Multimode optomechanical dynamics in a cavity with avoided crossings

Cavity optomechanics offers powerful methods for controlling optical fields and mechanical motion. A number of proposals have predicted that this control can be extended considerably in devices where multiple cavity modes couple to each other via the motion of a single mechanical oscillator. Here we study the dynamic properties of such a multimode optomechanical device, in which the coupling between cavity modes results from mechanically induced avoided crossings in the cavity's spectrum. Near the avoided crossings we find that the optical spring shows distinct features that arise from the interaction between cavity modes. Precisely at an avoided crossing, we show that the particular form of the optical spring provides a classical analogue of a quantum non-demolition measurement of the intracavity photon number. The mechanical oscillator's Brownian motion, an important source of noise in these measurements, is minimized by operating the device at cryogenic temperature (500 mK).