Swapping mechanical excitations in multi-mode optomechanics

High displacement sensitivity of an optical cavity combined with effective quantum state transfer open up a possibility to study quantum mechanics on a macroscopic level. We study the interaction of the mechanical motion of a thin dielectric membrane with light in a rigid optical cavity in a "membrane in the middle setup". The membrane is partly reflective which effectively splits the cavity into to two cavities and gives rise to non-zero optomechanical coupling. The cavity is coupled to multiple vibrational modes of the membrane. Using two laser beams we show high efficiency energy transfer between modes of highly disparate frequencies which are otherwise not mechanically coupled. We also study theoretically another possibility which is state transfer between the modes using the stimulated Raman adiabatic passage technique (STIRAP) with the light cavity mode being the "dark" state. The ultimate goal of the state transfer in the quantum regime is to study macroscopic entanglement and decoherence models.