realizing strongly-correlated topological phases of ultracold gases is a central goal for ongoing experiments. And while fractional quantum Hall states could soon be implemented in small atomic ensembles, detecting their signatures in few-particle settings remains a fundamental challenge. In this talk, we analyze the center-of-mass Hall drift of a small ensemble of hardcore bosons, initially prepared in the ground state of the Harper-Hofstadter-Hubbard model. By extracting the Hall conductivity in a wide range of the magnetic flux, we identify an emergent Hall plateau compatible with a fractional Chern insulator state: the width of the plateau agrees with the spectral and topological properties of the prepared ground state, while the Hall conductivity approaches a fractional value determined by the many-body Chern number. A comparison with a direct application of Streda's formula is also discussed. Our calculations suggest that fractional Chern insulators can be detected in cold-atom experiments, using available detection methods

Several theories of ergodic to many-body localized transition suggest the existence of an avalanche mechanism, in which ergodic bubbles (local, thermal fluctuations of the system properties) thermalize their surroundings, leading to delocalization of the entire system, unless the disorder is sufficiently strong to suppress this process. In this talk we present a tool based on neural networks that allows one to directly identify the ergodic bubbles using experimentally accessible two-site correlation functions. Studying time evolutions of the disordered Heisenberg spin chain, we observe a logarithmic in time growth of the ergodic bubbles in the MBL phase. Investigating the distributions of the bubble sizes, we find an exponential decay in the MBL regime and a power-law distribution with a thermal peak in the critical regime, confirming the presence of the avalanche mechanism. We also find quantitative differences in time evolution of chains with random and quasiperiodic disorder, as well as detect rare (Griffiths) events. These results open new pathways in the research of the mechanisms of thermalization in disordered many-body systems.

Thanks to recent impressing experimental progress, the investigation of non-equilibrium properties of driven-dissipative quantum systems has received an impressive boost. Rydberg atoms in optical lattices, systems of trapped ions, exciton-polariton condensates, cold atoms in cavities, arrays of coupled QED cavities, are at present the most intensively investigated experimental platforms to this aim. While in many cases the effect of an external bath is detrimental for quantum information protocols, it has been shown that by proper engineering of the environment, quantum manipulations are possible. I will discuss several aspects associated with the physics of engineered environments. I will first focus on quantum state preparation, I will then address features of the steady-state phase diagram displaying a variety of phenomena peculiar of non-equilibrium systems. I will consider, in particular, the possible existence of exotic phases in the steady-state with connections to time crystals and quantum synchronization.

Time-space crystalline structures merge the ideas of time and space crystals to form a system that is periodic both temporally and spatially. The spatial part of the crystalline structure is created by an optical lattice and the temporal periodicity is engineered by choosing a proper resonant periodic driving of the system. In this talk we present the procedure to create a two-dimensional time-space crystalline structure. Using the highly excited resonant states of a driven one-dimensional lattice we construct periodically oscillating localized wavepackets at each spatial site that constitute the emergence of the two-dimensional time-space crystalline structure. Extending the system to three spatial dimensions realizes a six-dimensional crystalline structure which allows to probe higherdimensional condensed matter phenomena.

Discrete time crystals, alike ordinary space crystals, can host condensed matter physics. I will present how different two-dimensional inseparable time lattices with the Möbius strip geometry can be engineered using ultra-cold atoms. As a specific example of a many body Hamiltonian with tunable parameters, I will show how one can realize a Lieb lattice model with a flat band and how to control long-range hopping of pairs of atoms in the model.

In this talk I will describe the out-of-equilibrium evolution of 2D, weakly interacting disordered Bose gases in momentum space. I will first recall the scenario expected in the non-interacting limit, where multiple scattering leads to beautiful disorder-induced interference phenomena such as coherent backscattering (a.k.a. weak localization) or coherent forward scattering (associated with Anderson localization). For nonzero interaction, I will then show that two well distinct out-of-equilibrium regimes emerge at short time depending on the relative strengths of interactions and disorder. While weak interactions essentially lead to dephasing of localization effects, when interactions become stronger than the disorder multiple scattering completely ceases and the gas reaches a pre-thermalized state, associated with algebraic correlations spreading within a light cone. I will conclude with a discussion of the long-time thermalized state of the Bose gas, where a normal to superfluid transition emerges.

