Universal non-equilibrium properties of dissipative Rydberg gases

TL;DR

This paper studies the out-of-equilibrium phase transition in dissipative Rydberg gases, identifying its universality class and explaining experimental observations of bistability and relaxation dynamics.

Contribution

It reveals the universality class of the dynamical transition and clarifies the nature of the order parameter in dissipative Rydberg gases.

Findings

The dynamical transition belongs to the 'model A' universality class.

The observed power-law relaxation is due to non-equilibrium dynamics near a spinodal line.

The proper dynamical order parameter is not the excitation density.

Abstract

We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the "model A" universality class, i.e. it features a non-trivial $\mathbb{Z}_2$ symmetry and a dynamics with non-conserved order parameter. This sheds light on some relevant and observable aspects of dynamical transitions in Rydberg gases. In particular, it permits a quantitative understanding of a recent experiment [C. Carr et al., Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behaviour as well as power-law scaling of the relaxation time. The latter emerges not due to critical slowing down in the vicinity of a second order transition, but from the non-equilibrium dynamics near a so-called spinodal line.