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Here we show that quantum states of a mechanical oscillator can be generatedin an optomechanical analogue of the micromaser, in absence of any atom-likesubsystem, thus exhibiting single-atom masing effects in a system composedsolely of oscillator components. In the regime where the single-photon couplingstrength is on the order of the cavity decay rate, a cavity mode with at most asingle-excitation present gives rise to sub-Poissonian oscillator limit-cyclesthat generate quantum features in the steady state just above the renormalizedcavity resonance frequency and mechanical sidebands. The merger of multiplestable limit-cycles markedly reduces these nonclassical signatures. Varying thecavity-resonator coupling strength, corresponding to the micromaser pumpparameter, reveals transitions for the oscillator phonon number that are thehallmark of a micromaser. The connection to the micromaser allows for aphysical understanding of how nonclassical states arise in this system, and howbest to maximize these signatures for experimental observation.

Nonclassical mechanical states in an optomechanical micromaser analogue