Lieb-Liniger model: cold atoms as quantum simulators

Élliott H. Lieb

W. Zwerger

We provide a brief review of how a gas of bosons in one dimension with zero-range interactions, a model that was solved exactly by Lieb and Liniger in 1963, can be realized experimentally with ultracold atoms. This has allowed a number of their predictions to be tested. Moreover, we mention some of the developments that have emerged from the work by Lieb and Liniger in this context, restricting the discussion to problems in thermal equilibrium.

Hui Zhai

Isabelle Bouchoule, Jérôme Dubail

Abstract We review the recent theoretical and experimental progress regarding the generalized hydrodynamics (GHD) behavior of the one-dimensional (1D) Bose gas with contact repulsive interactions, also known as the Lieb–Liniger gas. In the first section, we review the theory of the Lieb–Liniger gas, introducing the key notions of the rapidities and of the rapidity distribution. The latter characterizes the Lieb–Liniger gas after relaxation and is at the heart of GHD. We also present the asymptotic regimes of the Lieb–Liniger gas with their dedicated approximate descriptions. In the second section we enter the core of the subject and review the theoretical results of GHD in 1D Bose gases. The third and fourth sections are dedicated to experimental results obtained in cold atom experiments: the experimental realization of the Lieb–Liniger model is presented in section 3, with a selection of key results for systems at equilibrium, and section 4 presents the experimental tests of the GHD theory. In section 5 we review the effects of atom losses, which, assuming slow loss processes, can be described within the GHD framework. We conclude with a few open questions.

B. Laburthe-Tolra, Thierry Lahaye, Hélène Perrin

B. Laburthe-Tolra, Thierry Lahaye, Hélène Perrin