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We report the experimental observation of a cross-Kerr nonlinearity in afree-space medium based on resonantly-excited, interacting Rydberg atoms andelectromagnetically induced transparency. The nonlinearity is used to implementcross-phase modulation between two optical pulses. The nonlinear phase writtenonto the probe pulse is measured to be as large as $8$ mrad per nW of signalpower, corresponding to a $\chi^{(3)}$ of $10^{-8}\textrm{m}^2/\textrm{V}^2$.Potential applications range from optical quantum information processing toquantum non-demolition measurement of photon number.

Observation of a large, resonant, cross-Kerr nonlinearity in a free-space Rydberg medium