Dynamics of coupled multimode and hybrid optomechanical systems

Recent experimental developments have brought into focus optomechanical systems containing multiple optical and mechanical modes interacting with each other. Examples include a setup with a movable membrane between two end-mirrors and "optomechanical crystal" devices that support localized optical and mechanical modes in a photonic crystal type structure. We discuss how mechanical driving of such structures results in coherent photon transfer between optical modes, and how the physics of Landau-Zener-Stueckelberg oscillations arises in this context. Another area where multiple modes are involved are hybrid systems. There, we review the recent proposal of a single atom whose mechanical motion is coupled to a membrane via the light field. This is a special case of the general principle of cavity-mediated mechanical coupling. Such a setup would allow the well-developed tools of atomic physics to be employed to access the quantum state of the 'macroscopic' mechanical mode of the membrane.