Nonclassical mechanical states in an optomechanical micromaser analog

Here we show that quantum states of a mechanical oscillator can be generated in an optomechanical analog of the micromaser in the absence of any atomlike subsystem, thus exhibiting single-atom masing effects in a system composed solely of oscillator components. In the regime where the single-photon coupling strength is on the order of the cavity decay rate, a cavity mode with at most a single-excitation present gives rise to sub-Poissonian oscillator limit-cycles that generate quantum features in the steady state just above the renormalized cavity resonance frequency and mechanical sidebands. The merger of multiple stable limit-cycles markedly reduces these nonclassical signatures. Varying the cavity-resonator coupling strength, corresponding to the micromaser pump parameter, reveals transitions for the oscillator phonon number that are the hallmark of a micromaser. The connection to the micromaser allows for a physical understanding of how nonclassical states arise in this system and how best to maximize these signatures for experimental observation.