Simultaneous near-field and far-field spatial quantum correlations in the high-gain regime of parametric down-conversion

We study the spatial correlations of quantum fluctuations that can be observed in multimode parametric
down-conversion in the regime of high gain. We investigate both a type-I and a type-II phase-matching
configuration: in the latter case spatial correlations at the quantum level are shown to exist both in the
near-field and in the far-field zones of the down-converted light. In the stationary and plane-wave approximation
we treat the problem analytically. A stochastic model is solved numerically to obtain quantitative results
beyond this approximation. The finite transverse size and pulse duration of the pump beam and other features
of the system, such as spatial walk-off and diffraction are taken into account, and we show that correlations
beyond the standard quantum limit exist for values of parameters consistent with realistic experiments.