Full counting statistics of the photocurrent through a double quantum dot embedded in a driven microwave resonator

Detection of single, itinerant microwave photons is an important functionality for emerging quantum technology applications as well as of fundamental interest in quantum thermodynamics experiments on heat transport. In a recent experiment [W. Khan et al., Nat. Commun. 12, 5130 (2021)], it was demonstrated that a double quantum dot (DQD) coupled to a microwave resonator can act as an efficient and continuous photodetector by converting an incoming stream of photons to an electrical photocurrent. In the experiment, average photon and electron flows were analyzed. Here we theoretically investigate, in the same system, the fluctuations of the photocurrent through the DQD for a coherent microwave drive of the resonator. We consider both the zero-frequency full counting statistics as well as the finite-frequency noise (FFN) of the photocurrent. Numerical results and analytical expressions in limiting cases are complemented by a mean-field approach neglecting dot-resonator correlations, providing a compelling and physically transparent picture of the photocurrent statistics. We find that for ideal, unity efficiency detection, the fluctuations of the charge current reproduce the Poisson statistics of the incoming photons, while the statistics for nonideal detection is sub-Poissonian. Moreover, the FFN provides information of the system parameter dependence of detector short-time properties. Our results give insight into microwave photon-electron interactions in hybrid dot-resonator systems and provide guidance for further experiments on continuous detection of single microwave photons.