Observation of the nonlinear phase shift due to single post-selected photons

Over the past years, much effort has gone towards generating interactions between two optical beams so strong that they could be observed at the level of individual photons(1-3). Interactions this strong, beyond opening up a new regime in optics', could lead to technologies such as all-optical quantum information processing(5,6). However, the extreme weakness of photon-photon scattering has hindered any attempt to observe such interactions at the level of single particles. Here we present an implementation of a strong optical nonlinearity using electromagnetically induced transparency(7), and a direct measurement of the resulting nonlinear phase shift for single post-selected photons. We show that the observed phase shift depends not only on the incident intensity of the (coherent-state) input signal, but also in a discrete fashion on whether 0 or 1 photons are detected at the output. We believe that this constitutes the first direct measurement of the cross-phase shift due to single photons, whose presence or absence is established based on a discrete detection event. It opens a door to future studies of nonlinear optics in the quantum regime, and potential applications in areas such as quantum information processing.