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

Electrical quantum conductors coupled to microwave resonators have in the last decade emerged as a versatile testbed for controllable light-matter interaction on the nanometer scale. Recent experimental progress with high impedance resonators has resulted in conductor-resonator systems with a large, dimensionless coupling parameter $\lambda \gtrsim 0.1$, well beyond the small coupling regime $\lambda \ll 1$. Motivated by this progress, we here analyse theoretically the joint statistics of transported electrons and emitted photons in a single level quantum dot coupled to a microwave resonator, for arbitrarily large $\lambda$. Describing the electron-photon dynamics via a number-resolved master equation, we evaluate the joint long-time probability distribution as well as joint short-time, $g^{(2)}(t)$, correlation functions. Considering the high-bias regime, with sequential electron tunneling and working in the damping basis, allows us to obtain analytical results for both transport cumulants and $g^{(2)}(t)$ functions. It is found that the photons emitted out of the resonator are bunched and display a super-Poissonian statistics, for all system parameters. However, the electron transport properties are found to be unaffected by the coupling to the resonator, anti-bunched and with sub-Poissonian statistics. From the joint distribution we identify regimes of electron 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 resonator photon state.