Fröhlich condensate of phonons in optomechanical systems

We propose that the Fr\"ohlich condensate of phonons can be realized in optomechanical systems. The system consists of 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 demonstrate that the high phonon occupancy of the lowest or highest mechanical mode is achievable depending on the detuning of the driving laser, the optomechanical strength, and the temperature. The feasibility of experimental implementation is discussed. Our results shed light on energy conversion and transfer, heat control, and multimode cooling using optomechanical systems.