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