We develop a wideband traveling-wave formalism for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations—spatial Langevin equations—that propagate temporal Fourier components of the field operators through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion (phase mismatching), and pump quantum fluctuations. We analyze the dominant effects of phase mismatching and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier.
© 1987 Optical Society of America
Carlton M. Caves and David D. Crouch, "Quantum wideband traveling-wave analysis of a degenerate parametric amplifier," J. Opt. Soc. Am. B 4, 1535-1545 (1987)