  We experimentally investigate the nonlinear transmission spectrum of coherent
light fields propagating through a Rydberg EIT medium with strong atomic
interactions. In contrast to previous investigations, which have largely
focused on resonant control fields, we explore here the full two-dimensional
spectral response of the Rydberg gas. Our measurements confirm previously
observed spectral features for a vanishing control-field detuning, but also
reveal significant differences on two-photon resonance. In particular, we find
qualitative deficiencies of mean-field models and rate-equation simulations as
well as a third-order nonlinear susceptibility that accounts for pair-wise
interaction effects at low probe-field intensities in describing the nonlinear
probe-field response under EIT conditions. Our results suggest that a more
complete understanding of Rydberg-EIT and emerging photon interactions requires
to go beyond existing simplified models as well as few-photon theories.
