Observation of a large, resonant, cross-Kerr nonlinearity in a cold Rydberg gas and progress towards quantum non-demolition measurement of photon number

We report an experimental observation of a dispersive cross-Kerr nonlinearity based on resonant Rydberg EIT. We observe that the phase shift acquired by a resonant optical pulse propagating through a cold cloud of atoms under EIT conditions depends linearly on the intensity of a second optical pulse. Our observations are consistent with a simple theoretical treatment based on van der Waals interactions, which provides an intuitive explanation for the origin and scaling of the cross-Kerr nonlinearity. Finally, we discuss various ways to increase the per-photon phase shifts and decrease measurement uncertainty, both of which will be required in order to realize a quantum non-demolition measurement of photon number.