  Periodically-driven quantum systems can exhibit a plethora of intriguing
non-equilibrium phenomena that can be analyzed using Floquet theory. Naturally,
Floquet theory is employed to describe the dynamics of atoms interacting with
intense laser fields. However, this semiclassical analysis can not account for
quantum-optical phenomena that rely on the quantized nature of light. In this
paper, we take a significant step to go beyond the semiclassical description of
atom-photon coupled systems by unifying Floquet theory with quantum optics
using the framework of full-counting statistics. This is achieved by
introducing counting fields that keep track of the photonic dynamics. This
formalism, which we dub ``photon-resolved Floquet theory" (PRFT), is based on
two-point tomographic measurements, instead of the two-point projective
measurements used in standard full-counting statistics. Strikingly, the PRFT
predicts the generation of macroscopic light-matter entanglement when atoms
interact with multimode electromagnetic fields, thereby leading to complete
decoherence of the atomic subsystem in the basis of the Floquet states. This
decoherence occurs rapidly in the optical frequency regime, but is negligible
in the radio frequency regime. Our results thus pave the way for the design of
efficient quantum memories and quantum operations. Finally, employing the PRFT,
we propose a quantum communication protocol that can significantly outperform
the state-of-art few-photon protocols by two orders of magnitude or better. The
PRFT potentially leads to insights in various Floquet settings including
spectroscopy, thermodynamics, quantum metrology, and quantum simulations.
