Semiclassical Mode-Coupling Factorizations of Coherent Nonlinear Optical Response

TL;DR

This paper introduces a semiclassical approach to factorize nonlinear optical response functions, incorporating quantum corrections and simplifying classical simulations of complex molecular systems.

Contribution

It develops a systematic method using an $bar$ expansion to factorize multitime response functions into lower-order correlations, bridging quantum and classical descriptions.

Findings

Provides closed-form expressions for linear, second, and third-order responses.

Offers a unified framework to compare classical simulation methods.

Demonstrates quantum corrections improve computational efficiency in MD simulations.

Abstract

The identification of relevant collective coordinates is crucial for the interpretation of coherent nonlinear spectroscopies of complex molecules and liquids. Using an $\hbar$ expansion of Liouville space generating functions, we show how to factorize multitime nonlinear response functions into products of lower-order correlation functions of collective coordinates, and derive closed expressions for linear, second and third order response functions. In addition to providing systematic quantum corrections, $\hbar$ offers a convenient bookkeeping device even for the purely classical response, since including quantum fluctuations allows to circumvent the expensive computation of stability matrices which is a major bottleneck in Molecular Dynamics (MD) simulations. The existing classical simulation strategies, including Mode-Coupling in $\mathbf{k}$ space and in real-space, Langevin equations, and Instantaneous Normal Modes are compared from a unified viewpoint.