A Floquet analysis perspective of driven light-matter interaction models
arXiv:2403.17866 · doi:10.1364/JOSAB.524005
Abstract
In this paper, we analyze the harmonically driven Jaynes-Cummings and Lipkin-Meshkov-Glick models using both numerical integration of time-dependent Hamiltonians and Floquet theory. For a separation of time-scales between the drive and intrinsic Rabi oscillations in the former model, the driving results in an effective periodic reversal of time. The corresponding Floquet Hamiltonian is a Wannier-Stark model, which can be analytically solved. Despite the chaotic nature of the driven Lipkin-Meshkov-Glick model, moderate system sizes can display qualitatively different behaviors under varying system parameters. Ergodicity arises in systems that are neither adiabatic nor diabatic, owing to repeated multi-level Landau-Zener transitions. Chaotic behavior, observed in slow driving, manifests as random jumps in the magnetization, suggesting potential utility as a random number generator. Furthermore, we discuss both models in terms of what we call Floquet Fock state lattices.
arXiv comment12 pages, 8 figures. Submitted to JOSA B feature issue "The Jaynes-Cummings Model: 60 Years and Still Counting"
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