Observation of the Nonlinear Phase Shift Due to Single Post-Selected Photons

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.