Relaxation towards negative temperatures in bosonic systems: Generalized Gibbs ensembles and beyond integrability

TL;DR

This paper explores how negative temperature states form in bosonic systems, using theoretical models and simulations to show relaxation to generalized Gibbs ensembles and the role of dynamic symmetries.

Contribution

It demonstrates the formation of negative temperature states in bosonic systems through relaxation to generalized Gibbs ensembles and reveals a duality with positive temperatures beyond one dimension.

Findings

Relaxation to negative temperature generalized Gibbs ensembles in 1D Bose-Hubbard model.

Negative temperature states can be understood via a duality with positive temperatures.

Exact diagonalization supports the emergence of negative temperature states at finite interactions.

Abstract

Motivated by the recent experimental observation of negative absolute temperature states in systems of ultracold atomic gases in optical lattices [Braun et al., Science 339, 52 (2013)], we investigate theoretically the formation of these states. More specifically, we consider the relaxation after a sudden inversion of the external parabolic confining potential in the one-dimensional inhomogeneous Bose-Hubbard model. First, we focus on the integrable hard-core boson limit which allows us to treat large systems and arbitrarily long times, providing convincing numerical evidence for relaxation to a generalized Gibbs ensemble at negative temperature T<0, a notion we define in this context. Second, going beyond one dimension, we demonstrate that the emergence of negative temperature states can be understood in a dual way in terms of positive temperatures, which relies on a dynamic symmetry of the Hubbard model. We complement the study by exact diagonalization simulations at finite values of the on-site interaction.