How can be sub-poissonian and super poissonian statistics distinguished from bunching and antibunching?
This is my first post here, so I apologize if there's something wrong.
I am studying quantum optics and I found myself in trouble with the difference between bunching/antibunching and super poissonian/sub-poissonian light.
According to <PERSON>, Quantum theory of light, pag. 248 bunching and anti bunching depends on the fact that $g^{(2)}(\tau)$ (the degree of second order coherence) is less or greater than $g^{(2)}(0)$:
* bunching $g^{(2)}(\tau)$ < $g^{(2)}(0)$
* random $g^{(2)}(\tau)$ = $g^{(2)}(0)$
* anti-bunching $g^{(2)}(\tau)$ > $g^{(2)}(0)$
And <PERSON> and <PERSON>, Photon anti-bunching and sub-Poissonian photon statistics, 1989 stated that the joint probability for detecting one photon at time t and another at time $t + \tau$ is proportional to $g^{(2)}$, hence $p_2(t, t + \tau)$ decreasing or increasing when $\tau$ increases according to bunching and anti-bunching, while the value of $g^{(2)}(0)$ dictate sub or super poissonian statistics. I think this is the correct definition and it's coherent with the treatment of <PERSON>, while other textbooks and papers seem to make confusion on the two different aspects.
For example this answer doesn't seem correct: https://physics.stackexchange.com/q/139833/
A threefold classification of light according to the second-order correlation function can be made as following: - bunched light: $g^{(2)}(0) > 1$, - coherent light: $g^{(2)}(0)= 1$, - antibunched light: $g^{(2)}(0) < 1$.
This implies sub or super poissonian not bunched or anti bunched.
So, I have three related questions:
1. Why there is this confusion and what is the correct answer? I almost sure that <PERSON>, <PERSON> and <PERSON> are right.
2. I understand the math but I don't see completly the physical meaning and how to distinguish the different effects experimentally. 346
I understand that bunching means that photons tend to come in bunches on the detector, but super poissonian seems similar because you have $\Delta n^{2} = + ^{2}$. It seems to imply an excess of number of photons.
3. The Hanbury Brown and Twiss interferometer measure the correlation of intensity of electric field. This tell us automatically if the source is bunched or anti bunched and super or sub poissonian at the same time? (I guess yes because if we have knowledge of $g^{(2)}(\tau)$, we can know it's value at zero and if it increases or decreases with $\tau$. This is valid only if the definition of Loudon is correct). 795