Many-body dark solitons in one-dimensional hard-core Bose gases

TL;DR

This paper explores the existence and stability of many-body dark solitons in one-dimensional hard-core Bose gases, revealing that certain solitonic features can be understood within a linear many-body framework, but dynamics differ from mean-field predictions.

Contribution

It provides explicit solutions for many-body dark solitons in the Tonks-Girardeau limit and compares them to Gross-Pitaevskii results, highlighting differences in formation dynamics.

Findings

Stationary, shape-invariant solitonic states are explicitly found.

Features attributed to nonlinearity are recovered in a linear many-body theory.

Gross-Pitaevskii dynamics differ significantly from exact many-body evolution.

Abstract

The existence and stability of solitonic states in one-dimensional repulsive Bose-Einstein condensates is investigated within a fully many-body framework by considering the limit of infinite repulsion (Tonks-Girardeau gas). A class of stationary, shape-invariant states propagating at constant velocity are explicitly found and compared to the known solution of the Gross-Pitaevskii equation. The typical features attributed to nonlinearity are thus recovered in a purely linear theory, provided the full many-particle physics is correctly accounted for. However, the formation dynamics predicted by the Gross-Pitaevskii approximation considerably differs from the exact many-body evolution.