COHERENCE PROPERTIES OF ENTANGLED LIGHT-BEAMS GENERATED BY PARAMETRICDOWN-CONVERSION - THEORY AND EXPERIMENT

Using a multidimensional Gaussian approximation of the wave function f or the signal and idler light generated by spontaneous parametric down -conversion, we derive analytical expressions for the second-order coh erence function and the fourth-order coherence function (which is prop ortional to the signal-idler photon coincidence rate). The magnitudes of these functions are expressed as products of Gaussian functions of the azimuthal angles, the polar angles, and the time delay. Their widt hs determine six parameters: the coherence angles and coherence time, and the entanglement angles and entanglement time. We show how these p arameters are governed by the pump-beam waist, the pump spectral width , and the crystal length. We thereby derive relations analogous to the van Cittert-Zernike theorem and the Siegert relation for thermal ligh t. We show that the normalized photon coincidence rate decreases sharp ly as the signal and idler apertures become mismatched or misaligned. We experimentally confirm this latter prediction by using parametrical ly down-converted light obtained from a LiIO3 crystal pumped by Kr+-io n laser radiation at 413 nm.