Strong and tunable nonlinear optomechanical coupling in a low-loss system

A major goal in optomechanics is to observe and control quantum behaviour in a system consisting of a mechanical resonator coupled to an optical cavity. Work towards this goal has focused on increasing the strength of the coupling between the mechanical and optical degrees of freedom. However, the form of this coupling is crucial in determining which phenomena can be observed in such a system. Here we demonstrate that avoided crossings in the spectrum of an optical cavity containing a flexible dielectric membrane enable us to realize several different forms of the optomechanical coupling. These include cavity detunings that are (to lowest order) linear, quadratic or quartic in the membrane's displacement, and a cavity finesse that is linear in (or independent of) the membrane's displacement. All these couplings are realized in a single device with extremely low optical loss and can be tuned over a wide range in situ. In particular, we find that the quadratic coupling can be increased three orders of magnitude beyond previous devices. As a result of these advances, the device presented here should be capable of demonstrating the quantization of the membrane's mechanical energy.