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

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 $χ^{(2)}$, 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.

Figures (4)

• Figure 1: Time resolved emission: (a) Streak camera image of time (y-axis) and energy (x-axis) resolved signal from $7S$ and adjacent states. The average excitation power is 100 $mW$, centered on 1142.6 nm and inducing a signal around 2.1702 eV. The colored vertical lines indicate the energies of the selected $nS$ states. (b) Time traces of the $nS$ states shown in (a), vertically shifted for clarity. The black dashed line indicates the transition from SHG (yellow) to SE (green).
• Figure 2: Temperature dependence: (a) Time-resolved emission traces recorded at different sample temperatures under resonant excitation centered on the $7S$ state. The average pump power was fixed at 100 $mW$. The black dashed line separates the SHG- (left) and SE- (right) dominated regions. (b) Sample temperature dependence of the time-integrated SE (blue circles) and SHG (orange circles) contributions, numerically separated from the time traces. The red solid curve is a phenomenological Mott--Seitz-type fit to the SE intensity. (c) Mott-Seitz fits for different $nS$ states at an average power of 50 $mW$. They all yield the same effective activation energies.
• Figure 3: Power dependence.(a) Total integrated signal (SE+SHG) of the $4S$ state and (b) separated SHG (orange) and SE (blue) intensities from the $7S$ state as a function of excitation power. Solid lines are quadratic saturation fits. (c) Saturation powers versus the principal quantum number $n$. Orange and blue denote SHG and SE, respectively. The dashed line is a power law fit yielding $P_{\mathrm{sat}}\propto n^{-1.9}$.
• Figure 4: Dependence on sample quality: (a) Raw streak camera images obtained under the same conditions but varying sample quality (b) Typical time traces obtained from the streak images at different sample quality: good (blue), intermediate (orange) and poor (red). (c) Ratio of SE to SHG intensities as a function of the crystal quality for different states. (d-e) Scaling of the SE and the SHG intensity with $n$, for the three crystal quality. The pump power is fixed to 100 $mW$. Solid lines are power-law fits. (f) SHG-SE delay (SE rise time) versus $n$ for the three qualities. The black squares show a half-period for the beating between nS and nD states, versus $n$.