Two independent photon pairs versus four-photon entangled states in parametric down conversion

We study the physics of four-photon states generated in spontaneous parametric down-conversion with a pulsed pump field. In the limit where the coherence time of the photons t_c is much shorter than the duration of the pump pulse Delta t, the four photons can be described as two independent pairs. In the opposite limit, the four photons are in a four-particle entangled state. Any intermediate case can be characterized by a single parameter chi, which is a function of t_c/Delta t. We present a direct measurement of chi through a simple experimental setup. The full theoretical analysis is also provided.