The conditions for the analog of QED photons in semi-classical periodically driven systems

Abstract

The Floquet and quantum electrodynamics (QED) Hamiltonians are widely used in various contexts for light-matter interactions. While they exhibit structural similarity, the QED Hamiltonian has a bounded spectrum while the Floquet Hamiltonian does not. Thus, it remains uncertain if they share the same or similar spectra, even at high energy with a substantial average photon count. Using the Gershgorin circle theorem, we bound analytically the difference between the spectra of the QED and Floquet Hamiltonians. We establish a common spectrum by imposing the constraints of high photon numbers and narrow photon statistics. Following the analytic proof, we numerically demonstrate this bound’s implications on a model Xe atom previously used in high harmonic generation, showing correspondence between Floquet and QED photons.