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We study a superconducting single-electron transistor (SSET) which is coupledto a LC-oscillator via the phase difference across one of the Josephsonjunctions. This leads to a strongly anharmonic coupling between the SSET andthe oscillator. The coupling can oscillate with the number of photons whichmakes this system very similar to the single-atom injection maser. However, theadvantage of a design based on superconducting circuits is the strong couplingand existence of standard methods to measure the radiation field in theoscillator. This makes it possible to study many effects that have beenpredicted for the single-atom injection maser in a circuit quantumelectrodynamics setup.

Circuit-QED analogue of a single-atom injection maser: Lasing, trapping states and multistability