Correlated two-photon scattering in cavity optomechanics

TL;DR

This paper provides an exact analytical solution for two-photon scattering in cavity optomechanics, revealing photon correlations, blockade effects, and the influence of phonon sidebands, advancing understanding of photon-phonon interactions.

Contribution

It introduces a novel exact analytical approach to two-photon scattering in cavity optomechanics, detailing the physical processes and resonance conditions involved.

Findings

Photon frequency anti-correlation observed in joint spectrum

Photon blockade effect induced by radiation pressure coupling

Explicit expression for optomechanical coupling strength related to sideband peaks

Abstract

We present an exact analytical solution of the two-photon scattering in a cavity optomechanical system. This is achieved by solving the quantum dynamics of the total system, including the optomechanical cavity and the cavity-field environment, with the Laplace transform method. The long-time solution reveals detailed physical processes involved as well as the corresponding resonant photon frequencies. We characterize the photon correlation induced in the scattering process by calculating the two-photon joint spectrum of the long-time state. Clear evidence for photon frequency anti-correlation can be observed in the joint spectrum. In addition, we calculate the equal-time second-order correlation function of the cavity photons. The results show that the radiation pressure coupling can induce photon blockade effect, which is strongly modulated by the phonon sideband resonance. In particular, we obtain an explicit expression of optomechanical coupling strength determining these sideband modulation peaks based on the two-photon resonance condition.