# Qn on photon statistics (second order correlation function)

• A
• Tainty
In summary: The chaotic field limit is related to the degree of coherence (G2(τ)). In a laser, the chaotic field limit is the point at which the second order correlation function ceases to decrease with increasing time. This occurs when τ approaches 0.5 or 2.0. Beyond this point, the second order correlation function is no longer decreasing but instead increases exponentially. A practical laser can be thought of as a quasi-chaotic light source with a corresponding coherence time. This means that the coherence time is much longer than most thermal light sources. This is due to the fact that a practical laser is a laser that produces pulses rather than continuous light.

#### Tainty

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.

Last edited:
Paul Colby
Tainty said:
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.)

## 1. What is the second order correlation function in photon statistics?

The second order correlation function, also known as the g2 function, is a measure of the probability of finding two photons at different points in space and time. It is used to study the statistical properties of light, such as its coherence and photon bunching or antibunching behavior.

## 2. How is the second order correlation function calculated?

The g2 function is calculated by taking the ratio of the probability of detecting two photons at a specific time delay, to the product of the probabilities of detecting a single photon at each of the two time points. This ratio is then normalized to account for any background noise in the measurement.

## 3. What is the significance of the g2 function in photon statistics?

The g2 function provides valuable information about the nature of light, such as its coherence and the degree of correlation between different photons. It is used in various applications, including quantum optics, quantum information processing, and single photon sources.

## 4. How does the g2 function differ for different types of light sources?

The g2 function can vary significantly depending on the type of light source. For example, thermal light sources typically exhibit a g2 function greater than 1, indicating photon bunching behavior. On the other hand, single photon sources usually have a g2 function close to 0, indicating antibunching behavior.

## 5. Can the g2 function be used to distinguish between different types of light sources?

Yes, the g2 function can be used to distinguish between different types of light sources based on their statistical properties. For example, it can be used to differentiate between coherent and incoherent light sources, as well as between classical and quantum light sources.

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