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We investigate the optical Kerr nonlinearities of an ensemble of cold Rydbergatoms under the condition of electromagnetically induced transparency (EIT). Byusing an approach beyond mean-field theory, we show that the system possessesnot only enhanced third-order nonlinear optical susceptibility, but also giantfifth-order nonlinear optical susceptibility, which has a cubic dependence onatomic density. Our results demonstrate that both the third-order and thefifth-order nonlinear optical susceptibilities consist of two parts,contributed respectively by photon-atom interaction and Rydberg-Rydberginteraction. The Kerr nonlinearity induced by the Rydberg-Rydberg interactionplays a leading role at high atomic density. We find that the fifth-ordernonlinear optical susceptibility in the Rydberg-EIT system may be five ordersof magnitude larger than that obtained in traditional EIT systems. The resultsobtained may have promising applications in light and quantum informationprocessing and transmission at weak-light level.

Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction