# Quantum dark solitons in Bose gas confined in a hard wall box

## TL;DR

This paper investigates quantum dark solitons in a one-dimensional Bose gas confined within a hard wall box, analyzing eigenstates, their relation to mean-field solitons, and the quantum nature of these excitations across interaction regimes.

## Contribution

It extends the understanding of quantum dark solitons by analyzing Gaudin's eigenstates in a hard wall potential and exploring their properties in weak and strong interaction limits.

## Key findings

- Dark solitons are present in the weak interaction regime.
- Quantum nature of solitons becomes prominent under strong interactions.
- Eigenstates are parametrized by their relation to single and multiple dark solitons.

## Abstract

Schr\"odinger equation for Bose gas with repulsive contact interactions in one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that in such a system there exist many-body eigenstates directly corresponding to dark soliton solutions of the mean-field equation. The system is still integrable if one switches from the periodic boundary conditions to an infinite square well potential. The corresponding eigenstates were constructed by M. Gaudin. We analyze weak interaction limit of Gaudin's solutions and identify parametrization of eigenstates strictly connected with single and multiple dark solitons. Numerical simulations of detection of particle's positions reveal dark solitons in the weak interaction regime and their quantum nature in the presence of strong interactions.