Fröhlich Condensate of Phonons in Optomechanical Systems

We propose that the optomechanical systems can be potential platforms to implement the Fr\"{o}hlich condensate of phonons. We consider a one-dimensional array of membranes coupled to the cavity field via a quadratic interaction, and the cavity is pumped by an external laser. Analytical and numerical results predict that the high phonon occupancy of the lowest or highest mechanical mode is achievable depending on the detuning of the driving laser, the optomechnical strength, and the temperature. The decoherence of the Fr\"{o}hlich condensate can be largely suppressed by the large number of membranes. Our results shed light on narrow-linewidth phonon laser, energy conversion/transfer, and efficient multimode cooling.