Thermalization of a strongly interacting 1D Rydberg lattice gas

TL;DR

This paper investigates how a 1D Rydberg lattice gas reaches a steady state through purely coherent evolution, revealing that the steady state resembles a microcanonical ensemble of zero-energy eigenstates.

Contribution

It introduces an equation of motion for the excitation number space in a 1D Rydberg lattice and shows the steady state is highly localized and microcanonical-like.

Findings

The steady state is well approximated by the microcanonical ensemble.

Derived expressions for the mean number of excited Rydberg atoms.

Provided formulas for the Mandel Q-parameter at equilibrium.

Abstract

When Rydberg states are excited in a dense atomic gas the mean number of excited atoms reaches a stationary value after an initial transient period. We shed light on the origin of this steady state that emerges from a purely coherent evolution of a closed system. To this end we consider a one-dimensional ring lattice, and employ the perfect blockade model, i.e. the simultaneous excitation of Rydberg atoms occupying neighboring sites is forbidden. We derive an equation of motion which governs the system's evolution in excitation number space. This equation possesses a steady state which is strongly localized. Our findings show that this state is to a good accuracy given by the density matrix of the microcanonical ensemble where the corresponding microstates are the zero energy eigenstates of the interaction Hamiltonian. We analyze the statistics of the Rydberg atom number count providing expressions for the number of excited Rydberg atoms and the Mandel Q-parameter in equilibrium.