  We present an experiment using a sample of laser-cooled Rb atoms to show that
cross-phase modulation schemes continue to benefit from
electromagnetically-induced transparency (EIT) even as the transparency window
is made narrower than the signal bandwidth (i.e., for signal pulses much
shorter than the response time of the EIT system). Addressing concerns that
narrow EIT windows might not prove useful for such applications, we show that
while the peak phase shift saturates in this regime, it does not drop, and the
time-integrated effect continues to scale inversely with EIT window width. This
integrated phase shift is an important figure of merit for tasks such as the
detection of single-photon-induced cross phase shifts.
