# Few-boson localization in a continuum with speckle disorder

## TL;DR

This paper investigates localization phenomena of a few interacting bosons in a continuum with speckle disorder, showing that interactions do not necessarily lead to ergodic behavior and localization persists.

## Contribution

It demonstrates that contact interactions do not induce a transition to Wigner-Dyson statistics, confirming localization in few-body continuum systems with speckle disorder.

## Key findings

- Poisson level-spacing observed in single-particle case
- Interactions do not shift the system towards Wigner-Dyson statistics
- Localization persists in few-body systems despite interactions

## Abstract

The disorder-induced localization of few bosons interacting via a contact potential is investigated through the analysis of the level-spacing statistics familiar from random matrix theory. The model we consider is defined in a continuum and describes one-dimensional bosonic atoms exposed to the spatially correlated disorder due to an optical speckle field. % First, we identify the speckle-field intensity required to observe, in the single-particle case, the Poisson level-spacing statistics, which is characteristic of localized quantum systems, in a computationally and experimentally feasible system size. Then, we analyze the two-body and the three-body systems, exploring a broad interaction range, from the noninteracting limit up to moderately strong interactions. Our main result is that the contact potential does not induce a shift towards the Wigner-Dyson level-spacing statistics, which would indicate the emergence of an ergodic chaotic state, indicating that localization can occur also in interacting few-body systems in a continuum. We also analyze how the ground-state energy evolves as a function of the interaction strength