Optomechanics assisted by a qubit: From dissipative state preparation to many-partite systems

We propose and analyze nonlinear optomechanical protocols that can be implemented by adding a single atom to an optomechanical cavity. In particular, we show how to engineer the environment in order to dissipatively prepare the mechanical oscillator in a superposition of Fock states with fidelity close to 1. Furthermore, we demonstrate that a single atom in a cavity with several mechanical oscillators can be exploited to realize nonlinear many-partite systems by stroboscopically driving the mechanical oscillators. This can be used to prepare nonlinear many-partite states by applying either coherent protocols or engineering dissipation. The analysis of the protocols is carried out using a perturbation theory for degenerate Liouvillians and numerical tools. Our results apply to other systems where a qubit is coupled to a mechanical oscillator via a bosonic mode, e.g., in cavity quantum electromechanics.