# About me

I am a PhD student at Jagiellonian University in Kraków. I work in a theoretical group (Atomic Optics Department) under supervision of Prof. Krzysztof Sacha.

As for now my research is focused on ultracold systems in lower dimensions. I perform numerical simulations of measurement process in the so-called Lieb-Liniger model (Bose gas with contact interactions) and Gaudin-Yang model (Fermi case). In order to solve problems in aforementioned models we employ the Bethe ansatz approach. During my master research we showed that the measurement process breaks the translation symmetry and causes the emergence of dark soliton structures if the system is prepared in the type II excited state (Lieb-Liniger model). In the case of weak coupling limit both probability densities and phases for the last particle in the system match very well to the corresponding mean-field solutions. We showed that soliton-like structures survive also in the strong interaction regime (beyond the mean-field description). The results were published in Phys. Rev. A **92**, 032110 (2015).

In the collaboration with Prof. Krzysztof Sacha, Prof. Mariusz Gajda and Prof. Mirosław Brewczyk we analyzed strong interaction regime and time evolution of one and multiple soliton states (including collisions). The effects of our work were published in Phys. Rev. A **94**, 023623 (2016).

During one month research stay at UPMC Paris (November 2015) I started the investigation of dark solitons in Gaudin-Yang model. The model describing mixture of two species (for instance spin-up and spin-down) of fermions with contact interaction between particles from different species. Choosing the attractive type of interactions we expect to observe pairing of fermions (one with spin-up and one with spin-down). In consort with Prof. D. Delande and Prof. K. Sacha we want to show that in the model exists a state corresponding to dark soliton (Bethe ansatz approach developed during studies of the correspondence between the second branch of elementary excitations and dark solitons in the Lieb-Liniger model). Moreover, the dark soliton should reveal in the probability density after the proper phase imprinting on one type of fermions (according to K. Sacha, D. Delande, Phys. Rev. A **90**, 021604(R) (2014)). Using TEBD method and proper phase imprinting we believe to observe soliton structures.

Additionally, we try to solve the problem of the so-called time crystal formation (F. Wilczek, Phys. Rev. Lett. **109**, 160401 (2012)). My main aim is to show that the measurement process breaks not only the space translation symmetry but also the time translation symmetry and causes the formation of crystalline structure which is periodic in time domain.