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Journal of Atomic and Molecular Physics

Signal-background-ratio dependence of single molecular photon sources

Xiao Lian

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

This paper presents the theoretical research on the synchronization sample gate time determination considering the optimal signal-to-noise(SNR) via differentsignal-to-background(SBR) where the background shows time-uniformity distribution or time-exponential distribution.Based on Hanbury-Brown-Twiss (HBT) method,the photon statistics P(n,n=0、1、2) are analyzed by recording of every incident from the single photon source.When P(1)2P(2)-3P(2),an efficient method to determine the SBR of triggered single photons source,which shows SBR=2/2P(2),is carried out.Additionally,we have obtained an efficient method to distinguish single molecular by the double-photon statistics probability P(2),which shows P(2)(2-4-2An-G)2/2,when SBR2.4.

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Acta Physica Sinica•Jan 1, 2005•0 citations
This paper presents the theoretical research on the synchronization sample gate time determination considering the optimal signal-to-noise(SNR) via differentsignal-to-background(SBR) where the background shows time-uniformity distribution or time-exponential distribution.Based on Hanbury-Brown-Twiss (HBT) method,the photon statistics P(n,n=0、1、2) are analyzed by recording of every incident from the single photon source.When P(1)2P(2)-3P(2),an efficient method to determine the SBR of triggered single photons source,which shows SBR=2/2P(2),is carried out.Additionally,we have obtained an efficient method to distinguish single molecular by the double-photon statistics probability P(2),which shows P(2)(2-4-2An-G)2/2,when SBR2.4.
The principle of single photon source based on three-levels single molecule is introduced. By use of Hanbury-Brown-Twiss method, the photon statistics P(n, n=0、1、2) and the Mandel parameter are analyzed by recording of every photo-electrical event from the single photon source. When signal to background ratio SBR2.4, an efficient method to distinguish single molecules by the double-photon statistics probability P(2), which shows P(2)12(2-4-2n-)~2, is presented. Here, n- is the mean photon number.
The real triggered single molecule source is recognized as an ideal single photon source with a Poissonian statistics background. By considering the effect of the triplet state in single molecule energy level, an explicit function is given for the signaltobackgound ratio(SBR) by use of photoncounting statistics. When PRS(1)2PRS(2)-3PRS(2), we present an effici ent method to determine the SBR of the triggered single photons source, which s hows SBR=P2RS(1)/2PRS(2).In addition, the expression of Q, as a function of signaltobackgound ratio, has been obtained. It turns o ut that this method is simpler and gives a greater accuracy than previous proce dures.
We theoretically derive exact expressions for Mandel's Q parameter of the triggered single molecular source, which is inferred from the probabilities P RS ( 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 Q RS of the real single triggered molecular with Q C 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.
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 recorded 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 decease 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.
Signal-to-noise ratio of fluorescence detection from a single molecule is analysed by using time-gated techniques. It is found that the optimal signal-to-noise ratio can be obtained by choosing an appropriate gate time with a certain optical background. The dependences of molecular fluorescence lifetime and the optimal signal-to-noise ratio on the appropriate gate time are respectively discussed with two kinds of background sources, chaotic state with uniform distribution and coherent state with exponential distribution in time domain. For chaotic state background we find that a certain range for appropriate gate time can be obtained with a definite fluorescence lifetime, larger fluorescence lifetime would lower the value of optimal signal-to-noise ratios. For coherent state background we find that there is also a narrow range of appropriate gate time when lifetime of single molecule is less than that of background photons.
We theoretically study the photon counting statistics characterizations of the real single molecular photon source with a Poisson statistics background and that of an ideal double molecular system based on the standard HBT detection. Mandel parameter Q of each source with the same mean photons n—was analyzed. We have obtained an efficient method to identify single molecule by the two-photon statistics probability P(2), which shows the relation P(2)2. Additionally, we studied the effect of single-to-background ratio of the single molecular photon source on the criterion.