Single-photon quadratic optomechanics

TL;DR

This paper provides exact analytical solutions for single-photon interactions in quadratic optomechanics, revealing spectral features, entanglement properties, and conditions for phonon sidebands visibility.

Contribution

It introduces exact solutions for single-photon emission and scattering in quadratic optomechanics, advancing understanding of spectral features and photon-phonon entanglement.

Findings

Spectral features relate to system parameters like coupling strength and decay rate.

Conditions for phonon sidebands visibility are clarified.

Photon-phonon entanglement is characterized using linear entropy.

Abstract

We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon.