Theory of two-photon entanglement for spontaneous parametric down-conversion driven by a narrow pump pulse

Spontaneous parametric down-conversion (SPDC) has been extensively studied for the case of a continuous wave pump. In this paper SPDC is studied for the case in which the pump is a pulse. The pump pulse acts like a clock with an uncertainty equal to its width. This makes it possible to distinguish pairs of photons born at sufficiently different depths inside the crystal with a consequent decrease in two-photon interference. We study this effect in detail for degenerate collinear type-II SPDC and degenerate type-I SPDC. It may be possible in the type-II case to eliminate the clock effect of the pump by judicious choice of materials and wavelengths.