ULTRASHORT PULSED SQUEEZING BY OPTICAL PARAMETRIC AMPLIFICATION

We investigate temporal effects in pulsed squeezing by parametric ampl ification, including effects of group-velocity dispersion. Our calcula tions show that the local oscillator pulse used to detect the squeezed field cannot be made shorter than the inverse phase-matching bandwidt h of the generation process without degrading the amount of squeezing detected. This result generalizes an earlier result that showed that i n the absence of dispersion, the local oscillator pulse duration shoul d approach zero for optimum squeezing detection. We further show that by using local oscillator amplitude and phase pulse shaping it should be possible to achieve more than 20 dB of detectable quadrature squeez ing. This is applicable where it is possible to neglect transverse spa tial dimensions and diffraction, such as in a waveguide. We derive the s-parametrized quasiprobability evolution equation for the traveling- wave parametric amplifier. As the Wigner representation results in thi rd-order derivatives, we also use the positive-P representation as an exact representation with equivalent Ito stochastic differential equat ions. This allows us to compare approximate - but easily simulated - W igner representation results with those using the positive-P represent ation.