Plasma-enhanced interaction and optical nonlinearities of Cu$_2$O Rydberg excitons

We theoretically investigate the nonlinear optical transmission through a cuprous oxide crystal for wavelengths that cover the series of highly excited excitons, observed in recent experiments. Since such Rydberg excitons have strong van der Waals interactions, they can dynamically break the conditions for resonant exciton creation and dramatically modify the refractive index of the material in a nonlinear manner. We explore this mechanism theoretically and determine its effects on the optical properties of a semiconductor for the case of degenerate pair-state asymptotes of Rydberg excitons in Cu$_2$O. Upon analyzing the additional effects of a dilute residual electron-hole plasma, we find quantitative agreement with previous transmission measurements, which provides strong indications for the enhancement of Rydberg-induced nonlinearities by surrounding free charges.