# Dark solitons revealed in Lieb-Liniger eigenstates

## TL;DR

This paper demonstrates how dark solitons can be derived from the eigenstates of the Lieb-Liniger model of interacting bosons, unifying previous approaches and revealing solitonic structures through measurement-based analysis.

## Contribution

It introduces a simple Ansatz that unifies prior methods and enables the study of large systems, showing solitons emerge from many-body eigenstates via measurements.

## Key findings

- Dark solitons emerge in the mean-field limit from Lieb-Liniger eigenstates.
- The Ansatz allows analysis of systems with hundreds of atoms.
- Post-measurement states are wave packets of yrast states.

## Abstract

We study how dark solitons, i.e. solutions of one-dimensional single-particle nonlinear time-dependent Schr\"odinger equation, emerge from eigenstates of a linear many-body model of contact interacting bosons moving on a ring, the Lieb-Liniger model. This long-standing problem was addressed by various groups, which presented different, seemingly unrelated, procedures to reveal the solitonic waves directly from the many-body model. Here, we propose a unification of these results using a simple Ansatz for the many-body eigenstate of the Lieb-Liniger model, which gives us access to systems of hundreds of atoms. In this approach, mean-field solitons emerge in a single-particle density through repeated measurements of particle positions in the Ansatz state. The post-measurement state turns out to be a wave packet of yrast states of the reduced system.