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Physical Review Letters

Observation of Sub-Poissonian Photon Statistics

R. Short, L. Mandeļ

Published Aug 1, 1983• 616 citations
Publisher

Abstract

The number of photons emitted in a short time interval by a single atom in the process of resonance fluorescence is measured, and it is shown that the probability distribution of this number is sub-Poissonian.
DOI
10.1103/physrevlett.51.384

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We have discussed the photon statistics of the spectral components of N-atom time-dependent resonance fluorescence. It is shown that in contrast to the stationary limit, sub-Poissonian photon statistics in the sidebands occur for any number N of atoms including the case N\ensuremath{\gg}1. Reduction in Mandel's parameters Q+1{\mathit{Q}}_{+1}Q+1​ is found with increasing numbers of atoms. The typical time for the presence of sub-Poissonian statistics is proportional to 1/N.
Statistics of fluorescence photons emitted by a single two-level atom interacting with a continuous wave laser field are analyzed. The photon-counting distribution is calculated for the so-called intermediate fluorescence photons, i.e., those counted during the time interval between instants at which photons are emitted. The result is a sub-Poissonian (narrower than Poisson) distribution, which agrees with experimental observations. This intermediate-photon distribution is used to calculate the average number of fluorescence photons, the second factorial moment of the photon-counting distribution, and Mandel’s Q parameter commonly used to evaluate the deviation of photon statistics from the Poisson distribution. The theoretical expressions obtained for moments of the intermediate-photon distribution are different from well-known Mandel’s formulas.
The method previously used by the author for the measurement and calculation of the distribution function w N(T)of fluorescence photons from a single two-level atom that is continuously excited by laser light and has a unity fluorescence quantum yield is generalized to the case of a single molecule whose fluorescence quantum yield is smaller than unity and to the case of a three-level molecule whose fluorescence is blinking. The functions w N(T) calculated for these two cases demonstrate a sub-Poissonian distribution of fluorescence photons.
According to the exact solution of a two-level atomic system interacting with a single-mode field in a cavity and including a pumping mechanism, sub-Poissonian photon statistics can be generated either by regular pumping or by resonance absorption of the lower level. When the atomic lifetime is much smaller than the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\gg}1), which corresponds to a usual laser system, the sub-Poissonian photon distribution can be obtained only by regular pumping. On the other hand, if the atomic lifetime is comparable with the interaction time (${\ensuremath{\gamma}}_{\mathit{a}\mathit{b}}$\ensuremath{\tau}\ensuremath{\le}1), the sub-Poissonian photon distribution can be generated by both mechanisms.
Photons spontaneously emitted from single atoms are necessarily antibunched in time. The statistics of the photon time record, however, can show sub-Poissonian or even super-Poissonian statistics and depend strongly on the time interval used for analysis. In this work we have analyzed photon arrival times from resonantly excited barium atoms in an atomic beam observed under single-atom conditions. The time-interval dependence of photon statistics is presented, showing the connection between antibunching and sub-Poissonian statistics (at times comparable to the spontaneous-decay lifetime of the atom) as well as the evolution of the statistics in the long-time limit.