Abstract

We consider a vector c-number Langevin equation describing a single mode of the radiation field under the influence of a quadratic nonlinear interaction. The nonlinearity of the interaction is found to give rise to a nonzero diffusion matrix which may be nonpositive-definite. Using this diffusion matrix, we derive and solve an equation for the variance matrix of the system. An analysis of the solution then yields information about the production and properties of squeezing. In particular, we find that pulsed pumping of the medium, compared to continuous pumping, can significantly enhance the maximum level of squeezing. Finally, we delineate the role of the nonpositive-definite diffusion matrix through a discussion of the physical source of squeezing.

© 1988 Optical Society of America