Physical Review A

Anderson localization in an oscillating Rydberg-dressed condensate with random disorder

Russell Ong, Che-Hsiu Hsueh, W. C. Wu

Published Nov 21, 2019• 4 citations

Abstract

We numerically study the Anderson localization in an oscillating one-dimensional Rydberg-dressed Bose-Einstein condensate with weak random disorder in which the range of the interaction, the blockade radius ${R}_{\mathrm{c}}$, is variable. Without disorder, the uniform system can undergo a superfluid-supersolid transition at ${R}_{\text{c}}={l}_{\mathrm{c}}\ensuremath{\simeq}1.7{\ensuremath{\xi}}_{0}$ with ${\ensuremath{\xi}}_{\text{0}}$ the zero-range healing length. When ${\ensuremath{\xi}}_{0}$ exceeds the disorder correlation length ${\ensuremath{\sigma}}_{\mathrm{D}}$, we show that exponential localization occurs in the equilibrium condensate when ${R}_{\mathrm{c}}\ensuremath{\le}{l}_{\mathrm{c}}$, while Gaussian localization occurs when ${R}_{\mathrm{c}}>{l}_{\mathrm{c}}$. The latter suggests that the $k$ wave for a long-ranged interacting system could decay Gaussianly with weak random disorder.

DOI: 10.1103/physreva.100.053619

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Physical Review A

Anderson localization in an oscillating Rydberg-dressed condensate with random disorder

Russell Ong, Che-Hsiu Hsueh, W. C. Wu

Published Nov 21, 2019• 4 citations

Publisher

Abstract

{R}_{\mathrm{c}}

, is variable. Without disorder, the uniform system can undergo a superfluid-supersolid transition at

{R}_{\text{c}}={l}_{\mathrm{c}}\ensuremath{\simeq}1.7{\ensuremath{\xi}}_{0}

with

{\ensuremath{\xi}}_{\text{0}}

the zero-range healing length. When

{\ensuremath{\xi}}_{0}

exceeds the disorder correlation length

{\ensuremath{\sigma}}_{\mathrm{D}}

, we show that exponential localization occurs in the equilibrium condensate when

{R}_{\mathrm{c}}\ensuremath{\le}{l}_{\mathrm{c}}

, while Gaussian localization occurs when

{R}_{\mathrm{c}}>{l}_{\mathrm{c}}

. The latter suggests that the

k

wave for a long-ranged interacting system could decay Gaussianly with weak random disorder.

DOI: 10.1103/physreva.100.053619

Related papers

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arXiv:0707.2918Physical Review LettersNov 2, 2007107 citations

{R}_{\mathrm{c}}

, is variable. Without disorder, the uniform system can undergo a superfluid-supersolid transition at

{R}_{\text{c}}={l}_{\mathrm{c}}\ensuremath{\simeq}1.7{\ensuremath{\xi}}_{0}

with

{\ensuremath{\xi}}_{\text{0}}

the zero-range healing length. When

{\ensuremath{\xi}}_{0}

exceeds the disorder correlation length

{\ensuremath{\sigma}}_{\mathrm{D}}

, we show that exponential localization occurs in the equilibrium condensate when

{R}_{\mathrm{c}}\ensuremath{\le}{l}_{\mathrm{c}}

, while Gaussian localization occurs when

{R}_{\mathrm{c}}>{l}_{\mathrm{c}}

. The latter suggests that the

k

wave for a long-ranged interacting system could decay Gaussianly with weak random disorder.

Previously we numerically showed that thermalization can occur in an oscillating Bose-Einstein condensate (BEC) with a disordered harmonic trap when healing length

ξ

of the condensate is shorter than the correlation length

σ_{D}

of the disorder [see, for example, the experiment reported in Phys. Rev. A \textbf{82}, 033603 (2010)]. In this work, we investigate the weakly interacting or Anderson localization regime

ξ>σ_{D}

and show that the oscillating BEC can also exhibit a relaxation process from nonequilibrium to equilibrium. In such an isolated quantum system, energy and particle number are conserved and the irreversible evolution towards thermodynamic equilibrium is induced by the disorder. The thermodynamic equilibrium is evidenced by the maximized entropy

S\left[n_{k}\right]

in which the waveaction spectrum

n_{k}

follows the Rayleigh-Jeans distribution. Besides, unlike a monotonic irreversible process of thermalization to equilibrium, the Fermi-Pasta-Ulam-Tsingou recurrence arises in this system, manifested by the oscillation of the non-equilibrium entropy.

k

, and we study the localization maximum

{k}_{\mathrm{max}﻿}

. For 1D speckle potentials, we find that ${k}_{\mathrm{max}}\ensuremath{\propto}1/\ensuremath{\xi}$ when $\ensuremath{\xi}\ensuremath{\gg}{\ensuremath{\sigma}}_{R}$ while ${k}_{\mathrm{max}}\ensuremath{\propto}1/{\ensuremath{\sigma}}_{R}$ when $\ensuremath{\xi}\ensuremath{\ll}{\ensuremath{\sigma}}_{R}$, and that the localization is strongest when $\ensuremath{\xi}\ensuremath{\sim}{\ensuremath{\sigma}}_{R}$. Numerical calculations support our analysis, and our estimates indicate that the localization of the Bogolyubov quasiparticles is accessible in experiments with ultracold atoms.