Fully quantum perturbative description of correlated Stokes--anti-Stokes scattering

TL;DR

This paper provides a comprehensive quantum theoretical framework for correlated Stokes--anti-Stokes scattering, revealing its fundamental quantum nature and how it can generate entangled photon pairs for quantum technologies.

Contribution

It introduces a fully quantum perturbative derivation of SaS scattering, connecting quantum and classical descriptions and clarifying the process's role in entangled photon generation.

Findings

Correlated SaS scattering appears at first order in perturbation theory.

The quantum formalism matches classical nonlinear susceptibility in stimulated Raman.

The approach enables a quantum description of entangled photon pair production.

Abstract

The process in which Raman scattering produces correlated Stokes and anti-Stokes radiation is known as Stokes--anti-Stokes (SaS) scattering. It has been shown recently that this process can generate entangled photon pairs, making it a promising tool for quantum optical technologies, but a proper quantum theoretical description was lacking. In this paper, a fully quantum derivation of the electric polarization in a medium with vibrational Raman response, with quantized electromagnetic fields, is developed. Using quantum perturbation theory for Heisenberg operators, we find the solution for the material electric polarization and show that a four-wave mixing-like correlated SaS scattering appears in the first order of perturbation and completely characterizes the non-resonant SaS photon pair production. We also discuss how to construct the third-order non-linear optical susceptibility for the SaS scattering from the quantum formalism, and show that it coincides with the one derived for classical fields in stimulated Raman.