Emission Dynamics of Rydberg Excitons in $\mathbf{\mathrm{Cu_2O}}$: Distinguishing Second Harmonic Generation from Secondary Emission

TL;DR

This study uses time-resolved two-photon excitation to distinguish and analyze second harmonic generation and secondary emission in Rydberg excitons of Cu2O, revealing their different sensitivities and providing a framework for future nonlinear optical research.

Contribution

It introduces a method to separate and characterize SHG and secondary emission in Rydberg excitons, clarifying their distinct signatures and dependencies.

Findings

SHG and secondary emission have different spectral and temporal signatures.

Their sensitivities vary with phonons, defects, and many-body effects.

Provides criteria to identify emission channels across conditions.

Abstract

Rydberg excitons in $\mathrm{Cu_2O}$ simultaneously give rise to two very different optical responses under resonant two-photon excitation: a coherent second-harmonic signal mediated by the excitonic second order susceptibility tensor $\chi^{(2)}$, and a secondary emission originating from the radiative decay of real exciton populations. Distinguishing these two channels is essential for interpreting nonlinear and quantum-optical experiments based on high-$n$ states, yet their temporal, spectral, and power-dependent signatures often overlap. Here we use time-resolved resonant two-photon excitation to cleanly separate SHG and SE and to map how each depends on $n$, temperature, excitation power, and crystal quality. This approach reveals the markedly different sensitivities of the two processes to phonons, defects, and many-body effects, and establishes practical criteria for identifying SE and SHG in a wide range of experimental conditions. Our results provide a unified framework for interpreting emission from Rydberg excitons and offer guidelines for future studies aiming to exploit their nonlinear response and long-range interactions.