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 backscattering 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-one-dimensional Bose-Einstein condensates. We first describe backscattering by using a Fermi golden rule approach, and then numerically confirm this picture by solving the time-dependent one-dimensional Gross-Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the tens of millisecond timescale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible backscattering, while without SOC these same states rapidly localize.
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 backscattering 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-one-dimensional Bose-Einstein condensates. We first describe backscattering by using a Fermi golden rule approach, and then numerically confirm this picture by solving the time-dependent one-dimensional Gross-Pitaevskii equation for a weakly interacting Bose-Einstein condensate with SOC and disorder. We find that on the tens of millisecond timescale of typical cold atom experiments moving in harmonic traps, initial states with momentum in the zero-momentum SOC gap evolve with negligible backscattering, while without SOC these same states rapidly localize.
We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation. Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose–Einstein condensate will experience spin relaxation in disorder potential.
Abstract We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is found that the increase of spin–orbit coupling delocalizes the condensate while the increase of detuning favors localization. After achieving the numerical ground state solutions, we examine the quench induced dynamics of the condensate by the complete cessation of the spin–orbit coupling. We show that at parameters where the ground state is not localized, the dynamics of the system is chaotic.
We perform theoretical studies of the interplay between disorder, spin-orbit coupling (SOC), and Rabi fields, and show that both SOC and Rabi fields can be used to dramatically control the degree of Anderson localization of a Bose-Einstein condensate in bichromatic lattices. We obtain ground-state phase diagrams in the SOC and Rabi field plane for different values of disorder strength and use realistic experimental parameters compatible with 39K. We find cases of fixed disorder and SOC (Rabi field), where the Rabi field (SOC) reduces the threshold for localization and controls the localization length. We also show regimes of fixed disorder and Rabi field, where the extent of the ground-state wave function is periodic in the SOC, leading to alternating regions of stronger and weaker localization as SOC changes. Lastly, we describe examples of fixed disorder and SOC, where tuning the Rabi field leads to a strong localization peak.
The coherence of a quantum system is one of the key signatures of many-body physics. While a three-dimensional Bose-Einstein condensate (BEC) exhibits true long-range coherence, a Bose gas confined in a one-dimensional (1D) potential displays quasi-long-range order. Experimentally, these coherence properties are typically probed via the momentum distribution, which corresponds to the Fourier transform of the one-body correlation function. In two-dimensional (2D) systems, for example, momentum distribution enables the observation of the Berezinskii-Kosterlitz-Thouless (BKT) transition from a thermal cloud to a superfluid. With trimodal distribution fitting, an intermediate quasicondensate phase is also revealed. In 1D systems, the momentum distribution of a quenched Tonks-Girardeau (TG) Bose gas can be mapped to that of a non-interacting Fermi gas at a specific evolution time, achieving the rapidity distribution. On the other hand, spin-orbit coupling (SOC) has emerged as one of the central topics in ultracold atomic physics. In additional to creating an artificial electric or magnetic field, researchers also observe negative-mass dynamics in a spin-orbit-coupled BEC by engineering the curvature of the band dispersion. This phenomenon is directly observable in the density distribution of the system. In 1D systems, SOC also introduces rich physical phenomena; while low-energy 1D quantum systems are conventionally described by Tomonaga-Luttinger liquid (TLL) theory, SOC notably alters the energy-momentum dispersion. This modification gives rise to unconventional Luttinger liquids whose properties are governed by the spin-orbit coupling strength.In this work, we first investigate the qualitative properties of a 1D Bose gas and demonstrate the temperature dependence of the momentum distribution, revealing how the thermal fluctuations destroy the quasi-long-range order. In the second part, we probe the effects of 1D SOC on a 1D Bose gas, focusing on how SOC modifies the energy-momentum dispersion and the resulting momentum distribution. We demonstrate that within a specific parameter regime, the momentum distribution and its associated coherence properties undergo distinct qualitative changes. The occupied higher momentum states induce phase fluctuations and destroy the coherence of the system, showing signals of the non-Luttinger liquid physics. We probe the coherence properties of a 1D system along these two parameter axes.
In this paper, we study-induced spin–orbit coupling (SOC) in one-dimensional ultracold quantum gases composed of atoms of different species. One species is subjected to an equal combination of Rashba and Dresselhaus SOC generated by Raman transition. The two species interact with each other through spin-independent and spin-exchange contact interactions. The spin-exchange interaction introduces a locking pattern of the momentum and spin degrees of freedom for the species without direct SOC. For small spin-independent interactions, the two species overlap and the induced SOC is effective. For large spin-independent interactions, however, the two species keep separate from each other and the induced SOC is negligible. We propose to generate inhomogeneous SOC by exploiting density engineering technique applied to the directly spin–orbit coupled Bose–Einstein condensate. When the effective potential is of Gaussian type, the single-particle eigenenergies and eigenstates are calculated by exact diagonalization method. For general cases, mean-field ground states are obtained by numerically searching for the minimum of energy functional. With the density engineering technique, it is possible to produce hybrid structures of plane wave, stripe and/or zero-momentum phases.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.