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Krzysztof Sacha

Publications and source records attributed to Krzysztof Sacha.

At least 73 records · Page 4Linked to original sources
arXiv2015

Anderson localization and Mott insulator phase in the time domain

Particles in space periodic potentials constitute standard models for investigation of crystalline phenomena in solid state physics. Time periodicity of periodically driven systems is a close analogue of space periodicity of solid state crystals. There is an intriguing question if solid state phenomena can be observed in the time domain. Here we show that wave-packets localized on resonant classical trajectories of periodically driven systems are ideal elements to realize Anderson localization or Mott insulator phase in the time domain. Uniform superpositions of the wave-packets form stationary states of a periodically driven particle. However, an additional perturbation that fluctuates in time results in disorder in time and Anderson localization effects emerge. Switching to many-particle systems we observe that depending on how strong particle interactions are, stationary states can be Bose-Einstein condensates or single Fock states where definite numbers of particles occupy the periodically evolving wave-packets. Our study shows that non-trivial crystal-like phenomena can be observed in the time domain.

cond-mat.quant-gas↗
arXiv2015

Modeling spontaneous breaking of time-translation symmetry

We show that an ultra-cold atomic cloud bouncing on an oscillating mirror can reveal spontaneous breaking of a discrete time translation symmetry. In many-body simulations we illustrate the process of the symmetry breaking that can be induced by atomic losses or by a measurement of particle positions. The results pave the way for understanding and realization of the time crystal idea where crystalline structures form in the time domain due to spontaneous breaking of continuous time translation symmetry.

cond-mat.quant-gas↗
arXiv2015

Artificial magnetic field induced by an evanescent wave

Cold atomic gases are perfect laboratories for realization of quantum simulators. In order to simulate solid state systems in the presence of magnetic fields special effort has to be made because atoms are charge neutral. There are different methods for realization of artificial magnetic fields, that is the creation of specific conditions so that the motion of neutral particles mimics the dynamics of charged particles in an effective magnetic field. Here, we consider adiabatic motion of atoms in the presence of an evanescent wave. Theoretical description of the adiabatic motion involves artificial vector and scalar potentials related to the Berry phases. Due to the large gradient of the evanescent field amplitude, the potentials can be strong enough to induce measurable effects in cold atomic gases. We show that the resulting artificial magnetic field is able to induce vortices in a Bose-Einstein condensate trapped close to a surface of a prism where the evanescent wave is created. We also analyze motion of an atomic cloud released from a magneto-optical trap that falls down on the surface of the prism. The artificial magnetic field is able to reflect falling atoms that can be observed experimentally.

cond-mat.quant-gas↗
arXiv2014

Proper phase imprinting method for a dark soliton excitation in a superfluid Fermi mixture

It is common knowledge that a dark soliton can be excited in an ultra-cold atomic gas by means of the phase imprinting method. We show that, for a superfluid fermionic mixture, the standard phase imprinting procedure applied to both components fails to create a state with symmetry properties identical to those of the dark soliton solution of the Bogoliubov-de Gennes equations. To produce a dark soliton in the BCS regime, a single component of the Fermi mixture should be phase imprinted only.

cond-mat.quant-gas↗
arXiv2014

Simulation of non-Abelian lattice gauge fields with a single component gas

We show that non-Abelian lattice gauge fields can be simulated with a single component ultra-cold atomic gas in an optical lattice potential. An optical lattice can be viewed as a Bravais lattice with a $N$-point basis. An atom located at different points of the basis can be considered as a {\it particle} in different internal states. The appropriate engineering of tunneling amplitudes of atoms in an optical lattice allows one to realize U$(N)$ gauge potentials and control a mass of {\it particles} that experience such non-Abelian gauge fields. We provide and analyze a concrete example of an optical lattice configuration that allows for simulation of a static U(2) gauge model with a constant Wilson loop and an adjustable mass of {\it particles}. In particular, we observe that the non-zero mass creates large conductive gaps in the energy spectrum, which could be important in the experimental detection of the transverse Hall conductivity.

