Time delay of mean-field interaction in thermal Rydberg atomic gases

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 a thermal Rydberg gas. Our findings provide compelling evidence for the contribution of ionization processes in the nonequilibrium dynamics of thermal Rydberg gases, a system of growing interest for quantum sensing and quantum information science.