Photon cooling: linear vs nonlinear interactions

Linear optics imposes a relation that is more general than the second law of thermodynamics: For modes undergoing a linear evolution, the full mean occupation number (i.e. photon number for optical modes) does not decrease, provided that the evolution starts from a diagonal state. This relation connects to noise-increasing (or heating), and is akin to the second law, though for the linear evolution it holds for a wider set of initial states. We show that this general trend can be reversed via nonlinear interactions between the modes. They can cool -- i.e. decrease the full mean occupation number and the related noise -- an equilibrium system of modes provided that their frequencies are different. Such an effect cannot exist in energy cooling, where only a part of an equilibrium system is cooled. We describe the cooling set-up via both efficiency and coefficient of performance, and relate the cooling effect to the Manley-Rowe theorem in nonlinear optics.Comment: 5+6 page