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We investigate the behavior of a quantum resonator coupled to asuperconducting single-electron transistor tuned to the Josephson quasiparticleresonance and show that the dynamics is similar in many ways to that found in amicromaser. Coupling to the SSET can drive the resonator into non-classicalstates of self-sustained oscillation via either continuous or discontinuoustransitions. Increasing the coupling further leads to a sequence of transitionsand regions of multistability.Comment: 4 pages, 4 figures. Clarifications as suggested by referee, adjusted  for length. References and typos correcte

Quantum Dynamics of a Resonator Driven by a Superconducting Single-Electron Transistor: A Solid-State Analogue of the Micromaser