The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas

TL;DR

This paper models how atom losses influence the rapidity distribution in a 1D Bose gas, providing equations, a numerical method, and analytic results for specific interaction regimes, revealing complex loss effects.

Contribution

It introduces a theoretical framework and numerical procedure to analyze the impact of atom losses on the rapidity distribution in the Lieb-Liniger model, including analytic solutions in certain limits.

Findings

Losses alter the rapidity distribution in a non-trivial, non-linear, and non-local manner.

Analytic formulas are derived for the ideal Bose and hard-core regimes.

Loss effects are characterized by a derived evolution equation for the rapidity distribution.

Abstract

We theoretically investigate the effects of atom losses in the one-dimensional (1D) Bose gas with repulsive contact interactions, a famous quantum integrable system also known as the Lieb-Liniger gas. The generic case of K-body losses (K = 1,2,3,...) is considered. We assume that the loss rate is much smaller than the rate of intrinsic relaxation of the system, so that at any time the state of the system is captured by its rapidity distribution (or, equivalently, by a Generalized Gibbs Ensemble). We give the equation governing the time evolution of the rapidity distribution and we propose a general numerical procedure to solve it. In the asymptotic regimes of vanishing repulsion -- where the gas behaves like an ideal Bose gas -- and hard-core repulsion -- where the gas is mapped to a non-interacting Fermi gas -- we derive analytic formulas. In the latter case, our analytic result shows that losses affect the rapidity distribution in a non-trivial way, the time derivative of the rapidity distribution being both non-linear and non-local in rapidity space.