Plasma effects on lifetimes and screening of Rydberg excitons

We simulate the effects of a neutral electron--hole plasma on Rydberg excitons in cuprous oxide (Cu$_2$O), focusing on the validity of Debye screening and the role of plasma-induced thermalization. Unlike atomic Rydberg states, excitons in Cu$_2$O consist of quasiparticles with comparable effective masses whose orbital frequencies can exceed the plasma frequency, invalidating the assumption of a stationary screened charge. Using two complementary approaches, a classical orbit model and a harmonic-oscillator representation evolved via the truncated Wigner approximation, we study exciton lifetimes and interaction screening under realistic plasma conditions. We find numerically that plasma-induced scattering induces finite exciton lifetimes with specific scaling relations with plasma density, principal quantum number $n$ and temperature, possibly providing an explanation for experimentally observed deviations from the $n^3$ scaling at high principal quantum numbers. By explicitly computing time-averaged electric fields, we show that Debye screening overestimates the screening of the exciton's internal field, especially for high angular momentum states. Furthermore, we demonstrate that exciton-exciton interactions are not Debye screened at separations comparable to the Debye length for Rydberg excitons that are well resolvable in absorption measurements.