OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 22, Iss. 6 — Jun. 1, 2005
  • pp: 1314–1320

Bunching, antibunching, and the Poisson limit of Bose–Einstein processes at low-degeneracy parameters

Lorenzo Basano, Pasquale Ottonello, and Bruno Torre  »View Author Affiliations

JOSA B, Vol. 22, Issue 6, pp. 1314-1320 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (150 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Random point processes are often classified as bunched, unbunched, or antibunched, depending on the value assumed by their variance-to-mean ratio (the Fano factor); in the low-degeneracy limit, the Fano factor of a Bose–Einstein process approaches the Poisson value of unity. This fact probably added strength to the conjecture that in the limit of zero degeneracy a Bose–Einstein process reduces to a memoryless Poisson process. After considering some statistics related both to counting and to arrival times, we have experimentally verified that a Bose–Einstein process retains its correlation properties down to values of the degeneracy parameter of the order of 0.01. It also follows that the two most common definitions of photon bunching, the one based on the Fano factor and the one based on the correlation function, are not equivalent at low degeneracy levels.

© 2005 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.5290) Coherence and statistical optics : Photon statistics
(030.6600) Coherence and statistical optics : Statistical optics

Lorenzo Basano, Pasquale Ottonello, and Bruno Torre, "Bunching, antibunching, and the Poisson limit of Bose-Einstein processes at low-degeneracy parameters," J. Opt. Soc. Am. B 22, 1314-1320 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. B. A. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley-Interscience, New York, 1999).
  2. B. A. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978). [CrossRef]
  3. D. Snyder, Random Point Processes (Wiley-Interscience, New York, 1975).
  4. L. Mandel, "Fluctuations of photon beams: the distribution of the photo-electrons," Proc. Phys. Soc. London 74, 233-243 (1959), p. 236. [CrossRef]
  5. M. C. Teich and B. A. A. Saleh, "Effects of random deletion and additive noise on bunched and antibunched photon-counting statistics," Opt. Lett. 7, 365-367 (1982). [CrossRef] [PubMed]
  6. G. Vannucci and M. C. Teich, "Computer simulation of superposed coherent and chaotic radiation," Appl. Opt. 19, 548-553 (1980). [CrossRef] [PubMed]
  7. J. Goodman, Statistical Optics (Wiley, New York, 1985), Sect. 9.2.2.
  8. P. Holgate, "The use of distance methods for the analysis of spatial distribution of points," in Stochastic Point Processes, P.A. W.Lewis, ed. (Wiley-Interscience, New York, 1972), p. 122.
  9. L. Mandel, "Fluctuations of light beams," in Progress in Optics Vol. 2, E.Wolf ed. (North-Holland, Amsterdam, 1963), p. 230.
  10. B. A. A. Saleh and M. C. Teich, "Multiplied-Poisson noise in pulse, particle and photon detection," Proc. IEEE 70, 229-245 (1982). [CrossRef]
  11. Ref. , pp. 168-169.
  12. K. Matsuo, M. C. Teich, and B. A. A. Saleh, "Thomas point process in pulse, particle, and photon detection," Appl. Opt. 22, 1898-1908 (1983). [CrossRef] [PubMed]
  13. W. D. Oliver, J. Kim, R. C. Liu, and Y. Yamamoto, "Hanbury Brown and Twiss-type experiments with electrons," Science 284, 299-301 (1999). [CrossRef] [PubMed]
  14. D. R. Cox and P. A. W. Lewis, The Statistical Analysis of Series of Events (Methuen, London, 1966). [CrossRef]
  15. L. Mandel, "Coherence properties of photons," in Proceedings of the Symposium on Modern Optics (Polytechnic Press of Polytechnic Institute of Brooklyn, New York, 1967), pp. 143-165.
  16. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995). [CrossRef]
  17. L. Basano and P. Ottonello, "Direct memory access digital events analyzer," Rev. Sci. Instrum. 60, 1184-1188 (1989). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited