Distinguishing N Photons in an Entangled State from N Separate Photons

Distinguishing N Photons in an Entangled State from N Separate Photons

We present a multimode model to describe an arbitrary N-photon state. In general, the N photons can be distinguished through their temporal modes. From this model, we can find the criterion for the N photons in an indistinguishable state of a single temporal mode. We find that simple multi-photon detection scheme cannot distinguish N photons in different temporal modes and only a multi-photon interference experiment can accomplish the goal. We apply the theory to the four-photon case in the process of parametric down-conversion. We will present the results for various four-photon interference schemes and identify a quantity to characterize how well the four photons are indistinguishable.