# Optical coherence

Hello all, I'm studying classical and quantum coherence in optics and I can't understand what's the physical meaning of second order coherence. I mean, what's the fundamental difference between it and the first order one? I know they are defined differently but I can't see in which case and why it could give more info than 1st order (exception made for recognizing if the light beam is classical or quantum). And, regarding this, what are, physically, quantum coherent states? why are they defined so? The common answer could be "because they are all orders coherent" but what does it mean?
Sorry for all those questions but i'm really confused Cthugha
I mean, what's the fundamental difference between it and the first order one? I know they are defined differently but I can't see in which case and why it could give more info than 1st order (exception made for recognizing if the light beam is classical or quantum).
This is already a huge difference, isn't it? First-order coherence basically gives you the coherence time or length. Second-order coherence allows to distinguish between several kinds of light fields (coherent, quantum, thermal). It gives you some information about the underlying photon number distribution of your light field. However, as this distribution is difficult to measure directly as detectors are never ideal, it is easier to measure the variance and other normalized higher order moments of the probability distribution in terms of the second- and higher-order correlation functions.

Alternatively you can interpret $$g^{(n)}(\tau)$$ as the relative probability to detect a photon at a time delay tau after a first one was detected, normalized to the mean photon detection rates at the corresponding times. As you said this allows to distinguish quantum light (detection of a photon lowers the probability to detect another one directly afterwards), thermal light (detection of a photon increases the probability to detect another one directly afterwards) and coherent light (detection of a photon does not alter the probability to detect another one directly afterwards).

And, regarding this, what are, physically, quantum coherent states? why are they defined so? The common answer could be "because they are all orders coherent" but what does it mean?
Sorry for all those questions but i'm really confused Well, it indeed means that all orders of correlation functions are unity valued. That also usually means that your photon numbers will be Poisson-distributed which is the distribution of statistically independent events. It also means that your mean photon pair count rates factorize into the product of the mean single photon count rates at the same times which was the criterion for coherence that Glauber introduced.
It also means that you are working in a regime which is as classical as it gets. If g2 is 1 that means that the detection of a photon does not give you more information about the light field and does not increase or decrease the probability to detect others afterwards. This is rather close to the classical limit, in which you assume that a measurement does not change the examined system.

I really have to thank you, I'm not still sure about it but your simple explanation has opened me a world :D I'll keep studying, maybe the fog is clearing, thanks again