cond-mat.quant-gas↗
arXiv2014

Condensate Phase Microscopy

We show that the phase of a Bose-Einstein condensate wave-function of ultra-cold atoms in an optical lattice potential in two-dimensions can be detected. The time-of-flight images, obtained in a free expansion of initially trapped atoms, are related to the initial distribution of atomic momenta but the information on the phase is lost. However, the initial atomic cloud is bounded and this information, in addition to the time-of-flight images, is sufficient in order to employ the phase retrieval algorithms. We analyze the phase retrieval methods for model wave-functions in a case of a Bose-Einstein condensate in a triangular optical lattice in the presence of artificial gauge fields.

cond-mat.quant-gas↗
arXiv2013

Many-body Matter-wave Dark Soliton

The Gross-Pitaevskii equation - which describes interacting bosons in the mean-field approximation - possesses solitonic solutions in dimension one. For repulsively interacting particles, the stationary soliton is dark, i.e. is represented by a local density minimum. Many-body effects may lead to filling of the dark soliton. Using quasi-exact many-body simulations, we show that, in single realizations, the soliton appears totally dark although the single particle density tends to be uniform.

cond-mat.quant-gas↗
arXiv2013

Matter-Wave Interference versus Spontaneous Pattern Formation in Spinor Bose-Einstein Condensate

We describe effects of matter-wave interference of spinor states in the $^{87}$Rb Bose-Einstein condensate. The components of the F=2 manifold are populated by forced Majorana transitions and then fall freely due to gravity in an applied magnetic field. Weak inhomogeneities of the magnetic field, present in the experiment, impose relative velocities onto different $m_F$ components, which show up as interference patterns upon measurement of atomic density distributions with a Stern-Gerlach imaging method. We show that interference effects may appear in experiments even if gradients of the magnetic field components are eliminated but higher order inhomogeneity is present and the duration of the interaction is long enough. In particular, we show that the resulting matter-wave interference patterns can mimic spontaneous pattern formation in the quantum gas.

cond-mat.quant-gas↗
arXiv2013

Many-body Anderson localization in one dimensional systems

We show, using quasi-exact numerical simulations, that Anderson localization of one-dimensional particles in a disordered potential survives in the presence of attractive interaction between particles. The localization length of the composite particle can be computed analytically for weak disorder and is in good agreement with the quasi-exact numerical observations using Time Evolving Block Decimation. Our approach allows for simulation of the entire experiment including the final measurement of all atom positions.

quant-ph↗
arXiv2013

Simulation of frustrated classical XY models with ultra-cold atoms in 3D triangular optical lattices

Miscellaneous magnetic systems are being recently intensively investigated because of their potential applications in modern technologies. Nonetheless, a many body dynamical description of complex magnetic systems may be cumbersome, especially when the system exhibits a geometrical frustration. This paper deals with simulations of the classical XY model on a three dimensional triangular lattice with anisotropic couplings, including an analysis of the phase diagram and a Bogoliubov description of the dynamical stability of mean-field stationary solutions. We also discuss the possibilities of the realization of Bose-Hubbard models with complex tunneling amplitudes in shaken optical lattices without breaking the generalized time-reversal symmetry and the opposite, i.e. real tunneling amplitudes in systems with the time-reversal symmetry broken.

cond-mat.quant-gas↗
arXiv2012

Breakdown of Anderson localization of interacting quantum bright solitons in a disorder potential

The center of mass of a bright soliton in a Bose-Einstein condensate may reveal Anderson localization in the presence of a weak disorder potential. We analyze the effects of interactions between two bright solitons on the Anderson localization phenomenon. Perturbation calculus shows that even very weak interactions modify localization properties of the system eigenstates. For stronger interactions, i.e. when the solitons are close to each other, the localization is totally broken. It implies that in order to experimentally observe the Anderson localization effects, a single bright soliton has to be prepared and excitation of soliton trains must be avoided.

