Exploring the thermodynamic limit of optomechanical systems

Optomechanical systems have allowed exciting explorations combining precise engineering in the optical and mechanical domains. Recently, symmetric membrane-in-the-middle systems have been shown to have stable buckling configurations, where the membrane will spontaneously break the $\mathbb{Z}_2$ symmetry and buckle to a fixed position. We identify a parameter regime in which a natural thermodynamic limit arises for the optical spring. In this regime, we describe the phase diagram for the experimental system, a many-mode membrane with two optical modes. We discuss generalizations to other symmetries.