Recent works on observation of discrete time-crystalline signatures throw up major puzzles on the necessity of localization for stabilizing such out-of-equilibrium phases. Motivated by these studies, we delve into a clean interacting Floquet system whose quasi-spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline order in the absence of fine-tuning or any explicit local constraint. We relate such behavior to a measure zero set of nonthermal Floquet eigenstates with long-range spatial correlations, which coexist with otherwise thermal states at near-infinite temperature and develop a high overlap with a family of translationally invariant, symmetry-broken initial conditions. This resembles the notion of 'dynamical scar states' that remain robustly localized throughout a thermalizing Floquet spectrum with fractured structure. We dub such a long-lived discrete time crystal formed in partially nonergodic systems, 'scarred discrete time crystal' which is distinct by nature from those stabilized by either many-body localization or prethermalization mechanism.

Anderson-Holstein model elucidates the most fundamental physics of correlated quantum transport since it deals with the interaction between the electronic energy modes with strong Coulomb repulsion and a single phonon mode. From the practical stand-point, this model can be utilized to design a bias-driven heat engine to accomplish power generation or a refrigerator with substantial cooling efficiency [1]. In the first course of the presentation, an in-depth analysis of the physics related to the interplay between the quantum-dot level quantization, the on-site Coulomb interaction, and the electron-phonon coupling on the thermoelectric performance reveals that an n-type engine performs better than a p-type engine. In addition, with the aid of system temperature estimated by a thermometer bath, one can reveal the nature of optimum thermoelectric efficiency [2]. In the subsequent phase, it is demonstrated that, a phonon Peltier effect may arise in the non-linear thermoelectric transport regime, leading to an electron induced phonon current in the absence of a thermal gradient. In further exploring possibilities that can arise from this effect, we propose a novel charge-induced phonon switching mechanism that may be incited via electrostatic gating [3]. Consequently, the observed cumulative effects of voltage and electronic temperature gradients on the non-linear phonon currents is explained by introducing a new trans- port coefficient, termed as the electron-induced phonon thermal conductivity [4]. Under suitable operating conditions, it can demonstrate two counter- intuitive situations: (a) the electronic system can pump in phonons into the hotter phonon reservoirs by exploiting voltage bias and (b) the electronic system can extract phonons out of the colder phonon reservoirs by utilizing voltage bias. For future analysis, this theoretical model can be implemented in designing hybrid refrigeration systems [5], light amplifying devices based on cavity-QED [6], thermal rectifiers [7] to name a few.

References
[1] Muralidharan, B. and Grifoni, M., 2012. Performance analysis of an in- teracting quantum dot thermoelectric setup. Physical Review B, 85(15), p.155423.
[2] De, B. and Muralidharan, B., 2016. Thermoelectric study of dissipative quantum-dot heat engines. Physical Review B, 94(16), p.165416.
[3] De, B. and Muralidharan, B., 2018. Non-linear phonon Peltier effect in dissipative quantum dot systems. Scientific reports, 8(1), pp.1-9.
[4] De, B. and Muralidharan, B., 2019. Manipulation of non-linear heat currents in the dissipative Anderson-Holstein model. Journal of Physics: Condensed Matter, 32(3), p.035305.
[5] Mukherjee, S., De, B. and Muralidharan, B., 2020. Three terminal vibron coupled hybrid quantum dot thermoelectric refrigeration. arXiv preprint arXiv:2004.12763.
[6] Liu, Y.Y., Petersson, K.D., Stehlik, J., Taylor, J.M. and Petta, J.R., 2014. Photon emission from a cavity-coupled double quantum dot. Physical review letters, 113(3), p.036801.
[7] Lu, J., Wang, R., Ren, J., Kulkarni, M. and Jiang, J.H., 2019. Quantum- dot circuit-QED thermoelectric diodes and transistors. Physical Review B, 99(3), p.035129.

Periodically driven quantum many-body systems can stabilize to interesting non-equilibrium states despite the lack of energy conservation. The statistical mechanics of such systems have been developed through the last decade. The stability of the phases and the structure of the statistical mechanics rests on conservation laws that come out of the dynamics. Some of them are exact, and some of them are emergent. I intend to provide an overview of these developments and the underlying physical pictures. I will touch upon the concepts of Periodic Gibbs' ensemble, Floquet ETH, Floquet MBL, and emergent symmetries and conservation laws that allow stability in clean, interacting Floquet systems.

