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Electrical quantum conductors coupled to microwave resonators have in thelast decade emerged as a versatile testbed for controllable light-matterinteraction on the nanometer scale. Recent experimental progress with highimpedance resonators has resulted in conductor-resonator systems with a large,dimensionless coupling parameter $\lambda \gtrsim 0.1$, well beyond the smallcoupling regime $\lambda \ll 1$. Motivated by this progress, we here analysetheoretically the joint statistics of transported electrons and emitted photonsin a single level quantum dot coupled to a microwave resonator, for arbitrarilylarge $\lambda$. Describing the electron-photon dynamics via a number-resolvedmaster equation, we evaluate the joint long-time probability distribution aswell as joint short-time, $g^{(2)}(t)$, correlation functions. Considering thehigh-bias regime, with sequential electron tunneling and working in the dampingbasis, allows us to obtain analytical results for both transport cumulants and$g^{(2)}(t)$ functions. It is found that the photons emitted out of theresonator are bunched and display a super-Poissonian statistics, for all systemparameters. However, the electron transport properties are found to beunaffected by the coupling to the resonator, anti-bunched and withsub-Poissonian statistics. From the joint distribution we identify regimes ofelectron tunneling induced photon cascades and very large $g^{(2)}(t)$functions. All $g^{(2)}(t)$-functions are found to be independent of $\lambda$.We also identify conditions for and transport signatures of a thermal resonatorphoton state.

Charge-photon transport statistics and short-time correlations in a single quantum dot-resonator system with arbitrarily large coupling parameter