Pulsed quadrature-phase squeezing of solitary waves inχ(2)parametric waveguides

It is shown that coherent quantum simultons (simultaneous solitary waves at two different frequencies) can undergo quadrature-phase squeezing as they propagate through a dispersive ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ waveguide. This requires a treatment of the coupled quantized fields including a quantized depleted pump field. A technique involving nonlinear stochastic parabolic partial differential equations using a nondiagonal coherent state representation in combination with an exact Wigner representation on a reduced phase space is outlined. We explicitly demonstrate that group-velocity matched ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ waveguides which exhibit collinear propagation can produce quadrature-phase squeezed simultons. Quasi-phase-matched KTP waveguides, even with their large group-velocity mismatch between fundamental and second harmonic at 425 nm, can produce 3 dB squeezed bright pulses at 850 nm in the large phase-mismatch regime. This can be improved to more than 6 dB by using group-velocity matched waveguides.