Inducing and controlling many-body systems via light extends the methodology for the design of materials and functionalities in a profound manner. In this talk, I will present our proposal to induce a time crystalline state in a high Tc superconductor. This realization constitutes the creation of a dynamically induced state that has a genuine non-equilibrium order with no equilibrium counterpart, and utilizes a sum resonance of the plasma frequency and the Higgs frequency of the superconductor. Secondly, I will present a mechanism for light-enhanced superconductivity that utilizes parametric enhancement via the Higgs mode. This proposed mechanism induces a periodic collective motion of the Higgs mode, which in turn acts as a parametric amplifier of the conductivity of the material. Thirdly, I will present our proposal for demonstrating parametric control of conductivity in a cold atom system, which imitates our proposed mechanism for parametrically enhanced superconductivity. We propose to probe the conductivity of an atomic Josephson junction, composed of two weakly coupled condensates, and to enhance or suppress the low-frequency regime of the conductivity, which provides a direct confirmation of this mechanism in a cold-atom environment. Time permitting, I will discuss our conceptual progress on generalizing the Feynman path integral, and its application to superconducting states.

Key to understanding the difficulty of multiqubit state preparation is the control landscape -- the mapping assigning to every control protocol its cost function value. Optimization algorithms strive to find a better local minimum of the control landscape; the global minimum corresponds to the optimal protocol. We found rapid changes in the search for optimal protocols, reminiscent of phase transitions. These 'control phase transitions' can be interpreted within Statistical Mechanics by viewing the cost function as 'energy' and control protocols - as 'spin configurations'. I will show that optimal qubit control exhibits continuous and discontinuous phase transitions familiar from macroscopic systems: correlated/glassy phases and spontaneous symmetry breaking. I will then present numerical evidence for a universal spin-glass-like transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Across the glassy transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with random satisfiability problems.

In this talk I will describe the mean-field, out-of-equilibrium evolution of a 2D, weakly interacting disordered Bose gas in momentum space. I will first recall the scenario expected in the non-interacting limit, where multiple scattering leads to beautiful disorder-induced interference phenomena such as coherent backscattering (a.k.a. weak localization) or coherent forward scattering (associated with Anderson localization). For nonzero interaction, I will then show that two well distinct out-of-equilibrium regimes emerge depending on the relative strengths of interactions and disorder. While for weaker interactions the Bose gas essentially undergoes dephasing and localization effects are washed out, when interactions become stronger than the disorder multiple scattering ceases and the gas reaches a pre-thermalized state, associated with algebraic correlations spreading within a light cone.

Reservoir computing is a recent and increasingly popular bio-inspired computing scheme which holds promise for efficient information processing. We demonstrate the applicability and performance of reservoir computing in a general complex Ginzburg-Landau lattice model, which adequately describes dynamics of a wide class of systems, including coherent photonic devices and trapped Bose-Einstein condensates. In particular, we propose that the concept can be readily applied in exciton-polariton lattices, which are characterized by unprecedented photonic nonlinearity, opening the way to signal processing at rates of the order of 1 Tbit/s [1]. Based on this idea, reservoir computing was recently realized in a polariton system [2].

[1] A. Opala, S. Ghosh, T. C. H. Liew, M. Matuszewski, Phys. Rev. Applied 11, 064029 (2019).
[2] D. Ballarini, A. Gianfrate, R. Panico, A. Opala, S. Ghosh et. al, Nano Lett. 20, 35063512 (2020).

For many years magnetic Feshbach resonances have been viewed as an essential tool of controlling the interaction strength in ultracold gases of alkali dimers. In the past few years, the experiments on entirely new quantum gases emerged, and it is now alkaline-earth, lanthanides, I will discuss two kinds of Feshbach resonances which were discovered in systems other than alkali-metal dimers: the resonances originating from anisotropy of the interactions between atoms, and a (very tiny!) coupling between spins of nuclei and electrons. These resonances open pathways toward new, more complex quantum systems with intriguing properties.

The talk will be focused on the eigenstates of interacting 1D gases. I would like to advertise a simple single-particle equation, which is employed to show the existence of quantum droplets in dipolar 1D gas.

