  We study dispersive optical nonlinearities of short pulses propagating in
high number density, warm atomic vapors where the laser resonantly excites
atoms to Rydberg $P$-states via a single-photon transition. Three different
regimes of the light-atom interaction, dominated by either Doppler broadening,
Rydberg atom interactions, or decay due to thermal collisions between
groundstate and Rydberg atoms, are described. We show that using fast Rabi
flopping and strong Rydberg atom interactions, both in the order of gigahertz,
can overcome the Doppler effect as well as collisional decay, leading to a
sizable dispersive optical nonlinearity on nanosecond timescales. In this
regime, self-induced transparency (SIT) emerges when areas of the nanosecond
pulse are determined primarily by the Rydberg atom interaction, rather than the
area theorem of interaction-free SIT. We identify, both numerically and
analytically, the condition to realize Rydberg-SIT. Our study contributes to
efforts in achieving quantum information processing using glass cell
technologies.
