Squeezing Exchange and Entanglement between Resonantly Coupled Modes

We study the problem of squeezing exchange between two modes of the electromagnetic field modeled by quantum oscillators for the most general weak bilinear resonance coupling. Also we introduce a new measure of entanglement based on the cross covariances of the quadrature components of interacting modes. We compare the covariance measure with the measures based on the von Neumann and linear entropies of the subsystems, studying their dependences on time, coupling constants, and the initial state in the cases of parametric amplification and parametric conversion. In particular, we show that coherent states remain disentagled for all times and for any choice of coupling constants in the case of parametric converter (with accuracy up to second-order terms with respect to the strength of coupling). Also, we demonstrate that no bilinear coupling can squeeze the initial coherent state or improve the squeezing of the initial squeezed state in the case of a parametric amplifier. A strong sensitivity of the character of evolution to the choice of the set of coupling constants is discovered in the case of a parametric converter.