Effect of Background Noise on the Photon Statistics of Triggered Single Molecules

We theoretically derive exact expressions for Mandel's Q parameter of the triggered single molecular source, which is inferred from the probabilities PRS(n) using the record of each photon detection event based on Hanbury Brown and Twiss detection. The real triggered source is recognized as an ideal single photon source with a Poissonian statistics background. How to decrease the background and to increase the efficiency are discussed. It is established that the sub-Poissonian statistics formation can be determined by comparing the measured QRS of the real single triggered molecular with QC of the Poissonian source containing the same mean photons. By this method, we also give an efficient way to measure signal-to-background ratios of triggered single photons.