High resolution nanosecond spectroscopy of even-parity Rydberg excitons in Cu$_{2}$O

We present a study of even parity Rydberg exciton states in cuprous oxide using time-resolved second harmonic generation (SHG). Excitonic states with principal quantum number n = 5 - 12 were excited by nanosecond pulses around 1143 nm. Using time-resolved single-photon counting, the coherently generated second harmonic was isolated both temporally and spectroscopically from inelastic emission due to lower-lying free and bound excitonic states, which included narrow resonances at 1.99 eV associated with an exceptional lifetime of 641 $\pm$ 7 $\mu$s. The near transform-limited excitation bandwidth enabled detailed measurements of the exciton lineshape and position, from which we obtained values for the quantum defects of the S and D excitonic states associated with the appropriate crystal symmetries. Odd parity P and F excitonic states were also observed, in accordance with predicted quadrupole-allowed two-photon excitation processes. We compared our measurements to conventional one-photon spectroscopy in the same sample, and find that the SHG spectrum is cut off at a lower principal quantum number (n = 12 vs n = 15). We attribute this effect to a combination of spatial inhomogeneities and local heating, and discuss the prospects for observing higher principal quantum number even parity states in future experiments.