Quasiperiodic Floquet-Gibbs states in Rydberg atomic systems

TL;DR

This paper demonstrates that periodically driven Rydberg atomic systems naturally evolve into Floquet-Gibbs states under certain conditions, supported by analytical arguments and numerical simulations of multi-atom models.

Contribution

It provides a general theoretical framework showing Floquet-Gibbs states emerge in quasiperiodic Rydberg systems, supported by numerical validation.

Findings

Floquet-Gibbs states arise in Rydberg systems with quasiperiodic Hamiltonians.

Numerical simulations of five-atom models confirm analytical predictions.

Steady states match Redfield equation solutions under high-frequency driving.

Abstract

Open systems that are weakly coupled to a thermal environment and driven by fast, periodically oscillating fields are commonly assumed to approach an equilibrium-like steady state with respect to a truncated Floquet-Magnus Hamiltonian. Using a general argument based on Fermi's golden rule, we show that such Floquet-Gibbs states emerge naturally in periodically modulated Rydberg atomic systems, whose lab-frame Hamiltonian is a quasiperiodic function of time. Our approach applies as long as the inherent Bohr frequencies of the system, the modulation frequency and the frequency of the driving laser, which is necessary to uphold high-lying Rydberg excitations, are well separated. To corroborate our analytical results, we analyze a realistic model of up to five interacting Rydberg atoms with periodically changing detuning. We demonstrate numerically that the second-order Floquet-Gibbs state of this system is essentially indistinguishable from the steady state of the corresponding Redfield equation if the modulation and driving frequencies are sufficiently large.