Thermalization in a 1D Rydberg gas: validity of the microcanonical ensemble hypothesis

TL;DR

This paper examines whether the microcanonical ensemble accurately describes thermalization in a 1D Rydberg atom chain, revealing limitations and conditions for its validity through comparison with exact simulations.

Contribution

It critically assesses the microcanonical hypothesis in a specific quantum system, identifying its applicability and limitations.

Findings

Microcanonical assumption can fail to accurately predict excitation distributions.

Exact numerical simulations reveal deviations from thermal predictions.

Conditions for the validity of the microcanonical ensemble are clarified.

Abstract

We question the microcanonical hypothesis, often made to account for the thermalization of complex closed quantum systems, on the specific example of a chain of two-level atoms optically driven by a resonant laser beam and strongly interacting via Rydberg-Rydberg dipole-dipole interactions. Along its (necessarily unitary) evolution, this system is indeed expected to thermalize, i.e. observables, such as the number of excitations, stop oscillating and reach equilibrium-like expectation values. The latter are often calculated through assuming the system can be effectively described by a thermal-like microcanonical state. Here, we compare the distribution of excitations in the chain calculated either according to the microcanonical assumption or through direct exact numerical simulation. This allows us to show the limitations of the thermal equilibrium hypothesis and precise its applicability conditions.