Quantum to classical relaxation dynamics of the dissipative Rydberg gas

TL;DR

This paper explores how relaxation dynamics in Rydberg gases transition from classical to quantum regimes, revealing transient kinetically constrained behavior in large, two-dimensional systems using phase-space methods.

Contribution

It introduces the use of the truncated Wigner approximation to study large, two-dimensional Rydberg gases and uncovers quantum kinetically constrained dynamics beyond classical models.

Findings

Observed slowdown in magnetisation relaxation in both 1D and 2D.

Identified transient signatures of quantum kinetically constrained dynamics.

Demonstrated the emergence of quantum effects in relaxation timescales.

Abstract

We investigate the relaxation dynamics of a Rydberg gas in regimes where coherent processes and dissipation compete. In the strongly dissipative limit, the dynamics is known to be governed by an effective classical rate equation and to exhibit kinetically constrained, glassy relaxation towards a trivial stationary state. This behaviour originates from the Rydberg blockade, which prevents simultaneous excitations within a characteristic blockade radius. However, the fate of kinetic constraints in the weakly dissipative limit remains unexplored in large systems above one dimension. To access large system sizes and two-dimensional geometries, we employ the truncated Wigner approximation, a phase-space method that captures correlated many-body dynamics beyond classical rate equations. To probe the emergence of kinetic constraints on timescales where coherent and dissipative processes are comparable, we analyse the relaxation dynamics starting from two initial states: a fully polarised state and a N\'eel state, which belongs to a manifold of so-called quantum scars. In both cases, we observe a pronounced slowdown in the relaxation of the magnetisation towards the stationary state and identify transient signatures of quantum kinetically constrained dynamics in one and two dimensions.