Quantum Theory of Continuum Optomechanics

We present the basic ingredients of continuum optomechanics, i.e. the suitable extension of cavity-optomechanical concepts to the interaction of photons and phonons in an extended waveguide. We introduce a real-space picture and argue which coupling terms may arise in leading order in the spatial derivatives. This picture allows us to discuss quantum noise, dissipation, and the correct boundary conditions at the waveguide entrance. The connections both to optomechanical arrays as well as to the theory of Brillouin scattering in waveguides are highlighted. We identify the 'strong coupling regime' of continuum optomechanics that may be accessible in future experiments.