The substantial part of this talk will be devoted to recall the typical methods applied to study interacting slow bosons: a) ab initio many-body calculation (usually limited to a small number of atoms), b) single-body equations, e. g. Gross-Pitaevskii equation (very approximated). Firstly, I will remind these two viewpoints, and correspondence between them, on the well-understood case of atoms interacting via short-range potential. Interestingly, the simple single-body picture like (b) can be still useful even in the regime of strong correlations. Then I will continue to non-local interactions, and present our understanding of ground state having properties of quantum droplets.

References:
[1] W. Golletz, W. Górecki, R. Ołdziejewski, K. Pawłowski, Phys. Rev. Research 2, 033368 (2020)
[2] R. Ołdziejewski, W. Górecki, K. Pawłowski, K. Rzążewski, Phys. Rev. Lett. 124, 090401 (2020)

In a broad variety of physical scenarios ranging from classical meta-materials to open quantum systems, non-Hermitian (NH) Hamiltonians have proven to be a powerful and conceptually simple tool for effectively describing dissipation. Motivated by recent experimental discoveries, investigating the topological properties of such NH systems has become a major focus of current research. In this talk, I give an introduction to this rapidly growing field, and present our latest results. Specifically, we discuss the occurrence of novel gapless topological phases unique to NH systems. There, the role of spectral degeneracies familiar from Hermitian systems such as Weyl semimetals is played by exceptional points at which the effective NH Hamiltonian becomes non-diagonalizable. Furthermore, we show how guiding principles of topological matter such as the bulk boundary correspondence are qualitatively changed in the NH realm. Finally, we demonstrate that the sensitivity of NH systems to small changes in the boundary conditions may be harnessed to devise novel high-precision sensors.

During the seminar, I will talk about our latest work [1] concerning dynamical generation and storage of spin squeezed states, as well as more entangled states up to macroscopic superpositions, in a system composed of a few ultra-cold atoms trapped in a one-dimensional optical lattice. The system, initially in the superfluid phase with each atom in a superposition of two internal states, is first dynamically entangled by atom-atom interactions then adiabatically brought to the Mott-insulator phase with one atom per site where the quantum correlations are stored. Exact numerical diagonalization allows us to explore the structure of the stored states by looking at various correlation functions, on-site and between different sites, both at zero temperature and at finite temperature, as it could be done in an experiment with a quantum-gas microscope.

[1] M. Płodzień, M. Kościelski, E. Witkowska, A. Sinatra, Phys. Rev. A 102, 013328 (2020)

Topological materials have potential applications for quantum technologies. Non-interacting topo- logical materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is instead only partially understood how interactions affect topological properties. Here, we discuss a model where topology emerges from the quantum in- terference between single-particle dynamics and global interactions. The system is composed by soft-core bosons that interact via global correlated hopping in a one-dimensional lattice. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry, the corresponding phase resembles nontrivial states of the celebrated Su-Schriefer-Heeger model. Like the fermionic Peierls instability, the emerging quantum phase is a topological insulator and is found at half fillings (namely, when the number of sites is twice as large as the number of bosons). Nevertheless, here it arises from an interference phenomenon that has no known fermionic analog. We argue that these dynamics can be realized in existing experimental platforms, such as cavity quantum electrodynamics setups, where the topological features can be revealed in the light emitted by the resonator.

In my talk, I will discuss ground-state properties of the system of a few attractively interacting fermionic atoms confined in a one-dimensional harmonic trap. Focusing on nontrivial interparticle correlations encoded in the noise correlation, I will show that evident signatures of strongly correlated fermionic pairs in the Fulde-Ferrell-Larkin-Ovchinnikov state are present. Importantly, these correlations can be detected by measurements directly accessible within state-of-the-art techniques.

I will discuss several scenarios when very few photocounting events carry plenty of information meant to be retrieved by the measurement. Examples include: beating the Rayleigh limit by imaging a composite light source through spatial mode demultiplexing and two-photon interference; transmission of classical information in the photon-starved regime, when the power of the transmitted signal is severely limited but modulation bandwidth can be high; and finally reducing the communication complexity of comparing large datasets using quantum fingerprinting.

The critical behaviors of many-body phase transition is one of the most fascinating but also challenging questions in quantum physics. In this report, we observe the dynamical phase transition of a Bose gas from a superfluid (SF) to a Mott insulator (MI) based on our improved band-mapping method, where the critical behaviors deviate from a universal power-law scaling. When the ramping is slow, we observe an asymmetric critical behavior on the SF side and MI side, where the SF to MI transition follows the power law scaling which is known as Kibble-Zurek mechanism. While the ramping speed increases, the critical behaviors of many-body phase transitions deviates from the power-law and enter a new regime, where the non-equilbrium transition dominated while cannot be captured by the Kibble-Zurek mechanism.

