Disorder in order: Localization without randomness in a cold atom system

TL;DR

This paper introduces a mapping between a disorder model and the Bose polaron problem, enabling experimental simulation of Anderson localization using cold atom systems, and provides insights into localization physics and benchmarking methods.

Contribution

It presents a novel mapping that connects disorder physics with Bose polaron systems, allowing experimental exploration and theoretical benchmarking of localization phenomena.

Findings

The mapping is valid in any space dimension.

A coherent state Ansatz captures Anderson localization physics.

The model can be extended to many-body localization studies.

Abstract

We present a mapping between the Edwards model of disorder describing the motion of a single particle subject to randomly-positioned static scatterers and the Bose polaron problem of a light quantum impurity interacting with a Bose-Einstein condensate (BEC) of heavy atoms. The mapping offers an experimental setting to investigate the physics of Anderson localization where, by exploiting the quantum nature of the BEC, the time evolution of the quantum impurity emulates the disorder-averaged dynamics of the Edwards model. Valid in any space dimension, the mapping can be extended to include interacting particles, arbitrary disorder or confinement, and can be generalized to study many-body localization. Moreover, the corresponding exactly-solvable disorder model offers means to benchmark variational approaches used to study polaron physics. Here, we illustrate the mapping by focusing on the case of an impurity interacting with a one-dimensional BEC through a contact interaction. While a simple wave function based on the expansion in the number of bath excitations misses the localization physics entirely, a coherent state Ansatz combined with a canonical transformation captures the physics of disorder and Anderson localization.