Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model

Area of Science:

• Quantum physics
• Optomechanics
• Condensed matter theory

Background:

• Optomechanical systems offer a platform for exploring quantum phenomena.
• Understanding quantum phase transitions is crucial for quantum technologies.
• Previous studies have explored quantum phase transitions in various models.

Purpose of the Study:

• To investigate the precursors of quantum phase transition in a finite, undamped two-mode optomechanical model.
• To analyze the behavior of observables in the ground state as indicators of quantum phase transition.
• To characterize the degenerate quantum states formed at the transition.

Main Methods:

• Theoretical study of a two-mode optomechanical model with a high-quality optical cavity and a thin, elastic, dielectric membrane.
• Analysis of the ground state properties by controlling the coupling between the membrane and optical modes.
• Examination of operator mean values and other quantifiers to identify state degeneracy.

Main Results:

• The two lowest energy eigenstates become degenerate upon controlling the coupling strength.
• These degenerate states are identified as Schrödinger's cat states, a coherent superposition of distinct quantum states.
• The delocalization of the coupled photon-membrane system leads to increased fluctuations, as shown by Robertson-Schrödinger uncertainty relations.

Conclusions:

• The study identifies key precursors to quantum phase transitions in the investigated optomechanical model.
• Schrödinger's cat states emerge as a signature of the quantum phase transition.
• The findings contribute to the understanding of quantum correlations and fluctuations in hybrid quantum systems.