The fate of a gray soliton in a quenched Bose-Einstein condensate

TL;DR

This paper studies how a gray soliton in a one-dimensional Bose-Einstein condensate evolves after a sudden change in interaction strength, revealing that the outcome depends on the ratio of initial and final sound speeds, with exact solutions for certain cases.

Contribution

It provides an explicit analysis of soliton dynamics after a quench in a Bose-Einstein condensate using inverse scattering, including detailed parameters for the resulting solitons.

Findings

For integer ratio η, the soliton splits into 2η-1 solitons.

For non-integer η, the soliton decays into multiple solitons and Bogoliubov modes.

The approach can be applied to similar quenches in classical integrable systems.

Abstract

We investigate the destiny of a gray soliton in a repulsive one-dimensional Bose-Einstein condensate undergoing a sudden quench of the non-linearity parameter. The outcome of the quench is found to depend dramatically on the ratio $\eta$ of the final and initial values of the speed of sound. For integer $\eta$ the soliton splits into exactly $2\eta-1$ solitons. For non-integer $\eta$ the soliton decays into multiple solitons and Bogoliubov modes. The case of integer $\eta$ is analyzed in detail. The parameters of solitons in the out-state are found explicitly. Our approach exploits the inverse scattering method and can be easily used for the similar quenches in any classical integrable system.