Quantum dynamics of a resonator driven by a superconducting single-electron transistor: A solid-state analogue of the micromaser

We investigate the behavior of a quantum resonator coupled to a superconducting single-electron transistor (SSET) tuned to the Josephson quasiparticle resonance and show that the dynamics is similar in many ways to that found in a micromaser. Coupling to the SSET can drive the resonator into nonclassical states of self-sustained oscillation via either continuous or discontinuous transitions. Increasing the coupling further leads to a sequence of transitions and regions of multistability.