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arXiv:0809.3696 · Physical Review A

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

Stephan Dürr, Juan José García‐Ripoll, Niels Syassen, D. M. Bauer, Matthias Lettner, J. I. Cirac, Gerhard Rempe

Published Feb 10, 2009• 83 citations
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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.

DOI
10.1103/physreva.79.023614

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Abstract The coordinate Bethe ansatz can be extended to a model, the Lieb–Liniger model, of a one-dimensional gas of Bosons interacting with repulsive δ-function potentials. It has attracted attention due to its relevance for experimental developments in the fields of ultracold gases and optical lattices. This chapter provides an exposition of the related classical nonlinear Schrödinger equation, followed by its generalization to the quantum model. It explores a limiting case, the Tonks-Girardeau gas. The δ-function potentials supply a kind of boundary condition on the wave functions allowing us to analyze the eigenfunctions of the Bethe ansatz, which are examined on the infinite line and for periodic boundary conditions. The latter leads to the Bethe ansatz equations. The solution of these equations is achieved in the thermodynamic limit for the ground state and for low-lying excited states.