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

Rydberg excitons in 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 χ⁽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.