Effective Hamiltonian for Stokes--anti-Stokes pair generation with pump and probe polarized modes

TL;DR

This paper develops a Hamiltonian model for Stokes--anti-Stokes pair generation in Raman scattering using pump-probe laser pulses, accounting for real and virtual processes, vibrational decay, and comparing with experimental data.

Contribution

It introduces a comprehensive Hamiltonian framework for SAS pair production, including decay effects and dynamics, bridging theory with recent experiments.

Findings

The model accurately predicts SAS pair production probabilities.

Inclusion of vibrational decay improves agreement with experiments.

Both real and virtual processes are effectively described by the Hamiltonian.

Abstract

In the correlated Stokes--anti-Stokes scattering (SAS) an incident photon interacts with a Raman-active material, creating a Stokes photon and exciting a quantum vibrational mode in the medium, which is posteriorly annihilated on contact with a second incident photon, producing in turn an anti-Stokes photon. This can be accomplished by real and virtual processes. In real process the quantum mode shared between the Stokes and anti-Stokes events is a real particle, whereas in virtual processes the pair formation is mediated by the exchange of virtual particles. Here, we introduce a Hamiltonian to describe the pair production in SAS scattering, for both types of process, when stimulated by two orthogonally polarized laser pulses in a pump-and-probe configuration. We also model the effect of the natural decay of the vibration created in the Stokes event and compute the probability of producing SAS pairs. Additionally, we follow the dynamics of the vibration by considering the Stokes and anti-Stokes fields as external reservoirs, obtaining thus a master equation for the reduced density matrix for the vibrational population. Finally, we compare our theoretical results with recently published experimental data.