Quantum Phase Transitions in Optomechanical Systems

TL;DR

This paper explores quantum phase transitions in an optomechanical system, revealing symmetry-breaking ground states, Goldstone modes, and the influence of squeezed fields and atom coupling on phase behavior.

Contribution

It provides an exact solution for the ground state in the large frequency ratio limit and uncovers novel phase transition phenomena involving symmetry breaking and hybrid critical points.

Findings

Ground state exhibits symmetry-breaking and quantum phase transitions.

Squeezed fields can modify phase regions and reduce coupling requirements.

Hybrid atom-cavity systems can undergo cooperative quantum phase transitions.

Abstract

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 $\eta$ 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 $Z_2$ symmetry, we discover the mutually (in the finite $\eta$) or unidirectionally (in $\eta \rightarrow \infty$) 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 $Z_2$-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.