Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps

TL;DR

This paper investigates the free expansion dynamics of a one-dimensional Bose gas released from various power-law traps, revealing how initial conditions and trap anharmonicity influence the asymptotic density profiles and momentum distributions.

Contribution

It provides a comprehensive analysis connecting initial Bethe rapidities to long-time profiles, extending known self-similar solutions to more general traps and interaction regimes.

Findings

Long-time density profiles depend on initial Bethe rapidities.

Expansion from harmonic traps recovers self-similar solutions.

Non-harmonic traps show non-self-similar expansion and strong anharmonic effects.

Abstract

We analyze free expansion of a trapped one-dimensional Bose gas after a sudden release from the confining trap potential. By using the stationary phase and local density approximations, we show that the long-time asymptotic density profile and the momentum distribution of the gas are determined by the initial distribution of Bethe rapidities (quasimomenta) and hence can be obtained from the solutions to the Lieb-Liniger equations in the thermodynamic limit. For expansion from a harmonic trap, and in the limits of very weak and very strong interactions, we recover the self-similar scaling solutions known from the hydrodynamic approach. For all other power-law traps and arbitrary interaction strengths, the expansion is not self-similar and shows strong dependence of the density profile evolution on the trap anharmonicity. We also characterize dynamical fermionization of the expanding cloud in terms of correlation functions describing phase and density fluctuations.