cond-mat.quant-gas↗
arXiv2012

Frustration and time reversal symmetry breaking for Fermi and Bose-Fermi systems

The modulation of an optical lattice potential that breaks time-reversal symmetry enables the realization of complex tunneling amplitudes in the corresponding tight-binding model. For a superfluid Fermi gas in a triangular lattice potential with complex tunnelings the pairing function acquires a complex phase, so the frustrated magnetism of fermions can be realized.Bose-Fermi mixture of bosonic molecules and unbound fermions in the lattice shows also an interesting behavior. Due to boson-fermion coupling, the fermions become slaved by the bosons and the corresponding pairing function takes the complex phase determined by bosons. In the presence of bosons the Fermi system can reveal both gap and gapless superfluidity.

cond-mat.quant-gas↗
arXiv2012

Dark soliton in a disorder potential

We consider dark soliton in a Bose-Einstein condensate in the presence of a weak disorder potential. Deformation of the soliton shape is analyzed within the Bogoliubov approach and by employing expansion in eigenstates of the Pöschl-Teller Hamiltonian. Comparison of the results with the numerical simulations indicates that the linear response analysis reveals good agreement even if the strength of the disorder is of the order of the chemical potential of the system. In the second part of the paper we concentrate on quantum nature of the dark soliton and demonstrate that the soliton may reveal Anderson localization in the presence of a disorder. The Anderson localized soliton may decay due to quasi-particle excitations induced by the disorder. However, we show that the corresponding lifetime is much longer than condensate lifetime in a typical experiment.

cond-mat.quant-gas↗
arXiv2011

Inert-states of spin-5 and spin-6 Bose-Einstein condensates

In this paper we consider spinor Bose-Einstein condensates with spin f=5 and f=6 in the presence and absence of external magnetic field at the mean field level. We calculate all of so-called inert-states of these systems. Inert-states are very unique class of stationary states because they remain stationary while Hamiltonian parameters change. Their existence comes from Michel's theorem. For illustration of symmetry properties of the inert-states we use method that allows classification of the systems as a polyhedron with 2f vertices proposed by R. Barnett et al., Phys. Rev. Lett. 97, 180412 (2006).

cond-mat.quant-gas↗
arXiv2011

Matter-wave analog of an optical random laser

The accumulation of atoms in the lowest energy level of a trap and the subsequent out-coupling of these atoms is a realization of a matter-wave analog of a conventional optical laser. Optical random lasers require materials that provide optical gain but, contrary to conventional lasers, the modes are determined by multiple scattering and not a cavity. We show that a Bose-Einstein condensate can be loaded in a spatially correlated disorder potential prepared in such a way that the Anderson localization phenomenon operates as a band-pass filter. A multiple scattering process selects atoms with certain momenta and determines laser modes which represents a matter-wave analog of an optical random laser.

cond-mat.quant-gas↗
arXiv2011

Huge quantum particle number fluctuations in a two-component Bose gas in a double-well potential

Two component Bose gas in a double well potential with repulsive interactions may undergo a phase separation transition if the inter-species interactions outweigh the intra-species ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components. That is, probability for observation of any mixture of particles in each potential well becomes uniform.

cond-mat.quant-gas↗
arXiv2010

Self-localization of a small number of Bose particles in a superfluid Fermi system

We consider self-localization of a small number of Bose particles immersed in a large homogeneous superfluid mixture of fermions in three and one dimensional spaces. Bosons distort the density of surrounding fermions and create a potential well where they can form a bound state analogous to a small polaron state. In the three dimensional volume we observe the self-localization for repulsive interactions between bosons and fermions. In the one dimensional case bosons self-localize as well as for attractive interactions forming, together with a pair of fermions at the bottom of the Fermi sea, a vector soliton. We analyze also thermal effects and show that small non-zero temperature affects the pairing function of the Fermi-subsystem and has little influence on the self-localization phenomena.

cond-mat.quant-gas↗