'Mechano-optics': an optomechanical quantum simulator

A widely-known paradigm in optomechanical systems involves coupling the square of the position of a mechanical oscillator to an electromagnetic field. We discuss how, in the so-called resolved sideband regime, this system allows to simulate dynamics similar to ordinary optomechanics, where the position of the oscillator is coupled to the field, but with the roles of the oscillator and the field interchanged. We show that realisation of this system is within reach, and that it opens the door to an otherwise inaccessible parameter regime. (paper)