Lieb-Liniger model of a dissipation-induced Tonks-Girardeau gas

TL;DR

This paper demonstrates that strong inelastic interactions in a one-dimensional bosonic system can induce a Tonks-Girardeau gas state, with a derived master equation and analytic pair correlation function, revealing loss suppression at high dissipation.

Contribution

It introduces a dissipative Lieb-Liniger model for inelastic bosonic interactions and analytically characterizes the resulting correlation functions and loss dynamics.

Findings

Strong inelastic interactions induce a Tonks-Girardeau gas.

Dissipation strength diverging suppresses actual loss rate.

Elastic interactions become irrelevant at high dissipation.

Abstract

We show that strong inelastic interactions between bosons in one dimension create a Tonks-Girardeau gas, much as in the case of elastic interactions. We derive a Markovian master equation that describes the loss caused by the inelastic collisions. This yields a loss rate equation and a dissipative Lieb-Liniger model for short times. We obtain an analytic expression for the pair correlation function in the limit of strong dissipation. Numerical calculations show how a diverging dissipation strength leads to a vanishing of the actual loss rate and renders an additional elastic part of the interaction irrelevant.