In this talk I will present a general mechanism for robust nonergodic behavior in the absence of disorder as a consequence of local constraints induced by gauge invariance. I will outline how this can give rise to genuinely nonequilibrium phases such as gauge time crystals in homogeneous systems protected by gauge invariance. Further, I will show that even genuinely interacting two-dimensional lattice gauge theories can become nonergodic. As a consequence this disorder-free localization scenario constitutes an ergodicity breaking mechanism even stronger than for inhomogeneous systems in the context of many-body localization, where nonergodicity in two dimensions has been argued to be unstable.

Electron beams with a well-defined longitudinal orbital angular momentum (OAM), known as twisted or vortex electrons, are attracting considerable interest in both fundamental and ap- plied physics. Their unique features (such as helical wavefronts, circulating probability den- sity currents, etc.) make these beams ideal tools for studies in various fields of modern physics. For instance, scattering of twisted electrons on a solid target can provide detailed in- formation about the magnetic properties of the target material. The same concerns helical properties of crystals or nanomolecules.

We investigate a possibility of generating vortex electrons in high-energy ionization. We show that photoelectrons of unprecedented large OAM can be emitted when a high-intensity laser pulse interacts with atomic targets. In order to analyze how OAM of photoelectrons may in- fluence the ionization spectrum we use the quasi-relativistic strong-field approximation. This approach (with the binding potential neglected during the electron dynamics in a laser field) is particularly well suited for describing high-energy ionization. In addition, it accounts for rela- tivistic effects, including the electron recoil due to the interaction with the laser field and the relativistic mass correction.

We consider a single quantum spin subject to an exotic external perturbation which is both random and periodic in time. For a suitable choice of the model parameters, we observe that the probability of detecting the spin around some fixed point on the Bloch sphere shows an exponential profile centered around some moment in time. Such behavior can be interpreted as Anderson localization in the time domain, a temporal analogue of the standard Anderson localization in space. We propose two experimental setups - a paramagnetic crystal with strong magnetic anisotropy and ultracold bosons trapped in a double-well potential - which could possibly serve as a platform to realize our model.

The number of topological defects created in a system driven through a quantum phase transition exhibits a power-law scaling with the driving time. This universal scaling law is the key prediction of the Kibble-Zurek mechanism (KZM), and testing it using a hardware-based quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. Specifically, we report on extensive experimental tests of topological defect formation via the one-dimensional transverse-field Ising model on two different D-Wave quantum annealing devices. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors, with certain quantitative deviations from the theory likely caused by factors such as random control errors and transient effects. In addition, we probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks and their decay, and again find agreement with the quantum simulator results. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system. We support this result by extensive numerical computations. To check whether an alternative, classical interpretation of these results is possible, we used the spin-vector Monte Carlo model, a candidate classical description of the D-Wave device. We find that the degree of agreement with the experimental data from the D-Wave annealing devices is better for the KZM, a quantum theory, than for the classical spin-vector Monte Carlo model, thus favoring a quantum description of the device. Our work provides an experimental test of quantum critical dynamics in an open quantum system, and paves the way to new directions in quantum simulation experiments.

Ref:
Yuki Bando, Yuki Susa, Hiroki Oshiyama, Naokazu Shibata, Masayuki Ohzeki, Fernando Javier Gómez-Ruiz, Daniel A. Lidar, Adolfo del Campo, Sei Suzuki, Hidetoshi Nishimori Journal-ref: Phys. Rev. Research 2, 033369 (2020)

Recently, protocols based on statistical correlations of randomized measurements were developed for probing synthetic quantum many-body systems, to access Rényi entropies, many- body state fidelities, out-of-time-ordered correlators (OTOCs) and topological invariants. After a general introduction to randomized measurements, I will first present our theory proposal for measuring OTOCs and the corresponding experimental demonstration in a ion chain implementing a Ising model with tunable-range interactions. I will then present a new protocol to measure many-body topological invariants of symmetry protected topological (SPT) phases of one-dimensional spin systems. I will show how to measure invariants arising from inversion, time- reversal and unitary onsite symmetries. This enables to systematically probe the complete classification of bosonic SPT phases in one dimension experimentally. I will illustrate the technique and its application in the context of the extended bosonic SSH model, as realized recently with Rydberg tweezer arrays.

