arXiv subjects

K. Sacha

Publications and source records attributed to K. Sacha.

8 recordsLinked to original sources

arXiv2022

Two-dimensional Thouless pumping in time-space crystalline structures

Dynamics of particle in a resonantly driven quantum well can be interpreted as that of a particle in a crystal-like structure, with the time playing the role of the coordinate. By introducing an adiabatically varied phase in the driving protocol, we demonstrate a realization of the Thouless pumping in such a time crystalline structure. Next, we extend the analysis beyond a single quantum well by considering a driven one-dimensional optical lattice, thereby engineering a 2D time-space crystalline structure. Such a setup allows us to explore adiabatic pumping in the spatial and the temporal dimensions separately, as well as to simulate simultaneous time-space pumping.

cond-mat.quant-gas↗

arXiv2019

Topological Time Crystals

By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger (SSH) model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system.

cond-mat.quant-gas↗

arXiv2009

Quantum bright soliton in a disorder potential

At very low temperature, a quasi-one-dimensional ensemble of atoms with attractive interactions tend to form a bright soliton. When exposed to a sufficiently weak external potential, the shape of the soliton is not modified, but its external motion is affected. We develop in detail the Bogoliubov approach for the problem, treating, in a non-perturbative way, the motion of the center of mass of the soliton. Quantization of this motion allows us to discuss its long time properties. In particular, in the presence of a disordered potential, the quantum motion of the center of mass of a bright soliton may exhibit Anderson localization, on a localization length which may be much larger than the soliton size and could be observed experimentally.

cond-mat.quant-gas↗

arXiv2008

Quantum phase transition and critical fluctuations of an attractive Bose gas in a double well potential

We consider a Bose gas with an attractive interaction in a symmetric double well potential. In the Hartree approximation, the ground state solution spontaneously breaks the symmetry of the trapping potential above certain value of the interaction strength. We demonstrate how the Landau-Ginzburg scheme of the second order phase transition emerges from the quantum model and show its link to the spontaneous symmetry breaking mentioned above. We identify the order parameter, the critical point and analyze quantum fluctuations around it.

cond-mat.other↗

arXiv2008

Second order quantum phase transition of a homogeneous Bose gas with attractive interactions

We consider a homogeneous Bose gas of particles with an attractive interaction. Mean field theory predicts for this system a spontaneous symmetry breaking at a certain value of the interaction strength. We show that at this point a second-order quantum phase transition occurs. We investigate the system in the vicinity of the critical point using Bogoliubov theory and a continuous description, that allows us to analyze {\it quantum fluctuations} in the system even when the Bogoliubov approach breaks down.

cond-mat.other↗

arXiv2008

Solitons in coupled atomic-molecular Bose-Einstein condensates in a trap

We consider coupled atomic-molecular Bose-Einstein condensate system in a quasi-one-dimensional trap. In the vicinity of a Feshbach resonance the system can reveal soliton-like behavior. We analyze bright soliton solutions for the system in the trap and in the presence of the interactions between particles. We show that with increasing number of particles in the system two bright soliton solutions start resembling dark soliton profiles known in an atomic Bose-Einstein condensate with repulsive interactions between atoms. We analyze also methods for experimental preparation and detection of the soliton states.

cond-mat.other↗

arXiv2006

Analysis of Localization Phenomena in Weakly Interacting Disordered Lattice Gases

Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases may be used for the production and observation of disordered quantum degenerate gases. A detailed analysis of localization effects for two possible realizations of a disordered potential is presented. In a theoretical analysis clear localization effects are observed when a superlattice is used to provide a quasiperiodic disorder. The effects of localization are analyzed by investigating the superfluid fraction and the localization length within the system. The theoretical analysis in this paper paves a clear path for the future observation of Anderson-like localization in disordered quantum gases.

cond-mat.dis-nn↗

arXiv2005

Routes towards Anderson-Like localization of Bose-Einstein condensates in disordered optical lattices

We investigate, both experimentally and theoretically, possible routes towards Anderson-like localization of Bose-Einstein condensates in disordered potentials. The dependence of this quantum interference effect on the nonlinear interactions and the shape of the disorder potential is investigated. Experiments with an optical lattice and a superimposed disordered potential reveal the lack of Anderson localization. A theoretical analysis shows that this absence is due to the large length scale of the disorder potential as well as its screening by the nonlinear interactions. Further analysis shows that incommensurable superlattices should allow for the observation of the cross-over from the nonlinear screening regime to the Anderson localized case within realistic experimental parameters.

cond-mat.dis-nn↗