Single-atom maser with engineered circuit for population inversion

We present a blueprint for a maser with a single three-level transmon superconducting artificial atom. The system can be pumped coherently via a two-photon process, and to achieve high population inversion, the relaxation rate of the metastable state is increased via an auxiliary low-$Q$ cavity coupled to a transition between the transmon excited states. We show numerically that such a maser can operate both in the intermediate-coupling regime with super-Poissonian photon statistics and in the strong-coupling regime, where the statistics is sub-Poissonian. For the former the maser exhibits thresholdless behavior, and for the latter there is a well-defined pumping threshold. A useful side effect of the auxiliary resonator is that it allows to overcome the photon blockade effect for the pump, which would otherwise prevent a high photon population. Finally, we observe the bistability of the steady-state Wigner function and the self-quenching effect for some parameters.