Seminarium Zakładowe - Archiwum

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