Violation of self-similarity in the expansion of a 1D Bose gas

TL;DR

This paper investigates the expansion dynamics of a 1D Bose gas, revealing that the density profile does not follow self-similar scaling during expansion, contrary to simple theoretical expectations, across various interaction regimes.

Contribution

It introduces a variational method to analyze the non-self-similar expansion of a 1D Bose gas using the Lieb-Liniger model, covering all interaction regimes.

Findings

Density profile does not follow self-similar expansion.

Variational approach matches numerical and experimental results.

Identifies parameter ranges where self-similarity breaks down.

Abstract

The expansion of a 1D Bose gas is investigated employing the Lieb-Liniger equation of state within the local density approximation. We show that during the expansion the density profile of the gas does not follow a self-similar solution, as one would expect from a simple scaling Ansatz. We carry out a variational calculation, which recovers the numerical results for the expansion, the equilibrium properties of the density profile, and the frequency of the lowest compressional mode. The variational approach allows for the analysis of the expansion in all interaction regimes between the mean field and the Tonks-Girardeau limits, and in particular shows the range of parameters for which the expansion violates self-similarity.