Time delay of mean field interaction in thermal Rydberg atomic gas

Mean field theory is commonly employed to study nonequilibrium dynamics in hot Rydberg atomic ensembles, but the fundamental mechanism behind the generation of the mean-field interactions remains poorly understood. In this work, we experimentally observe a time-delay effect in the buildup of mean-field interaction, which reveals the key role of collision ionization. We analyze the relevant collision channels and propose a microscopic mechanism that quantitatively explains the hysteresis window observed in optical bistability. Then, using square-wave modulation spectroscopy (SMS) to monitor the growth of the mean-field interaction, we experimentally demonstrate a delay in its dynamical buildup following the initial Rydberg excitation. Finally, we demonstrate how this delay effect may help understand the recently observed self-sustained oscillations in thermal Rydberg gases. Our findings provide compelling evidence for the contribution of ionization processes in the nonequilibrium dynamics of thermal Rydberg gas, a system of growing interest for quantum sensing and quantum information science.