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Acta Physica Sinica

Identifying single molecule based on the photon statistics

Peng Shuang-Yan, Huang Tao, Xiaobo Wang, Shao Jun-Hu, Xiao Liao-Tuan, Jia Suo-Tang, (1)量子光学与光量子器件国家重点实验室，山西大学物理电子工程学院，太原 030006; (2)量子光学与光量子器件国家重点实验室，山西大学物理电子工程学院，太原 030006;贵州毕节学院物理系，毕节 551700

Published Jan 1, 2005• 0 citations
Publisher

Abstract

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.

DOI
10.7498/aps.54.5116

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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.
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.
Theoretical research on the record of every incident output of the single-molecule photon source responded by two SPCM with standard Hanbury-Brown-Twiss technique is presented.The photon statistic measurement of a single molecule photon source based on the HBT configuration with an unbalanced detection system is studied.The photon counting statistics character of the real single molecular photon source with a Poisson statistics background is theoretically investigated.It is shown that the unbalanced detectors,the unbalanced beam-splitter and the unbalanced linear propagation efficiencies will cause the single event Mandel parameter to be less than that of balance system.In addition,the correction expression to the Mandel parameter based on unbalanced detection is given.
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.
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.
Identifying and distinguishing single-molecule by fluorescence photon statistic measuring have been widely applied in physics, biology, chemistry and information processing et al.. Two kinds of methods of identifying and distinguishing single-molecule are analyzed and reviewed. Firstly, two identification methods to identify singlemolecule photon source are introduced: one by measuring laser stimulated single-molecule fluorescence field twoorder autocorrelation function with start-stop method, the other based on single photon counting statistic measurement. Secondly, the other kind of methods are to distinguish which species molecules the single-molecule detected belongs to when a couple of species molecules are mixed. Two methods, based on property-correlated single-photon counting statistic measurement and probability calculation and analysis, are chiefly introduced: the maximum likelihood method and the lookup table method.
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.