An optomechanical approach to controlling the temperature and chemical potential for light

Massless bosons, including photons, do not have strict particle conservation and thus have no chemical potential. However, in driven systems, near equilibrium dynamics can lead to equilibration of photons with a finite number, describable using an effective chemical potential. Here we build upon this general concept with an implementation appropriate for a nonlinear photonic or microwave quantum simulator. We consider how laser cooling of a mechanical mode can provide an effective low frequency bath for other photon modes. The parametric optomechanical interaction between the optical system and the low frequency bath is provided through a beam-splitter coupling between the optical system and another laser-driven mode. The use of multiple photon modes enables control of both the chemical potential, by drive frequency, and temperature, by drive amplitude, of the resulting photonic grand canonical ensemble.