Expansion of a matter wave packet in a one-dimensional disordered potential in the presence of a uniform bias force

Abstract

We study numerically the expansion dynamics of an initially confined quantum wave packet in the presence of a disordered potential and a uniform bias force. For white-noise disorder, we find that the wave packet develops asymmetric algebraic tails for any ratio of the force to the disorder strength. The exponent of the algebraic tails decays smoothly with that ratio and no evidence of a critical behavior on the wave density profile is found. Algebraic localization features a series of critical values of the force-to-disorder strength where the m-th position moment of the wave packet diverges. Below the critical value for the m-th moment, we find fair agreement between the asymptotic long-time value of the m-th moment and the predictions of diagrammatic calculations. Above it, we find that the m-th moment grows algebraically in time. For correlated disorder, we find evidence of systematic delocalization, irrespective to the model of disorder. More precisely, we find a two-step dynamics, where both the center-of-mass position and the width of the wave packet show transient localization, similar to the white-noise case, at short time and delocalization at sufficiently long time. This correlation-induced delocalization is interpreted as due to the decrease of the effective de Broglie wave length, which lowers the effective strength of the disorder in the presence of finite-range correlations.

References in corpus (9)

• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Anderson localization in Bose-Einstein condensates
• One-dimensional Anderson localization in certain correlated random potentials
• Anderson localization of a Bose-Einstein condensate in a 3D random potential
• Disorder-induced trapping versus Anderson localization in Bose-Einstein condensates expanding in disordered potentials
• Localization of a matter wave packet in a disordered potential
• Lyapunov exponent for the laser speckle potential: a weak disorder expansion
• Tailoring Anderson localization by disorder correlations in 1D speckle potentials

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• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions
• Power-law localization in one-dimensional systems with nonlinear disorder under fixed input conditions