# Qn on photon statistics (second order correlation function)

• A
I am trying to better understand the concept of second order coherence G2(τ) (in particular G2(0)) and a few questions have arisen. Note that I am trying to get a physical idea of what is happening so I would appreciate it if your responses can keep the math to the minimum possible. :)

How do we physically think of the Siegert relation / chaotic field limit, i.e. G2(0) = 2 when it seems like the value of G2(0) can actually lie between 1 and infinity? Or a perhaps a better way of phrasing this is - what does it physically mean to say that G2(0) > 2?

In relation to qn 1, how should one attempt to classify a laser in the laboratory? Since a laser in practice can never be truly monochromatic, does that automatically imply that 1<G2(0)<=2 for a practical laser? Does the upper bound (chaotic field limit) apply for a practical laser? Is it correct to include this upper bound and model a practical laser as a quasi-chaotic light source with a corresponding (longer than most thermal light sources) coherence time?

Most of these ideas seem to be centered upon the condition of continuous intensity, i.e. the analogue of a CW laser, or at least to me, they are better understood when considered in such a manner. My final and real question is: how does the physical meaning and definition of G2(0) and G2(τ) change when we think of a laser pulse?

Obviously the idea of a laser pulse implicitly means that such light is no longer monochromatic so it follows that G2(0) cannot be = 1? Beyond that, i have trouble moving further.

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• Paul Colby

A. Neumaier
I think you should provide context by giving a reference.

Sorry for the lack of clarity in my post.
I have been referring mostly to online material as well as Rodney Loudon's "Quantum Theory of Light" which I have had trouble understanding mostly due to my own lack of knowledge in quantum optics. I have found this online response particularly helpful.
http://physics.stackexchange.com/qu...ify-in-quantum-optics-and-how-to-calculate-it
And the same for this wiki article
https://en.wikipedia.org/wiki/Degree_of_coherence
However, the questions in my initial post are new questions that have surfaced after reading the above articles.

The second order correlation function G2(τ) is defined here as = <I(t)*I(t+τ)>/<I(t)>2 where I denotes intensity and the angled brackets refer to time averaged quantities.
(The Siegert relation says that G2(τ) = 1 + |G1(τ)|2 where G1(τ) is the first order correlation function.)