Anderson localization is a single particle localization phenomena in disordered media that is accompanied by an absence of diffusion. Spin-orbit coupling (SOC) describes an interaction between a particle's spin and its momentum that directly affects its energy dispersion, for example creating dispersion relations with gaps and multiple local minima. We show theoretically that combining one-dimensional spin-orbit coupling with a transverse Zeeman field suppresses the effects of disorder, thereby increasing the localization length and conductivity. This increase results from a suppression of back scattering between states in the gap of the SOC dispersion relation. Here, we focus specifically on the interplay of disorder from an optical speckle potential and SOC generated by two-photon Raman processes in quasi-1D Bose-Einstein condensates. We first describe back-scattering using a Fermi's golden rule approach, and then numerically confirm this picture by solving the time-dependent 1D Gross Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the 10's of millisecond time scale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible back-scattering, while without SOC these same states rapidly localize.
We trap individual 1D Bose gases and obtain the associated equation of state by combining calibrated confining potentials with in-situ density profiles. Our observations agree well with the exact Yang-Yang 1D thermodynamic solutions under the local density approximation. We find that our final 1D system undergoes inefficient evaporative cooling that decreases the absolute temperature, but monotonically reduces a degeneracy parameter.
Investigating out-of-equilibrium dynamics with two-dimensional (2D) systems is of widespread theoretical interest, as these systems are strongly influenced by fluctuations and there exists a superfluid phase transition at a finite temperature. In this work, we realise matter-wave interference for degenerate Bose gases, including the first demonstration of coherent splitting of 2D Bose gases using magnetic trapping potentials. We improve the fringe contrast by imaging only a thin slice of the expanded atom clouds, which will be necessary for subsequent studies on the relaxation of the gas follo…
We review recent work on a kinetic model for very low temperature dilute Bose gases. The brief derivation, expressions for hydrodynamics modes, and the comparison with a experiment on a BEC of $^{87}{\rm Rb}$ atoms are presented.
Quantum simulations based on near-resonance Bose gases are limited by their short lifetimes due to severe atom losses. In addition to this, the recently predicted thermodynamical instability adds another constraint on accessing the resonant Bose gases. In this article, we offer a potential solution by proposing long-lived resonant Bose gases in both two and three dimensions, where the conventional few-body losses are strongly suppressed. We show that the thermodynamical properties as well as the lifetimes of these strongly interacting systems are universal, and independent of short-range physi…
Ultra-cold atomic gases provide new chance to study the universal critical behavior of phase transition. We study theoretically the matter wave interference for ultra-cold Bose gases in the critical regime. We demonstrate that the interference in the momentum distribution can be used to extract the correlation in the Bose gas. A simple relation between the interference visibility and the correlation length is found and used to interpret the pioneering experiment about the critical behavior of dilute Bose gases [Science {\bf 315}, 1556 (2007)]. Our theory paves the way to experimentally study v…
Strongly dipolar Bose gases can form liquid droplets stabilized by quantum fluctuations. In theoretical description of this phenomenon, low energy scattering amplitude is utilized as an effective potential. We show that for magnetic atoms corrections with respect to Born approximation arise, and derive modified pseudopotential using realistic interaction model. We discuss the resulting changes in collective mode frequencies and droplet stability diagram. Our results are relevant for recent experiments with erbium and dysprosium atoms.
