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.
We examine the coherence properties and photon statistics of stationary light obtained by the superposition of nonstationary emissions occurring at random times, in accordance with a homogeneous Poisson point process. The individual emissions are assumed to be in a coherent, chaotic, or
n state. The statistical nature of the emission times results in fluctuations of the relative contributions of different emissions at a given time. This is manifested by an additional positive term, exhibiting particlelike properties, in the normalized second-order correlation function. Thus, the photon-counting variance is increased. For coherent emissions, interference between the randomly delayed emissions produces additional wavelike noise. In the limit when the emissions overlap strongly, the field exhibits the correlation properties of chaotic light, regardless of the statistics of the individual emissions. In the opposite limit, when emissions seldom overlap, the light intensity is describable by a shot-noise stochastic process, and the detected photocounts show an enhanced particlelike noise, which has its largest value when the counting time is long. In that limit, the photocounts obey the Neyman type-
A and generalized Polya-Aeppli distributions, when the individual emissions are coherent and chaotic, respectively. When the individual emissions correspond to the
n state, the Poisson emission times result in bunching which reduces or eliminates the inherent antibunching associated with the
n state.
The use of dead time effects to generate sub-Poissonion photo-electron counting statistics is discussed. An experiment is described in which dead times are introduced using an optical shutter triggered by photo-detection events. Although the triggering photo-electron train is sub-Poissonion and antibunched, the light sampled by a second detector gives rise to a super-Poissonion and bunched train of photo-elecrons. A second experiment is proposed which would generate truly sub-Poisson light (ie detector independent). This is based on the use of optical dead times in parametric fluorescence.
A great deal of effort has been devoted during the last decade to the theory of nonclassical states of the radiation field. From a practical point of view some of the most interesting predictions of these theories concern the generation of light with sub-Poissonian photon counting statistics for which Such light is evidently less noisy than laser radiation with obvious implications for the improved performance of optical systems. When the temporal autocorrelation function of the photon counts increases as the delay time increases from zero the light is also said to be antibunched.
Two manifestations of the quantum nature of coherent, resonant light scattering from atoms are photon antibunching and sub-Poissonian statistics. The existence of both effects has been demonstrated previously; in the present work, using individual barium atoms, measurements of the dependence of the latter effect on the frequency of the radiation field are presented. The distinction between the two phenomena is demonstrated by data that exhibit antibunching, yet have a photon counting distribution with variance equal to the Poisson value.