Entanglement Rate for Gaussian Continuous Variable Beams

TL;DR

This paper derives a comprehensive formula for quantifying entanglement production rates in Gaussian continuous variable systems, applicable to sources with arbitrary spectra, and demonstrates its application in a resonant four-mode optomechanical setup.

Contribution

It introduces a general expression for entanglement rate in Gaussian beams with arbitrary spectra, useful for complex quantum optical systems.

Findings

Derived a universal entanglement rate formula for Gaussian beams.

Applied the formula to a resonant four-mode optomechanical system.

Showed the setup enables efficient entanglement generation through simultaneous processes.

Abstract

We derive a general expression that quantifies the total entanglement production rate in continuous variable systems, where a source emits two entangled Gaussian beams with arbitrary correlators.This expression is especially useful for situations where the source emits an arbitrary frequency spectrum,e.g. when cavities are involved. To exemplify its meaning and potential, we apply it to a four-mode optomechanical setup that enables the simultaneous up- and down-conversion of photons from a drive laser into entangled photon pairs. This setup is efficient in that both the drive and the optomechanical up- and down-conversion can be fully resonant.