We study a mechanical oscillator coupled to a two-level system driven by a blue-detuned coherent source in the resolved sideband regime. For weak mechanical damping, we find dynamical instabilities leading to limit cycles. They are signaled by strong fluctuations in the number of emitted photons, with a large Fano factor. The phonon-number fluctuations exhibit strikingly similar behavior. When the coupling strength becomes comparable to the mechanical frequency, nonclassical mechanical states appear. We demonstrate that these properties can be detected by measuring the photon-emission spectrum, which enables the reconstruction of the Wigner function. We then discuss the relation with cavity optomechanical systems. Candidates for observing these effects include superconducting qubits, NV centers, and single molecules coupled to oscillators.

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• Hybrid quantum systems
• Optomechanics
• Micromechanical & nanomechanical oscillators
• Perturbative methods
• Quantum master equation
• Two-level models