Sub-Poissonian photon statistics

Another nonclassical effect is referred to as sub-Poissonian photon statistics (see, e.g., Refs. 7 and 8 and papers cited therein). It is well known that in a coherent state dehned as an inhnite superposition of the number states... 

If the variance of the number of photons is smaller than its mean value, the held is said to exhibit the sub-Poissonian photon statistics. This effect is related to the second-order intensity correlation function... 

Negative values of this parameter indicate sub-Poissonian photon statistics, namely, nonclassical character of the field. One obvious example of the nonclassical field is a field in a number state n) for which the photon number variance is zero, and we have g 2 (0) = 1 — 1 /n and q = — 1. For coherent states, g (0) = 1 and q = 0. In this context, coherent states draw a somewhat arbitrary line between the quantum states that have classical analogs and the states that do not have them. The coherent states belong to the former category, while the states for which g (0) < 1 or q < 0 belong to the latter category. This distinction is better understood when the Glauber-Sudarshan quasidistribution function P(ct) is used to describe the field. 

Again, ((An)2) < (ii) only if P(a) is not positive definite, and thus sub-Poissonian photon statistics is a nonclassical feature. 

In this section, we will generalize our results of Section II. B to describe the processes of the Nth-harmonic generation. Again, we will focus on predictions of the sub-Poissonian photon-number statistics. 

It is seen that the photon-number statistics of fundamental mode exhibits, in the short-time regime, much stronger sub-Poissonian behavior than that of harmonic mode. 

As pointed out in many papers photon antibunching is a purely quantum phenomenon (see e.g. Refs. (2, 15). The fluorescence of a single ion displays the additional nonclassical property that the variance of the photon number is smaller than its mean value (i.e. it is sub-Poissonian). This is because the single ion can emit only a single photon and has to be re-excited before it can emit the next one which leads to photon emissions at almost equal time intervals. The sub-Poissonian statistics of the fluorescence of a single ion has been measured in a previous experiment (14) (see also Ref. (16) for comparison). 

The one-atom maser can be used to investigate the statistical properties of nonclassical light [14.106,107]. If the cavity resonator is cooled down to T < 0.5 K the number of thermal photons becomes very small and can be neglected. The number of photons induced by the atomic fluorescence can be measured via the fluctuations in the number of atoms leaving the cavity in the lower level n-l). It turns out that the statistical distribution does not follow a Poissonian statistics as in the output of a laser with many photons per mode, but shows a sub-Poissonian distribution with photon-number fluctuations 70% below the vacuum-state limit [14.108]. 

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