Multi-photon states and their measurement

Generation of multi-photon states (such as, for instance, three- and four-photon states) is one of the most challenging problems of modern quantum optics. In many works, the authors claim to have produced such states by means of overlapping photon pairs generated in spontaneous parametric down-conversion (SPDC). Moreover, three- and four-photon states generated this way have been used for observing Greenberger-Horne-Zeilinger (GHZ) polarization states, testing Bell's inequalities for spin-1 quantum systems, preparing W-states, and other applications. In this paper, we show that the criterion for obtaining three- or four-photon states is the behavior of the corresponding normalized Glauber's correlation function. Calculations carried out for the case of SPDC, or even PDC in the stimulated regime, demonstrate that these processes are not capable of generating three- or four-photon states: photon statistics reveals typically two-photon behaviour. We suggest a method of measuring higher-order correlation functions in the pulsed regime, which allows one to study multi-photon correlations for these and many other processes.