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
(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)