  We propose a simple model for the nondegenerate parametric inter- action that
takes into account the finite spectral bandwidth of the pump wave. The
Heisenberg equations of motion are solved exactly and we show that the bosonic
operators obey to a generalized Bogoliubov transforma- tion, where the degree
of squeezing depends on the spectral bandwidth. The average number of photons
produced in the interaction, the degree of squeezing as well as the degree of
entanglement are computed showing that they decrease with increasing spectral
bandwidth.

Quantum Physics