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Chinese Physics Letters

Appropriate Gate Time for Single Molecular Photon Detection Based on Optimal Signal-to-Noise Ratio Analyses

Shuangli Dong, Huang Tao, Liu Yuan, Jun Wang, Liantuan Xiao, Jia Suo-Tang

Published May 1, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0256-307x/24/5/027

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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.
从由使用时间门技术的单个分子 isanalysed 的荧光察觉的 Signal-to-noise 比率。最佳的 signal-to-noise 比率由与某个光背景选择一适当的门时间装 beobtained,这被发现。适当的门 timeare 上的依赖 ofmolecular 荧光一生和最佳的 signal-to-noise 比率分别地及时与指数的分发与二种背景来源,有 uniformdistribution 的混乱状态和协调状态讨论了领域。为混乱 statebackground,我们结束那在适当的门时间的某个范围能与 definitefluorescence 一生被获得,更大的荧光一生将降低最佳的 signal-to-noiseratios 的价值。当单个分子的一生是时,为我们发现那的协调州的背景,也有适当 gatetime 的一个狭窄的范围不到背景光子的。
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.
Traditional optical Kerr gates (OKG) often suffer from leakage fluorescence background when sampling and measuring fluorescence spectra due to the limited extinction of the polarizers used in optical Kerr gates. In this letter, we propose a cascaded optical Kerr gate (COKG) for measuring fluorescence spectroscopy with a high signal-to-noise ratio by suppressing this leakage fluorescence background. Our proposed COKG consists of an optical Kerr gate with a fast-switching time at the front stage and an optical Kerr gate with a high transmission at the back stage. The experimental results show that the signal-to-noise ratio for the COKG can be improved by about two orders of magnitude compared to the single OKG.
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.
In atomic and molecular phase measurements using laser-induced fluorescence detection, optical cycling can enhance the effective photon detection efficiency and hence improve sensitivity. We show that detecting many photons per atom or molecule, while necessary, is not a sufficient condition to approach the quantum projection limit for detection of the phase in a two-level system. In particular, detecting the maximum number of photons from an imperfectly closed optical cycle reduces the signal-to-noise ratio (SNR) by a factor of 2\sqrt{2}2​, compared to the ideal case in which leakage from the optical cycle is sufficiently small. We derive a general result for the SNR in a system in terms of the photon detection efficiency, probability for leakage out of the optical cycle per scattered photon, and the product of the average photon scattering rate and total scattering time per atom or molecule.