# Interpretation of different values of antibunching

When the frequency resolved second order correlation function at zero time delay, $$g^{(2)}(\omega_1, \omega_2) = \frac{\langle a_1^\dagger a_1(t) a_2^\dagger a_2(t)\rangle}{\langle a_1^\dagger a_1(t)\rangle\langle a_2^\dagger a_2(t)\rangle}$$ is larger then one, called "bunched", the photons have a tendency to be emitted together from the system. When smaller then one, called "antibunched", the probability of detecting them together is smaller then detecting them separate in time.

What is the difference between different values of antibunching? If I find for two frequencies for which $g^{(2)} = 0.4$, how is this different from a situation for which I find $g^{(2)} = 0.1$?

As you have correctly stated, the second order correlation function measures the coincidence of two events. The case of $g^{(2)}=0.4$ means any two events are less likely to happen coincidently than the case of $g^{(2)}=0.1$, although both of the two cases tending to have antibunching events.
• You can think of some extremes. Like what if $g^{(2)}=0$? It means if one event was observed at time t and the counterpart event must not or is forbidden to happen at the same time. For $g^{(2)}=1$, it just means the two events are randomly happening, maybe sometimes they happen at the same time but other cases may happen randomly--absolutely no correlation. Any number in between is just to have some negative correlation but not as strong as absolutely antibunching. – Xiaodong Qi Oct 6 '15 at 19:17