How is the third-order autocorrelation measured in quantum optics?

1

The third order autocorrelation is defined as

$$\bar g^{(3)} = \frac{\langle \hat a^\dagger \hat a^\dagger\hat a^\dagger \hat a\hat a\hat a\rangle}{\bar n^3}.$$

How is this quantity measured in quantum optics, and how can it be interpreted in terms of probabilities?

What happens to this value, if we consider a monomode field coherent state, a Fock state, or a thermal state?

Update****************

For measuring this quantity in quantum optics, we need 3 detectors and we need it for processes where we are interested in the possibility to have three photons at the same time. And g3 is proportional to <n(n-1)(n-2)> with n the operator

what do you mean with "interpreted in terms of probability"? You can reduce it to combinations of different moments of the probability distribution in the Fock basis by using the commutation relations, is that what you mean? Also, can you provide some context as to where this problem arose? There might be different ways to measure this quantity in quantum optics – glS – 2021-01-05T11:53:31.330

the only text I have, I wrote in the question :( but ok I found some very very abstract explanation. Not enough but ok ... – quest – 2021-01-07T19:34:37.667

I don't know what you mean. Where did you read about this? Also note that if you figure out the answer to your own question you can also share it, either editing the question or posting an answer to it – glS – 2021-01-07T21:39:04.070