We have investigated formation of structures of Rydberg atoms excited from a disordered gas of ultracold atoms, using rate equations for two-photon Rydberg excitation in a single atom without eliminating the intermediate state. We have explored the validity range of these rate equations and defined a simple measure to determine, whether our model is applicable for a given set of laser parameters. We have applied these rate equations in Monte Carlo simulations of ultracold gases, for different laser beam profiles, and compared these simulations to experimental observations and find a general ag…
The strongly interacting Bose gas is one of the most fundamental paradigms of quantum many-body physics and the subject of many experimental and theoretical investigations. We review recent progress on strongly correlated Bose gases, starting with a description of beyond mean-field corrections. We show that the Efimov effect leads to non universal phenomena and to a metastability of the low temperature Bose gas through three-body recombination to deeply bound molecular states. We outline differences and similarities with ultracold Fermi gases, discuss recent experiments on the unitary Bose gas…
We have studied thermodynamic properties of noninteracting gases in periodic lattice potential at arbitrary integer fillings and compared them with that of ideal homogeneous gases. Deriving explicit expressions for thermodynamic quantities and performing exact numerical calculations we have found that the dependence of e.g. entropy and energy on the temperature in the normal phase is rather weak. In the Bose condensed phase their power dependence on the reduced temperature is nearly linear, which is in contrast to that of ideal homogeneous gases. We evaluated the discontinuity in the slope of …
By studying the zero-temperature and nonzero-temperature phase diagrams of the ferromagnetic spin-1 Bose-Hubbard model under an external magnetic field, we find that the competition between ferromagnetism and the quadratic Zeeman energy yields two superfluid phases, which feature discontinuous first-order phase transitions between them for a strongly spinor Bose gas such as ${}^7$Li, contrary to the corresponding continuum system.
We review some recent results on interacting Bose gases in thermal equilibrium. In particular, we study the convergence of the grand-canonical equilibrium states of such gases to their mean-field limits, which are given by the Gibbs measures of classical field theories with quartic Hartree-type self-interaction, and to the Gibbs states of classical gases of point particles. We discuss various open problems and conjectures concerning, e.g., Bose-Einstein condensation, polymers and $\vert \boldsymbolϕ \vert^{4}$-theory.
In an equilibrium three-dimensional (3D) disordered condensate, it's well established that disorder can generate an amount of normal fluid equaling to $\frac{4}{3}$ of the condensate depletion. The concept that the superfluid is more volatile to the existence of disorder than the condensate is crucial to the understanding of Bose glass phase. In this Letter, we show that, by bringing a weakly disordered 3D condensate to nonequilibrium regime via a quantum quench in the interaction, disorder can destroy superfluid significantly more, leading to a steady state in which the normal fluid density f…
We study a one-dimensional disordered Bose fluid using bosonization, the replica method and a nonperturbative functional renormalization-group approach. The Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale, quantum tunneling between these metastable states leads to a rounding of the nonanalyticity in a quantum boundary layer that encodes the existence of rare superfluid regions responsibl…
We calculate the equation of state of Bose-Bose gases in one and three dimensions in the framework of an effective quantum field theory. The beyond-mean-field approximation at zero-temperature and the one-loop finite-temperature results are obtained performing functional integration on a local effective action. The ultraviolet divergent zero-point quantum fluctuations are removed by means of dimensional regularization. We derive the nonlinear Schrödinger equation to describe one- and three-dimensional Bose-Bose mixtures and solve it analytically in the one-dimensional scenario. This equation s…
The idea is advanced that strong perturbations of an initially equilibrium Bose-condensed gas lead to the sequence of nonequilibrium states whose order is inverse to the sequence of states arising in the process of the Bose-gas relaxation from an initial nonequilibrium state. An approach is described for constructing statistical models of nonequilibrium Bose gases. The method is based on the averaging over heterogenous configurations of a nonequilibrium system. A statistical model of grain turbulence is suggested. A simple model is analyzed consisting of a mixture of two phases, one gauge symm…
We clarify some technical issues in the present generalized effective-potential Landau theory (GEPLT) that makes the GEPLT more consistent and complete. Utilizing this clarified GEPLT, we analytically study the quantum phase transitions of ultracold Bose gases in bipartite superlattices at zero termparture. The corresponding quantum phase boundaries are analytically calculated up to the third-order hopping, which are in excellent agreement with the quantum Monte Carlo (QMC) simulations.
We study the signature of scale invariance in the far-from-equilibrium quantum dynamics of two dimensional Bose gases. We show that the density profile displays a scale invariant logarithmic singularity near the center. In addition, the density oscillates due to quantum beats with universal structures. Namely, the frequencies of the beats can be connected with one another by a universal discrete scale transformation induced by the scale invariance. The experimental applicability of these results is then discussed.
