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.Comment: 6 pages, 5 figures, version accepted for publication in EP

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.Comment: 6 pages, 3 figures, article + supplement, version accepted for publication in Physical Review Letter

Dynamical quantum phase transitions in discrete time crystals

Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry. Recently, the concept of phase transitions has been extended to non-equilibrium dynamics of time-independent systems induced by a quantum quench, i.e. a sudden change of some parameter of the Hamiltonian. There, the return probability of a system to the ground state reveals singularities in time which are dubbed dynamical quantum phase transitions. We show that the quantum quench in a discrete time crystal leads to dynamical quantum phase transitions where the return probability of a periodically driven system to a Floquet eigenstate before the quench reveals singularities in time. It indicates that dynamical quantum phase transitions are not restricted to time-independent systems and can be also observed in systems that are periodically driven. We discuss how the phenomenon can be observed in ultra-cold atomic gases.Comment: version accepted for publication in Physical Review A (9 pages, 3 figs

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.Comment: 10 pages, 9 figures, accepted for publication in Physical Review

Localization in random fractal lattices

We investigate the issue of eigenfunction localization in random fractal lattices embedded in two dimensional Euclidean space. In the system of our interest, there is no diagonal disorder -- the disorder arises from random connectivity of non-uniformly distributed lattice sites only. By adding or removing links between lattice sites, we change the spectral dimension of a lattice but keep the fractional Hausdorff dimension fixed. From the analysis of energy level statistics obtained via direct diagonalization of finite systems, we observe that eigenfunction localization strongly depends on the spectral dimension. Conversely, we show that localization properties of the system do not change significantly while we alter the Hausdorff dimension. In addition, for low spectral dimensions, we observe superlocalization resonances and a formation of an energy gap around the center of the spectrum.Comment: version accepted for publication in PRB, (7 pages, 8 figures

Unruh effect for interacting particles with ultracold atoms

The Unruh effect is a quantum relativistic effect where the accelerated observer perceives the vacuum as a thermal state. Here we propose the experimental realization of the Unruh effect for interacting ultracold fermions in optical lattices by a sudden quench resulting in vacuum acceleration with varying interactions strengths in the real temperature background. We observe the inversion of statistics for the low lying excitations in the Wightman function as a result of competition between the spacetime and BCS Bogoliubov transformations. This paper opens up new perspectives for simulators of quantum gravity.Comment: close to the published versio

Determination of Chern numbers with a phase retrieval algorithm

Ultracold atoms in optical lattices form a clean quantum simulator platform which can be utilized to examine topological phenomena and test exotic topological materials. Here we propose an experimental scheme to measure the Chern numbers of two-dimensional multiband topological insulators with bosonic atoms. We show how to extract the topological invariants out of a sequence of time-of-flight images by applying a phase retrieval algorithm to matter waves. We illustrate advantages of using bosonic atoms as well as efficiency and robustness of the method with two prominent examples: the Harper-Hofstadter model with an arbitrary commensurate magnetic flux and the Haldane model on a brick-wall lattice.Comment: Version accepted for publication in Phys. Rev. A (11 pages, 8 figures

Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter

In this study, we investigate the behavior of vortex singularities in the phase of the Green's function of a general non-interacting fermionic lattice model in three dimensions after an instantaneous quench. We find that the full set of vortices form one-dimensional dynamical objects, which we call vortex loops. The number of such vortex loops can be interpreted as a quantized order parameter that distinguishes between different non-equilibrium phases. We show that changes in this order parameter are related to dynamical quantum phase transitions (DQPTs). Our results are applicable to general lattice models in three dimensions. For concreteness, we present them in the context of a simple two-band Weyl semimetal. We also show that the vortex loops survive in weakly interacting systems. Finally, we observe that vortex loops can form complex dynamical patterns in momentum space due to the existence of band touching Weyl nodes. Our findings provide valuable insights for developing definitions of dynamical order parameters in non-equilibrium systems.Comment: 9 pages, 4 figure

Role of correlations and off-diagonal terms in binary disordered one dimensional systems

We investigate one dimensional tight binding model in the presence of a correlated binary disorder. The disorder is due to the interaction of particles with heavy immobile other species. Off-diagonal disorder is created by means of a fast periodic modulation of interspecies interaction. The method based on transfer matrix techniques allows us to calculate the energies of extended modes in the correlated binary disorder. We focus on $N$-mer correlations and regain known results for the case of purely diagonal disorder. For off-diagonal disorder we find resonant energies. We discuss ambiguous properties of those states and compare analytical results with numerical calculations. Separately we describe a special case of the dual random dimer model.Comment: 6 pages, 4 figure

Controlling disorder with periodically modulated interactions

We investigate a celebrated problem of one dimensional tight binding model in the presence of disorder leading to Anderson localization from a novel perspective. A binary disorder is assumed to be created by immobile heavy particles for the motion of the lighter, mobile species in the limit of no interaction between mobile particles. Fast periodic modulations of interspecies interactions allow us to produce an effective model with small diagonal and large off-diagonal disorder unexplored in cold atoms experiments. We present an expression for an approximate Anderson localization length and verify the existence of the well known extended resonant mode and analyze the influence of nonzero next-nearest neighbor hopping terms. We point out that periodic modulation of interaction allow disorder to work as a tunable band-pass filter for momenta.Comment: version close to published vesio