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It is well-known that sub-Poissonian photon statistics and light anti-bunching normally occur together, since both effects may be considered as a manifestation of photon streams being 'regular enough'.

Zou & Mandel (PRA 1990) provided an example of a sub-Poissonian light which is bunched.

That is, the statement "sub-Poissonian implies anti-bunched" is false.

Does any counterexample exist for the statement "anti-bunched implies sub-Poissonian statistics?"

Thank you!

glS
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J. Doe
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  • I think the definition of *anti-bunched" is "not Poissonian" – garyp Apr 30 '21 at 10:51
  • what are your definitions of "anti-bunched" and "sub-Poissonian" here? Because the two things are often defined as the same thing. – glS May 02 '21 at 10:49
  • sub-Poissonian means that the photon number statistics satisfy $\Delta n < \sqrt {\bar n}$. That is, the standard deviation of the photon number is smaller compared to the Poisson distribution case (with the same mean photon number).

    Being anti-bunched means that $g^{(2)}(0)<1$, where $g^{(2)}$ denotes the second-order correlation function of the light. @glS

     – J. Doe May 04 '21 at 15:10
  • @MocaAoba I see, that makes sense. I'd suggest you to edit the post to also include those definitions, as they make it easier to answer the question. By the way, have you seen this answer? I suppose the answer to your question might simply be the observation $g^{(2)}(0)=\frac{\langle n^2\rangle-\langle n\rangle^2}{\langle n\rangle^2}=1+\frac{\sigma_n^2-\langle n\rangle}{\langle n\rangle^2}$ – glS May 04 '21 at 16:08
  • @glS I see... That answer indeed answers my question. Thanks. (And that answer also implies that, in some sense, merely comparing $g^{(2)} (0)$ to 1 is not the "correct" definition for light being (anti)bunched.) – J. Doe May 07 '21 at 08:10

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