The photon shuttle: Landau-Zener-Stueckelberg dynamics in an optomechanical system

The motion of micro- and nanomechanical resonators can be coupled to electromagnetic fields. Such optomechanical setups allow one to explore the interaction of light and matter in a new regime at the boundary between quantum and classical physics. We propose an approach to investigate non-equilibrium photon dynamics driven by mechanical motion in a recently developed setup with a membrane between two mirrors, where photons can be shuttled between the two halves of the cavity. For modest driving strength we predict the possibility to observe an Autler-Townes splitting indicative of Rabi dynamics. For large drive, we show that this system displays Landau-Zener-Stueckelberg dynamics originally known from atomic two-state systems.