Photon statistics techniques

A final requirement arises if the stroboscopic technique is to be used, where the experiment is repeated many times and the resulting data summed to provide enough photon statistics. In this case the detector must be capable of being synchronised to the experiment. 

In the single-photon timing technique, the statistics obeys the Poisson distribution and the expected deviation o-(i) is approximated to so that Eq. (7.9) be-... 

Most of the work has been done using absorption techniques. Although this technique has excellent time resolution, it suffers from sensitivity problems. Photon statistics are the primary source of noise, and it is difficult to overcome this with increasingly stronger laser monitoring... 

One way of studying temporal coherence in laser systems is by measuring photon statistics [224]. In this technique the transient laser emission properties are measured using pulsed excitation and a time-resolved setup [225], The transient emission curve generated by each pulse above the laser threshold intensity is divided into time intervals that are smaller than the emission coherence time. The number of photons is then measured in each time interval and for each pulse, and a photon number histogram is calculated to obtain the probability distribution function (PDF) of the photons for each time interval. Photon statistics is achieved separately for each time interval, and correlation between different time intervals or between different wavelengths of the emission spectrum can be also studied. It is expected that for coherent radiation the Poisson distribution determines the PDF, whereas for noncoherent light... 

Fluorescence line-narrowing and coherent photon-echo techniques (Macfarlane 1992) could give some idea about the homogeneous part of an emission line, but the statistical analysis for the whole sample should still be performed. Supposing only a sensitizer-activator interaction, an average transfer efficiency can be calculated (Dexter 1953). This was studied in some detail by Inokuti and Hirayama (1965). They considered the number of activators located at random in a sphere around a sensitizer in such a way that the activator concentration remains constant when the volume of the sphere and the number... 

Time-correlated single photon counting (TCSPC) [28] is one of the most sensitive methods for studying time-resolved emission. In this technique, single photon events are detected after excitation and a statistical distribution of photons representing the decay of the excited state is built up over time. 

One could ask, "What would be the contribution of using special techniques, such as two-photon spectroscopy, to take advantage of the potentially high precision of ultra-narrow lines, such as the 1S-2S transition in H (width = one Hertz) The statistical part of the variance in Figure 1 reflects the "Q"... 

The frequency distribution of noise is characterized by a power spectrum. There a two types. First, white noise, whose noise power is independent of the frequency. This noise arises from the statistics of electrons or photons and of the thermal energy of conductors. White noise can be reduced by extending the measuring time. Second, excess low frequency noise, flicker, or 1// noise is due to fluctuations, drift and schlieren. It can be reduced by modulation. All types of noise are reduced by multiplex procedures, multichannel techniques, and multiple recording (Schrader, 1980). 

We now turn to a quantitative examination of the feasibility of conditional Fock state generation using our preparation and retrieval technique. For applications in long-distance quantum communication, the quality of the atomic state preparation is the most important quantity. Assuming perfect atom-photon correlations in the write Raman processes, we can find the density matrix p for the number of atomic spin-wave excitations conditioned on the detection of ns Stokes photons. Here we consider only the spin-wave modes correlated with our detection mode. For example, in the absence of losses and background, the conditional atomic density matrix is simply p(ns) = ns)(ns. Loss on the Stokes channel (characterized by transmission coefficient a.s) leads to a statistical mixture of spin-wave excitations,... 

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