Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: Generation of quadrature- and polarization-squeezed light

A quantum theory is derived for the propagation of two electromagnetic waves in an anisotropic medium with a cubic nonlinearity. In general, the dynamics are described by a Hamiltonian that corresponds to an anisotropic two-dimensional anharmonic oscillator. The degree of suppression of quantum fluctuations in the quadrature component of one wave decreases when another wave is present. When the nonlinear phase corrections associated with self-interaction of the waves are different, it is possible to create a polarization state of the optical field that is nonclassical, with quantum fluctuations in one of the Stokes parameters smaller than in the coherent state.