  Over the past years, there have been many efforts towards generating
interactions between two optical beams so strong that they could be observed at
the level of individual photons. Such strong interactions, beyond opening up a
new regime in optics, could lead to technologies such as all-optical quantum
information processing. However, the extreme weakness of photon-photon
scattering has hindered any attempt to observe such interactions at the level
of single particles. Here we implement a strong optical nonlinearity using
electromagnetically-induced transparency and slow light, and directly measure
the resulting nonlinear phase shift for individual photons. This is done by
illuminating the sample with a weak classical pulse with as few as 0.5 photons
per pulse on average, and using post-selection to determine whether a given
pulse contained (approximately) 0 or 1 photons. We present clear data showing
the quantized dependence of a probe beam's measured phase shift on the
post-selection result, for a range of input pulse intensities. We believe that
this represents the first direct measurement of the cross-phase shift due to
single photons.