Individually trapped neutral atoms provide a promising platform to engineer quantum many-body systems in a controlled, bottom-up approach. They can be readily manipulated in large numbers and interact strongly when excited to Rydberg states. In this talk I will discuss different approaches to use such systems for quantum information processing tasks. First, I will review the basic (many-body) physics of arrays of Rydberg atom arrays. I will show that such systems are naturally related to certain combinatorial optimization problems. In particular, I will show that one can encode the solution to maximum independent set problems in the ground state of properly positioned atoms. This allows to directly implement various quantum optimization algorithms with no experimental overhead and study their performance for system sizes that can’t be simulated on classical computers. In the second part of this talk I will focus on digital approaches to quantum computing with Rydberg atoms. In particular, I will introduce a new protocol for realizing fast multi-qubit gates between individual neutral atoms, based on the Rydberg blockade mechanism.

We show that, in generalized unitary parameter estimation problem the tight lower bound is greater by a factor of π than the conventional Heisenberg limit, derived from the properties of the quantum Fisher information. That is, the conventional bound is never saturable. Our result makes no assumptions on the measurement protocol, and is relevant not only in the noiseless case but also if noise can be eliminated using quantum error correction techniques.

In this talk, I will discuss our recent theory-plus-experiment collaboration focusing on a one-dimensional bichromatic lattice. The lattice is defined by superimposing two cosine potentials, and can be driven in to disctinct ways. The usual 'dipolar' driving corresponds to equal translation of both lattices whereas the novelty 'phasonic' driving is achieved by translating only the secondary lattice. In the latter case of phasonic driving, experiments revealed -- and theory was able to support -- strong multiphoton processes up to the 12th order indicating an efficient high-harmonic response.

Indeed.

Motivated by strongly correlated and frustrated systems, we propose a coupled bose-fermi model in two dimensions that describes the dynamics of pairs of opposite spin fermions scattering from localized bosons. Tracing out one of the degrees, either the bosons or fermions, generates temperature-dependent long range effective interactions between the entities that we investigate using Monte Carlo techniques. The behavior of bosons is dominated by vortex-antivortex unbinding, with effective interboson interactions beyond the nearest neighbor Josephson coupling of phases. Remarkably in the fermion sector we observe a temperature-induced BCS-BEC crossover followed by phase transitions to Anderson and Bose insulator phases, even without quenched disorder. Tunneling and angle resolved photoemission spectroscopy on bose-fermi mixtures in cold atomic systems and superconducting islands on graphene, are some of the promising experimental platforms to test our predictions.

Quantum frequency estimation constitutes a fundamental protocol of quantum metrology with applications to sensing tasks of magnetometry, accelerometry, or atomic spectroscopy. Although it proves the entanglement of probes (atoms, photons) to largely enhance attainable precisions, its practicality has been questioned due to the inevitable impact of decoherence. In particular, by considering local noise mechanisms that disturb each probe independently at a constant rate, it has been shown that ``beating'' the so-called standard quantum limit (SQL) typically becomes fiction in the regime of asymptotically many probes. However, peculiar decoherence models have been proposed to demonstrate that there must exist exceptions to such a rule. In our work, we present a general framework that allows to establish ultimate limits on asymptotic sensitivity in quantum frequency estimation. Not only it provides an overall picture explaining which unique noise properties are required for the SQL to be asymptotically surpassed, it also explicitly proves that non-Markovian properties are irrelevant in that respect. Nonetheless, we demonstrate that non-Markovianity of decoherence may still play an important role in quantum frequency estimation when the asymptotic precision scaling is no longer the main goal.

We study the final stages of the evolution of a binary system consisted of a black hole and a white dwarf star. As a model of a white dwarf star we consider a zero temperature droplet of attractively interacting degenerate atomic bosons and spin-polarized atomic fermions. Such mixtures are investigated experimentally nowadays. We find that the white dwarf star is stripped off its mass while passing the periastron. A charged mass, falling onto a black hole, could be responsible for recently discovered ultraluminous X-ray bursts. The binary system ends its life in a spectacular way, revealing quantum features underlying the white dwarf star's structure. Due to nonlinear effects, the accretion disc originated from the white dwarf becomes fragmented and the onset of a quantum turbulence with giant quantized vortices present in the bosonic accretion disc is observed.

