Floquet Theory of lattice electrons coupled to an off-resonant cavity

TL;DR

This paper develops a Floquet theory-based framework to analyze lattice electrons interacting with off-resonant cavities, revealing quantum fluctuation effects, cavity-mediated interactions, and dynamical behaviors in the SSH model under various light-matter coupling regimes.

Contribution

It introduces a novel Floquet high-frequency expansion approach to derive effective Hamiltonians for cavity-coupled electrons, capturing quantum fluctuations, entanglement, and cavity effects beyond mean-field approximations.

Findings

Quantum fluctuations induce long-range hopping and interactions.

Cavity-mediated interactions are crucial at strong coupling.

Dynamical behavior depends on cavity parameters under resonant drive.

Abstract

We use Floquet theory and the High-Frequency expansion to derive an effective Hamiltonian for electrons coupled to an off resonant cavity mode, either in its vacuum or driven by classical light. For vacuum fields, we show that long-range hopping and cavity-mediated interactions arise as a direct consequence of quantum fluctuations. As an application, this method is applied to the Su-Schrieffer-Heeger (SSH) model. At high light-matter coupling, our results reveal significant deviations from mean-field predictions, with our framework capturing light-matter entanglement through the Floquet micromotion. Furthermore, the cavity-mediated interactions appearing at first order are shown to be crucial to the description of the system at sufficiently strong light-matter coupling for a fixed cavity frequency. Finally, a drive resonant with the cavity is added with the SSH chain displaying dynamical behavior dependent on the cavity parameters.