Stochastic exciton-scattering theory of optical lineshapes: Renormalized many-body contributions

TL;DR

This paper develops a stochastic exciton-scattering model to analyze optical lineshapes, linking spectral fluctuations to environmental spectral density, with applications to condensed phase systems under pulsed laser excitation.

Contribution

It introduces a stochastic approach incorporating many-body bosonic fluctuations to connect spectral dynamics with environmental properties.

Findings

Spectral fluctuations can be modeled as arising from Brownian environments.

The model recovers Anderson-Kubo-like spectral correlations.

An upper limit for environmental spectral density is derived.

Abstract

Spectral line-shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by broad-band pulsed laser stimulation. In particular, we consider the contribution of pair-fluctuations arising from the full bosonic many-body Hamiltonian within a mean-field approximation, treating the coupling to the system as a stochastic noise term. Using the It{\^o} transformation, we consider two limiting cases for our model which lead to a connection between the observed spectral fluctuations and the spectral density of the environment. In the first case, we consider a Brownian environment and show that this produces spectral dynamics that relax to form dressed excitonic states and recover an Anderson-Kubo-like form for the spectral correlations. In the second case, we assume that the spectrum is Anderson-Kubo like, and invert to determine the corresponding background. Using the Jensen inequality, we obtain an upper limit for the spectral density for the background. The results presented here provide the technical tools for applying the stochastic model to a broad range of problems.