After the formulation of lattice gauge theories in 1970s, it has gained a renewed interest in recent years due to - (a) recently developing tensor network techniques to efficiently solve lattice problems, and (b) the possibilities of experimental realization / quantum simulation of high-energy physics in table-top experiments using ultra-cold atoms. In this talk, first I will introduce the field of lattice gauge theories in general from the perspective of ultra-cold atomic physics. Then I will present our latest results on out-of-equilibrium dynamics of a particular gauge theory with bosonic matter, where we drive the vacuum of a relativistic theory of bosons coupled to a U(1) gauge field in 1+1 dimensions (bosonic Schwinger model) by creating a spatially separated particle-antiparticle pair connected by a string of electric field. During the evolution, we observe a strong confinement of the bosons witnessed by the bending of their light cone. As a consequence, for the time scales we are able to simulate, the system evades thermalization and generates exotic asymptotic states. These states are made of two disjoint regions, an external deconfined region that seems to thermalize, and an inner core that reveals an area-law saturation of the entanglement entropy. Finally, I will conclude with concluding remarks and future directions.

It is an open question how fast information processing can be performed and whether quantum effects can speed up the best existing solutions. Signal extraction, analysis, and compression in diagnostics, astronomy, chemistry, and broadcasting build on the discrete Fourier transform. It is implemented with the fast Fourier transform (FFT) algorithm that assumes a periodic input of specific lengths, which rarely holds true. A lesser-known transform, the Kravchuk-Fourier (KT), allows one to operate on finite strings of arbitrary length. It is of high demand in digital image processing and computer vision but features a prohibitive runtime. Here, we report a one-step computation of a fractional quantum KT. The quantum d-nary (qudit) architecture we use comprises only one gate and offers processing time independent of the input size. The gate may use a multiphoton Hong-Ou-Mandel effect. Existing quantum technologies may scale it up toward diverse applications.

Układ okresowy pierwiastków powstał dzięki odkryciu prawidłowości we właściwościach pierwiastków, związanych ze wzrostem masy atomowej. Zapełnianie kolejnych powłok atomowych powoduje systematyczne zmiany własności atomów, lecz zmiany te ulegają rozmaitym zaburzeniom, wywołanym między innymi przez przemieszczenia powłok zewnętrznych oraz przez relatywistyczną kontrakcję powłok wewnętrznych. W ramach seminarium przedstawiona zostanie jakościowa analiza kilku najbardziej widowiskowych efektów relatywistycznych w mikroświecie.

Ogólna Teoria Względności przewiduje pewne efekty relatywistyczne, które obserwujemy w Układzie Słonecznym jako precesja peryhelium Merkurego, ugięcie i opóźnienie sygnału świetlnego oraz przesunięcie ku czerwieni. Podczas seminarium chcę przybliżyć matematyczne podstawy występowania tych efektów oraz ich praktyczne zastosowanie - zachowanie zegarów w polu grawitacyjnym Ziemi oraz działanie Globalnego Systemu Wyznaczania Pozycji GPS.

We study level statistics across the many-body localization transition. An analysis of the gap ratio statistics from the perspective of inter- and intra-sample randomness allows us to pin point differences between transitions in random and quasi-random disorder, showing effects due to Griffiths rare events for the former case. Defining a mean gap ratio for a single realization of disorder we show that it has a broad, system specific distribution across the whole transition. That explains the necessity of introducing weighted random matrix ensembles that correctly grasp the sample-to-sample variation of system properties including the rare events. We consider two such approaches. One is a weighted short-range plasma model, the other a weighted power--law random banded matrix model. Treating the single sample gap ratio distribution as input, the considered weighted models yield a very good agreement both for spacing distribution including its exponential tail and the number variance up to tens of level spacings. We show explicitly that our weighted models describe the level statistics across the whole ergodic to many-body localized transition much more faithfully than earlier predictions. We also demonstrate that our model describes level statistics in variety of spin, bosonic and fermionic systems. The remaining deviations for long-range spectral correlations are discussed and attributed mainly to the intricacies of level unfolding. [1] P. Sierant and J. Zakrzewski, Intermediate spectral statistics in the many--body localization transition, arXiv:1807.06983 [2] P. Sierant and J. Zakrzewski, Weighted models for level statistics across the many--body localization transition, arXiv:1808.02795

year=2015/16