Exploring the thermodynamic limit of optomechanical systems

Optomechanical systems enable exploration of novel nonlinear optical elements and even quantum domain experiments. Recently, symmetric membrane-in-the-middle systems have been driven into stable buckled configurations, where the membrane spontaneously breaks the $\mathbb{Z}_2$ symmetry and buckles to a fixed position. We identify a parameter regime in which a natural thermodynamic limit arises for the optical spring even though the system is nominally out of equilibrium. In this regime, we describe the phase diagram for the experimental system, a many-mode membrane with two optical modes. We discuss potential realizations of a $U(1)$ symmetry breaking experiment.