Poissonian counting statistics

If we assume a constant fluorescence rate, the noise is determined by Poissonian counting statistics. Then, the highest S/N level that can be achieved [32] is... 

It is easy to see that Qccrj, hence when rj Q, counts recorded in the measuring device tend to follow the Poissonian counting statistics. 

Both in the strong (Fig. 4.6) and the weak (Fig. 4.7) eases, we find Q(co = 0) 0, which is expected in the slow modulation case eonsidered here. Physically, when the laser detuning frequency is exactly in the middle of two frequency shifts, + v, the rate of photon emissions is identical whether the molecule is in the up state ( + v) or in the down state (—v). Therefore, the effect of bath fluctuation on the photon counting statistics is negligible, which leads to Poissonian counting statistics at o)f = 0. 

In the present work, we have used classical photon counting statistics in the weak laser field limit. In the case of strong laser intensity, quantum mechanical effects on the photon counting statistics are expected to be important. From theories developed to describe two-level atoms interacting with a photon field in the absence of environmental fluctuations, it is known that, for strong field cases, deviations from classical Poissonian statistics can become significant [68,99]. One of the well-known quantum mechanical... 

Figure 4.8(a) (including the detection efficiency). Therefore, even if we consider the imperfect detection of the photon counting device (e.g., rj = 15% has been reported recently [92]), deviation of the photon statistics from Poissonian is observable in the slow modulation regime of SMS. This is seemingly contrary to propositions made in the literature [51, 68, 84], in... 

Figure 4.4 An illustration of the statistical (Poissonian) nature of ion counting for moderate count rates. The data shown by the dashed line correspond to a higher overall signal level than for the solid line. The former is a reasonable match to a Gaussian (normal) distribution whereas the latter Is a relatively poor approximation.

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