The steady-state quantum dynamics of a compound sample consisting of a semiconductor double quantum dot (DQD) system, non-linearly coupled with a leaking superconducting transmission line resonator, is theoretically investigated. Particularly, the transition frequency of the DQD is taken equal to the doubled resonator frequency, whereas the inter-dot Coulomb interaction is being considered weak. As a consequence, the steady-state quantum dynamics of this complex non-linear system exhibits sudden changes of its features, occuring at a critical DQD-cavity coupling strength, respectively. We have shown that above the threshold, the electrical current through the double quantum dot follows the mean photon number into the microwave mode inside the resonator. This might not be the case anymore below that critical coupling strength. Furthermore, the photon quantum correlations vary from super-Poissonian to Poissonian photon statistics, i.e. towards single-qubit lasing phenomena at microwave frequencies.
Mihaescu et al. (Tue,) studied this question.