Disordered quantum walk-induced localization of a Bose-Einstein condensate

TL;DR

This paper proposes a method to induce localization of a Bose-Einstein condensate in a one-dimensional lattice using disordered quantum walk evolution with randomized coin operations, demonstrating controlled localization effects.

Contribution

It introduces a disordered quantum walk model for Bose-Einstein condensates, enabling controlled localization through randomized coin parameters in an optical lattice system.

Findings

Disordered quantum coin operations cause localization of the condensate.

Variance analysis shows strong localization compared to uniform coin walks.

The scheme is adaptable to other physical systems for controlled quantum walk experiments.

Abstract

We present an approach to induce localization of a Bose-Einstein condensate in a one-dimensional lattice under the influence of unitary quantum walk evolution using disordered quantum coin operation. We introduce a discrete-time quantum walk model in which the interference effect is modified to diffuse or strongly localize the probability distribution of the particle by assigning a different set of coin parameters picked randomly for each step of the walk, respectively. Spatial localization of the particle/state is explained by comparing the variance of the probability distribution of the quantum walk in position space using disordered coin operation to that of the walk using an identical coin operation for each step. Due to the high degree of control over quantum coin operation and most of the system parameters, ultracold atoms in an optical lattice offer opportunities to implement a disordered quantum walk that is unitary and induces localization. Here we present a scheme to use a Bose-Einstein condensate that can be evolved to the superposition of its internal states in an optical lattice and control the dynamics of atoms to observe localization. This approach can be adopted to any other physical system in which controlled disordered quantum walk can be implemented.