Quantum efficiency of a microwave photon detector based on a double quantum dot

Motivated by recent interest in implementing circuit quantum electrodynamics with semiconducting quantum dots, we consider a double quantum dot (DQD) capacitively coupled to a superconducting resonator that is driven by the microwave field of a superconducting transmission line. We analyze the DQD current response using input-output theory and show that the resonator-coupled DQD is a sensitive microwave single photon detector. Using currently available experimental parameters of DQD-resonator coupling and dissipation, including the effects of $1/f$ charge noise and phonon noise, we determine the parameter regime for which incident photons are completely absorbed and near unit $\gtrsim$ 98\% efficiency can be achieved. We show that this regime can be reached by using very high quality resonators with quality factor $Q\simeq 10^5$.