The object of study of this thesis are dipolar systems in the quantum degenerate regime. In general, dealing with many-body systems and evaluating their properties requires to deal with the Schrödinger equation. In the present study we employ different Monte Carlo methods, that are stochastic techniques that allow to find numerical solutions to it.
Using a variational method, we derive an exact upper bound for one-magnon excitation energy in ferromagnetic spinor gases, which limits the quantum corrections to the effective mass of a magnon to be positive. We also derive an upper bound for one-magnon excitation energy in lattice systems. The results hold for both Bose and Fermi systems in $d$ dimensions as long as the interaction is local and invariant under spin rotation.
The stability of Bose gases near resonance has been a puzzling problem in recent years. In this Letter, we demonstrate that in addition to generating thermal pressure, thermal atoms enhance the repulsiveness of the scale-dependent interactions between condensed atoms due to renormalization effect and further stabilize the Bose gases. Consequently, we find that, as a precursor of instability, the compressibility develops an anomalous structure as a function of scattering length and is drastically reduced compared with the mean-field value. Furthermore, the density profile of a Bose gas in a har…
We study the phase transition from Mott insulator (MI) to Bose glass (BG) of a disordered Bose-Hubbard model within the framework of Ginzburg-Landau effective action approach. By treating MI as unperturbed ground state and performing a systematic expansion with respect to tunneling matrix element, we extend such a field-theoretic method into the disordered lattice Bose systems. To the lowest order, a second order phase transition is confirmed to happen here and the corresponding phase boundary equation coincides with the previous mean-field approximation result. Keeping all the terms second or…
For ultra-cold atomic gases close to the critical temperature, there is a divergent correlation behavior within the critical regime. This divergent correlation behavior is the cornerstone of the universal behavior within the critical regime, e.g. the universal critical exponent for the same class with very different physical systems. It is still quite challenging to observe this divergent correlation behavior in experiments with ultra-cold atomic gases. Here we consider theoretically the interference effect of the critical atomic Bose gas by a Kapitza-Dirac scattering. We find that the Kapitza…
We present a stochastic matter field equation for an interacting many-body Bose system in equilibrium at ultracold finite temperature. Moreover, the proposed equation can be used for non-equilibrium dynamics on phenomenological grounds. This stochastic differential equation is based on a field phase space representation reflecting the underlying canonical density operator (fixed particle number N). Remarkably, it allows for an efficient numerical implementation. We apply our canonical c-field method to interference experiments with quasi-one dimensional Bose gases. Crucial features of these in…
We study the effect of disorder on the propagation of collective excitations in a disordered Bose superfluid. We incorporate local density depletion induced by strong disorder at the meanfield level, and formulate the transport of the excitations in terms of a screened scattering problem. We show that the competition of disorder, screening, and density depletion induces a strongly non-monotonic energy dependence of the disorder parameter. In three dimensions, it results in a rich localization diagram with four different classes of mobility spectra, characterized by either no or up to three mob…
We present a novel approach to modeling dynamics of trapped, degenerate, weakly interacting Bose gases beyond the mean field limit. We transform a many-body problem to the interaction representation with respect to a suitably chosen part of the Hamiltonian and only then apply a multimode coherent-state ansatz. The obtained equations are almost as simple as the Gross--Pitaevskii equation, but our approach captures essential features of the quantum dynamics such as the collapse of coherence.
We investigate the disorder effect on coherent fraction and the quantum phase transition of ultracold dilute Bose gases trapped in disordered optical lattices. Within the framework of Bogoliubov theory, an analytical expression for the particle density is derived and the dependence of coherent fraction on disorder strength as well as on lattice depth is discussed. In weak disorder regime, we find a decreased sensitivity of coherent fraction to disorder with the increase of on-site interaction strength. For strong disorder, the quantum phase boundary between superfluid phase and Bose glass phas…
