Antibunching is the tendency of photons to repulse each other in time, i.e., to be less likely to be found together than later apart in time. At such, this is a particular case of photon statistics, as measured by the so-called $g^{(2)}$. But this is a case of great importance as it signals, or is usually linked, to the quantum rgime. Unfortunately, there have been several differing definitions, based around the idea that antibunching describes single-photons, or suppression of two-photon (or multiphoton) coincidence. In particular, various authors (ourselves included, when convenient) understand antibunching as the condition $g^{(2)}(0)\approx 0$ (or even equal to zero, or less than unity). There is no good term that I know for the latter condition (some speak of "purity", which I also don't like very much; a better term would be sub-Poissonian but that's awkward). A more accurate, widespread, agreed-upon definition of antibunching itself is:

$$g^{(2)}(0)< g^{(2)}(\tau)$$

for all $\tau$ in a neigborhood of~$\tau=0$. Note that this allows $g^{(2)}(0)$ to be larger than unity and thus to have a super-Poissonian antibunched source, just as one can have sub-Poissonian bunched ones. The confusion (reconciliation?) with $g^{(2)}$ for typical cases is that they could be monotonic (or monotonic enough) to take the case $\tau\to\infty$ where $g^{(2)}(\infty)=1$. We discuss a bit the definition of antibunching for instance in Section~II of Ref. [1] but one could make a more thorough analysis, extending that of Zou and Mandel.[2]

The first antibunching is from Kimble et al.,[3] although according to Walls,[4] this was also simultaneously reported by Leuchs et al. who did not publish their findings, but that Walls provides in his review (along with, interestingly, much better results than the ones published by Kimble et al. in their text):

Screenshot 20240218 173113.pngScreenshot 20240218 173157.png


Here follows a collection of antibunching traces $g^{(2)}(\tau)$. It is of course impossible to be comprehensive, but hopefully this will grow to be representative enough of everything and everybody:

From Kimble et al.[3]

Screenshot 20240113 150223.png Screenshot 20240113 145952.png

From Diedrich et al.[5]

Screenshot 20240113 145518.png

From Basché et al.[6]

Screenshot 20240113 142622.png

From Ambrose et al.[7]

Screenshot 20231229 102949.png

They consider histograms of time-difference so with no normalization of their signal back to unity at long time delays. The identity of this histogram method with a complete~$g^{(2)}$ is valid only over times much smaller than the mean time between detections.[8]

From Lounis et al.[9]

Screenshot 20231229 102454.png

From Fleury et al.[10]

Screenshot 20240109 125540.png

From Kurtsiefer et al.[11]


The bunching elbows are accounted here for the first time with a rate-equation model (yielding a bi-exponential curve).

From Michler et al.[12]

Screenshot 20231229 115002.png

From Zwiller et al.[13]

Screenshot 20231229 100312.png

From Messin et al.[14]

Screenshot 20231229 101845.png

From Hübner et al.[15]

Screenshot 20231229 102130.png

From Ampem-Lassen et al.[16]

Screenshot 20231229 111058.png

From Neu et al.[17]

Screenshot 20240109 114851.png

From Nothaft et al.[18]


Top: raw-data; Bottom: with correction. But their optical pumping provides antibunching similar to the "corrected" electrically-pumped one. This is a log-linear plot, the red line is actually a single exponential.

From Davanço et al.[19]

Screenshot 20231231 192955.png

From Berthel et al.[20]


From Koperski et al.[21]

Screenshot 20231231 194404.png

From Wang et al.[22]

Screenshot 20231231 134450.png

From Boll et al.[23]


From Nahra et al.[24]

Screenshot 20240101 205332.png

From Fiedler et al.[25]

Screenshot 20231231 161337.png

The 'photon bunching at non-zero correlation times' is still attributed to a metastable (shelving) state, like in the original paper.[11]

Transitions between various types statistics

Something which frequency-filtering does very neatly.



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  2. Photon-antibunching and sub-Poissonian photon statistics. X. T. Zou and L. Mandel in Phys. Rev. A 41:475 (1990).
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