Theory of Second Order Optical Processes from A Luttinger Liquid

TL;DR

This paper develops a theoretical framework for understanding second order optical emission in a 1D interacting electron system modeled as a Luttinger liquid, distinguishing between hot luminescence and Raman scattering contributions.

Contribution

It introduces a novel theory that separates and analyzes the optical emission components in a Luttinger liquid, revealing a specific peak in Raman scattering and conditions where emission components relate to the structure factor.

Findings

Identifies a peak at  |q| in Raman scattering not from a structure factor.

Total emission generally cannot be separated into HL and RS.

At resonance, RS component relates to the structure factor.

Abstract

We develop a theory for the total optical secondary emission from a 1D interacting electron system modelled as a Tomonaga-Luttinger liquid. We separate the emission into two parts which may originate in {\em hot luminescence} (HL) and {\em Raman Scattering} (RS) respectively when we neglect the {\em interference} effect. We find a peak around $\Delta \omega = v_f |q|$ in the RS part which does not come from a structure factor peak. In general the total emission cannot be separated into HL and RS. However at resonance, and taking into account the $k$ dependence of the optical matrix element, a part of the RS is proportional to the structure factor $S(q_1-q_2, \omega_1-\omega_2)$.