Quantum Phase Transitions in Optomechanical Systems

In this letter, we investigate the ground state properties of an optomechanical system consisting of a coupled cavity and mechanical modes. An exact solution is given when the ratio η between the cavity and mechanical frequencies tends to infinity. This solution reveals a coherent photon occupation in the ground state by breaking continuous or discrete symmetries, exhibiting an equilibrium quantum phase transition (QPT). In the U(1)-broken phase, an unstable Goldstone mode can be excited. In the model featuring Z₂ symmetry, we discover the mutually (in the finite η) or unidirectionally in $η→ infty$ dependent relation between the squeezed vacuum of the cavity and mechanical modes. In particular, when the cavity is driven by a squeezed field along the required squeezing parameter, it enables modifying the region of Z₂-broken phase and significantly reducing the coupling strength to reach QPTs. Furthermore, by coupling atoms to the cavity mode, the hybrid system can undergo a QPT at a hybrid critical point, which is cooperatively determined by the optomechanical and light-atom systems. These results suggest that this optomechanical system complements other phase transition models for exploring novel critical phenomena.