Quantum state transfer of superposed multi-photon states via phonon-induced dynamic resonance in an optomechanical system

We propose a method to transfer macroscopically superposed states between two optical cavities mediated by a mechanical oscillator, which works in a nonlinear regime of optomechanical interaction. Our approach relies on the phonon-induced dynamic resonance, where the motion of mechanical oscillator dynamically sets on/off the resonance between two cavities. Our method assumes high amplitude limit of oscillator, weak coupling between optical cavities, and adiabatic approximation. We show that, under these conditions, various multi-photon quantum states, especially, Schr{\"o}dinger cat states, can be transferred with nearly perfect fidelity in a deterministic process. We show that transfer fidelity of 0.99 can be achieved using the experimental parameters in currently available technology.