  Photon-resolved Floquet theory keeps track of the photon exchange of a
quantum system with a coherent driving field. It thus complements the standard
full-counting statistics that counts the number of photons exchanged with
incoherent photon modes giving rise to dissipation. In this paper, we introduce
a unifying framework describing both situations. We develop methods suitable
for an analytical evaluation of low-order cumulants of photonic probability
distributions. Within this framework we analyze the two-mode Jaynes-Cummings
model to demonstrate that the Photon-resolved Floquet theory and the standard
full-counting statistics make consistent statistical predictions.
Interestingly, we find that the photon-flux fluctuations diverge for vanishing
dissipation, which can be related to an entanglement effect between the driven
matter system and the driving field. To substantiate our results, we use our
framework to describe efficient photon up-conversion in an ac-driven lambda
system, that is characterized by a high signal-to-noise ratio. As the framework
is non-perturbative and predicts fluctuations, it paves the way towards
non-perturbative spectroscopy, which will assist to improve metrological
methods.
