Single photon cross-phase shifts can be enhanced by localizing the photon in both frequency and time

Optical nonlinearities are strongest close to resonance of a nonlinear medium, meaning that the largest single-photon cross-phase shifts have all been observed for narrow-band photons tuned close to a resonance. However, a χ⁽³⁾ nonlinearity which generates cross-phase modulation yields an effect proportional to intensity, which for a single photon is maximized if the photon pulse is made as short as possible. There is a natural tradeoff due to the complementarity between the time and frequency content of a pulse, leading to a maximal peak phase shift when the pulse has a bandwidth on the order of the resonance linewidth. In this work, using ⁸⁵Rb cold atoms as the nonlinear medium, we measure the cross-phase shift created by a photon from a resonant narrowband source when that photon is later localized in time via fast detection. We find it exceeds the cross-phase shift predicted for a wave packet which is either short in time or narrowband, seeming to benefit simultaneously from time- and frequency-localization.