Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss

TL;DR

This paper develops an exact framework to compute energy loss due to atomic losses in the integrable one-dimensional Bose gas, revealing how integrability breaking affects experimental systems.

Contribution

It introduces a method for exact calculation of charge and energy loss in the Lieb-Liniger model caused by atomic loss processes.

Findings

Derived explicit formulas for energy loss for K=1,2,3 processes.

Provided a general integral expression for energy loss applicable to arbitrary K.

Enhanced understanding of integrability breaking effects in cold atom experiments.

Abstract

The one dimensional $\delta$-function interacting Bose gas (the Lieb-Liniger model) is an integrable system, which can model experiments with ultra cold atoms in one dimensional traps. Even though the model is integrable, integrability breaking effects are always present in the real world experiments. In this work we consider the integrability breaking due to atomic loss, which is the most relevant effect in the experiments. We set up a framework for the exact computation of the losses of the canonical charges of the model, and compute an exact result for the energy loss due to the local $K$-body processes, valid for arbitrary $K$. Our result takes the form of multiple integrals, which are explicitly factorized in the experimentally relevant cases of $K=1,2,3$.