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 ph c is much shorter than the duration of the pump pulse Δt, 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 χ, which is a function of t ph c Δt. We present a direct measurement of χ through a simple experimental set-up. The full theoretical analysis is also provided.