Lieb-Liniger model: emergence of dark solitons in the course of measurements of particle positions

TL;DR

This paper demonstrates that in the Lieb-Liniger model, dark solitons naturally emerge during particle position measurements when the system is prepared in a type II excitation eigenstate, across various interaction regimes.

Contribution

It shows, using Bethe ansatz, that dark solitons appear in measurement outcomes of the Lieb-Liniger model, linking the type II spectrum to observable soliton profiles.

Findings

Dark solitons emerge in measurement processes from type II eigenstates.

Dark solitons are observed in both weak and strong interaction regimes.

The study connects the type II spectrum to measurable dark soliton density profiles.

Abstract

Lieb-Liniger model describes bosons with contact interactions in one-dimensional space. In the limit of weak repulsive particle interactions, there are two types of low lying excitation spectrum. The first is reproduced by the Bogoliubov dispersion relation, the other is believed to correspond to dark soliton excitations. While there are various evidences that the type II spectrum is related to dark solitons, it has not been shown that measurements of positions of particles reveal dark soliton density profiles. Here, we employ the Bethe ansatz approach and show that dark solitons emerge in the measurement process if the system is prepared in an eigenstate corresponding to the type II spectrum. We analyze single and double dark solitons as well as weak and strong interaction regime.