Fano factor generation

Quasistationary Values of the Quantum Fano Factors Fp and their Semiclassical Approximations Ff, Given by Eq. (54), for the Fundamental Mode in Nth-Harmonic Generation with N = 1 — 5 in No-Energy-Transfer Regime11... 

Figure 7. Time evolution of the exact quantum Fano factors (a) Fp =F (N) for the fundamental mode and (b) F for the harmonic mode in Mh-harmonic generation for N = 2 (thickest curve), 3,4 and 5 (thinnest curve). Time t is rescaled with frequency fi, given by (52), and coupling constant g. The harmonic mode amplitude is r r 5. The dotted lines correspond to the semiclassical Fano factors, given by (54) and (55). It is seen that the fundamental mode is super-Poissonian, whereas the harmonic mode is sub-Poissonian for all nonzero evolution times.

Figure 8. Semiclassical (solid bars) and quantum (dithered bars) Fano factors versus order N of harmonic generation for (a) fundamental and (b) Ahh-harmonic modes in the quasistationary noenergy-transfer regime. Panels (a) and (b), for N = 1 — 5, correspond to Tables I and II, respectively. It is seen that the quantum results are well fitted by the semiclassical Fano factors. According to both analyses, the third-harmonic mode has the most suppressed photocount noise.

Fano factors have been calculated and also measured. For semiconductor detectors, F values as low as 0.06 have been reported. For gas-filled counters, reported F values lie between 0.2 and 0.5. Values of f < 1 mean that the generation of electron-hole pairs does not exactly follow Poisson statistics. Since Poisson statistics applies to outcomes that are independent, it seems that the ionization events in a counter are interdependent. 

Two sets of factors that work in opposite directions are not considered in Eq. (2.19). The equation overestimates the FWHM by -/f, where F is the empirically observed Fano factor. The existence of this factor is attributed to the circumstance that the generated electrons do not necessarily act independently in producing the ionization pulse, and so the peak is narrower than when attributed to random events. On the other hand, detector drift, noise, and incomplete carrier collection each contributes to widening the FWHM (Knoll 1989). 

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