Quantum statistics and dynamics of nonlinear couplers with nonlinear exchange

In this paper we derive the quantum statistical and dynamical properties of nonlinear optical couplers composed of two nonlinear waveguides operating by the second subharmonic generation, which are coupled linearly through evanescent waves and nonlinearly through nondegenerate optical parametric interaction. Main attention is paid to generation and transmission of nonclassical light, based on a discussion of squeezing phenomenon, normalized second-order correlation function, and quasiprobability distribution functions. Initially coherent, number and thermal states of optical beams are considered. In particular, results are discussed in dependence on the strength of the nonlinear coupling relatively to the linear coupling. We show that if the Fock state $|1>$ enters the first waveguide and the vacuum state $|0>$ enters the second waveguide, the coupler can serve as a generator of squeezed vacuum state governed by the coupler parameters. Further, if thermal fields enter initially the waveguides the coupler plays similar role as a microwave Josephson-junction parametric amplifier to generate squeezed thermal light.