Derivation of Threefold Coincidence g(2)

The threefold anticorrelation parameter, similarly to the twofold, is dependent on the probabilities of threefold coincidences and individual twofold coincidences:

(1)

\begin{align} A = {P _{ABB'} \over {P_{AB} P _{AB'}}} \left \end{align}

The probability of coincidences are each dependent on the number of measured coincidences over the number of measured counts in the trigger channel, A.

(2)

\begin{align} P _{ABB'} = {N _{ABB'} \over {N_{A} }} \left \end{align}

This holds true for the other two quantities as well. Substituting these equations into the original equation, we can find the anticorrelation parameter as a function of raw numbers of counts and coincidences:

(3)

\begin{align} A = {N _{ABB'} \over {N_{AB} N _{AB'}}} \left({N_A} \right) \end{align}

[1]

References

1. J. J. Thorn, M. S. Neel, V. W. Donato, G. S. Bergreen, R. E. Davies, and M. Beck, "Observing the quantum behavior of light in an undergraduate laboratory", Am. J. Phys. 72, 1210-1219 (2004).