  We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg
atoms under the condition of electromagnetically induced transparency (EIT). By
using an approach beyond mean-field theory, we show that the system possesses
not only enhanced third-order nonlinear optical susceptibility, but also giant
fifth-order nonlinear optical susceptibility, which has a cubic dependence on
atomic density. Our results demonstrate that both the third-order and the
fifth-order nonlinear optical susceptibilities consist of two parts,
contributed respectively by photon-atom interaction and Rydberg-Rydberg
interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction
plays a leading role at high atomic density. We find that the fifth-order
nonlinear optical susceptibility in the Rydberg-EIT system may be five orders
of magnitude larger than that obtained in traditional EIT systems. The results
obtained may have promising applications in light and quantum information
processing and transmission at weak-light level.
