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Chinese Physics Letters

Disorder Induced Dynamic Equilibrium Localization and Random Phase Steps of Bose—Einstein Condensates

Yafan Duan, Zhen Xu, Jun Qian, Jian-Fang Sun, Bo-Nan Jiang, Tao Hong

Published Oct 1, 2011• 1 citation
Publisher

Abstract

We numerically analyze the dynamic behavior of Bose—Einstein condensate (BEC) in a one-dimensional disordered potential before it completely loses spatial quantum coherence. We find that both the disorder statistics and the atom interactions produce remarkable effects on localization. We also find that the single phase of the initial condensate is broken into many small pieces while the system approaches localization, showing a counter-intuitive step-wise phase but not a thoroughly randomized phase. Although the condensates as a whole show less flow and expansion, the currents between adjacent phase steps retain strong time dependence. Thus we show explicitly that the localization of a finite size Bose—Einstein condensate is a dynamic equilibrium state.

DOI
10.1088/0256-307x/28/10/100302

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We numerically analyze the dynamic behavior of Bose—Einstein condensate (BEC) in a one-dimensional disordered potential before it completely loses spatial quantum coherence. We find that both the disorder statistics and the atom interactions produce remarkable effects on localization. We also find that the single phase of the initial condensate is broken into many small pieces while the system approaches localization, showing a counter-intuitive step-wise phase but not a thoroughly randomized phase. Although the condensates as a whole show less flow and expansion, the currents between adjacent phase steps retain strong time dependence. Thus we show explicitly that the localization of a finite size Bose—Einstein condensate is a dynamic equilibrium state.
We theoretically investigate the localization of an expanding Bose–Einstein condensate (BEC) with repulsive atom–atom interactions in a disordered potential. We focus on the regime where the initial inter-atomic interactions dominate over the kinetic energy and the disorder. At equilibrium in a trapping potential and for the considered small disorder, the condensate shows a Thomas–Fermi shape modified by the disorder. When the condensate is released from the trap, a strong suppression of the expansion is obtained in contrast to the situation in a periodic potential with similar characteristics. This effect crucially depends on both the momentum distribution of the expanding BEC and the strength of the disorder. For strong disorder as in the experiments reported by Clément et al 2005 Phys. Rev. Lett. 95 170409 and Fort et al 2005 Phys. Rev. Lett. 95 170410, the suppression of the expansion results from the fragmentation of the core of the condensate and from classical reflections from large modulations of the disordered potential in the tails of the condensate. We identify the corresponding disorder-induced trapping scenario for which large atom–atom interactions and strong reflections from single modulations of the disordered potential play central roles. For weak disorder, the suppression of the expansion signals the onset of Anderson localization, which is due to multiple scattering from the modulations of the disordered potential. We compute analytically the localized density profile of the condensate and show that the localization crucially depends on the correlation function of the disorder. In particular, for speckle potentials the long-range correlations induce an effective mobility edge in 1D finite systems. Numerical calculations performed in the mean-field approximation support our analysis for both strong and weak disorder.
We report on a rapid production of 87 Rb Bose-Einstein condensates(BECs) in a tight confinement hybrid trap based on single-beam optical dipole trap(ODT) and magnetic quadrupole trap(MQT). By the help of preliminary evaporation cooling in MQT, more atoms can be transferred to ODT. Then the BEC phase transition will be achieved by forced evaporation in ODT. This setup has good optical access for loading multiple optical lattices and laser speckle to quantum simulation. In theory, we numerically analyze the dynamic behavior of Bose-Einstein condensates in one-dimensional disordered potential before its completely losing spatial quantum coherence. We find that localization length can be remarkably affected by both the disorder statistics and the atom interaction. We also find that the phase of the condensates is broken into many small pieces while the system approaching localization, showing a counter-intuitive step-wise phase but not a thoroughly randomized phase. Although the condensates as a whole showing less flow and expansion, large currents occur where the phase changes abruptly. Thus we show explicitly that the localization of a finite size BEC is dynamic-equilibrium.
Static and dynamical properties of atomic Bose-Einstein condensate in a random potential. The presence of disorder in systems with long-range coherence leads to fascinating effects such as the localization of waves and the appearance of novels quantum phases. While it is often difficult to isolate the effects of disorder in experiments, atomic Bose-Einstein condensates can be manipulated in a controlled random environment. In this report, several aspects of atomic Bose-Einstein condensates in a random potential induced by laser speckles are discussed. After presenting the realization and the characterization of the speckle potential we first study some properties of the trapped, disordered condensates, in particular the enhancement of large density modulations during time-of-flight. We show that this effect is not related to initial phase fluctuations but originates from small initial density modulations in the trap. Secondly, we report on collective modes of a disordered Bose-Einstein condensate. The absence of frequency shifts and the damping of the dipole mode in the presence of disorder are discussed. Then we present measurements of the velocity of sound in a disordered condensate and we show the absence of shift compared to the non-disordered case. At last, we report on the suppression of the 1D expansion of an interacting matter-wave in the presence of disorder in two different regimes. In a regime of strong disorder a detailed experimental analysis supports the proposed scenario of trapping where reflexions on a single modulation of the random potential and interactions play a crucial role. A different regime of weak disorder is then investigated theoretically and we show that Anderson localization can happen in this case under the conditions we establish. This scheme has been realized recently in experiments, leading to the observation of the Anderson localization of a matter-wave.
We consider the quantum dynamics of interacting bosons in the mean-field regime when they are subjected to a disordered potential, which is either random or quasi-periodic. Starting from a spatially localized Bose-Einstein condensate, we prove that fluctuations around the condensate propagate with a small velocity due to the disorder. This provides an example of a disordered many-body system with provably slow transport behavior in any spatial dimension. The main technical novelty is an interaction picture analysis relative to the Anderson-localized one-body dynamics.
We study the effect of atomic interaction on the localization and the associated dynamics of Bose-Einstein condensates in a one-dimensional quasiperiodic optical lattice and random disordered potentials. When the interactions are absent, the condensates exhibit localization, which weakens as we increase the interaction strength beyond a threshold value for both potential types. We inspect the localized and delocalized states by perturbing the system via quenching the interaction strength instantaneously to zero and studying the dynamics of the condensate, which we further corroborate using the out-of-time-order correlator. The temporal behavior of the time correlator displays regular dynamics for the localized state, while it shows temporal chaos for the delocalized state. We confirm this dynamical behavior by analyzing the power spectral density of the time correlator. We further identify that the condensate admits a quasiperiodic route to chaotic dynamics for both the potentials. Finally, we present the variation of the maximal Lyapunov exponents for different nonlinearity and disorder strengths that have a positive value in the regime where the time-correlator function shows chaotic behavior. Through this, we establish the strong connection between the spatially delocalized state of the condensate and its temporal chaos.
We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose–Einstein condensate, in the framework of a mean-field description, using a highly efficient and fast converging numerical scheme. For repulsive interactions, we consider the Thomas–Fermi and Gaussian limits and for attractive interactions the behaviour of soliton solutions. We find that the average spatial extension of the stationary density profile decreases with an increasing disorder strength both for repulsive and attractive interactions among bosons. In the Thomas–Fermi limit, a strong localization of the bosons is obtained in momentum space around the state k = 0. The time-dependent density differs considerably in the cases we have considered. For attractive and disordered Bose–Einstein condensates, we show evidence of a bright soliton with an overall unchanged shape, but a disorder-dependent width. For weak disorder, the soliton is delocalized and for stronger disorder, it bounces back and forth between high potential barriers.