Resonant nonlinear optics in semiconductor quantum wells

a theoretical model of a quantum well layer is described for the purpose of analysing nonlinear optical interactions between an electromagnetic plane wave propagating normal to the plane of the quantum well in the ultrafast temporal regime. The model consists of the wave equation for the electromagnetic vector potential coupled to a finite-dimensional quantum system described by the Liouville equation for the density matrix. A 3-level example which represents vector interactions in an isotropic medium is shown to be completely integrable with rotational symmetry.