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The quantum confiment of Rydberg excitons (REs) in quantum structures opensthe way towards considering nonlinear interactions in such systems. We presenta theoretical calculation of optical functions in the case of a nonlinearcoupling between REs in a quantum well with an electromagnetic wave. Using theReal Density Matrix Approach (RDMA), the analytical expressions for a linearand nonlinear absorption are derived and numerical calculations for Cu$_2$0quantum wells are performed. The results indicate the conditions in whichquantum well confinement states can be observed in linear and nonlinear opticalspectra. The Kerr nonlinearity and self-phase modulation in such a system arestudied. The effect of Rydberg blockade and the associated optical bleachingare also discussed and confronted with available experimental data.

Nonlinear optical properties and Kerr nonlinearity of Rydberg excitons in Cu$_2$O quantum wells