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Chinese Science Bulletin

Photon statistics of driven single molecule:The effects of intersystem crossing process

Gu Li

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

We studied the photon statistics of the driven single molecule under intersystem crossing process which caused the fluorescence blinking via generating function approach.We give an analytical expression of the average emission photons N and the Mandel's Q parameter in long time limit.The results demonstrate that the Mandel's Q parameter has the same behavior as the average emission photons N with respect to the evolution time,both of them linearly increasing with the evolution time increase,when the intersystem crossing process occurred in the single molecule.

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We studied the photon statistics of the driven single molecule under intersystem crossing process which caused the fluorescence blinking via generating function approach.We give an analytical expression of the average emission photons N and the Mandel's Q parameter in long time limit.The results demonstrate that the Mandel's Q parameter has the same behavior as the average emission photons N with respect to the evolution time,both of them linearly increasing with the evolution time increase,when the intersystem crossing process occurred in the single molecule.
We studied the photon statistics of the driven single molecule under intersystem crossing process which caused the fluorescence blinking via generating function approach. We give an analytical expression of the average emission photons <N>and the Mandel's Q parameter in long time limit. The results demonstrate that the Mandel's Q parameter has the same behavior as the average emission photons <N> with respect to the evolution time, both of them linearly increasing with the evolution time increase, when the intersystem crossing process occurred in the single molecule.
In this paper, we summarize the photon emission statistical properties of single molecule system, using the recently developed generating function method. Through the introduce of one or double “auxiliary” variables, we can investigate the first moment and second moment of photon emission statistics driven by different external fields, such as the line shapes and Mandel's Q parameters, the photon emission probabilities, the probability distribution of time between successive emission, the waiting time and the waiting time distribution, the cross correlation, the joint probabilities, etc. Among, the first moment of photon statistics and the experimental results of optical amplification are in good agreement.
We investigate the reduction in the probability of single-photon emission from a single-emitter system caused by intersystem crossing. The physical model is that a single-emitter system with three levels is excited by a square pulse laser, and then a single photon is emitted at a controllable time. We find that the intersystem crossing always reduces the probability of single-photon emission. We obtain quantitative and analytical expressions for the probabilities of zero-, one-, and two-photon emission and Mandel's Q parameter as the function of the intersystem crossing rate under the conditions of finite field strength and finite interaction time with the laser pulse. We discuss the conditions for obtaining the maximal probability of single-photon emission in the presence of intersystem crossing. We find that one can obtain a high probability of single-photon emission from the single-emitter system using square pulse excitation in comparison with continuous wave excitation. Mandel's Q parameter exhibits a transition from a sub-Poissonian behavior to a super-Poissonian behavior due to the influence of intersystem crossing. The calculated Mandel's Q parameter and second-order correlation function of photon emission considering the coherent effect are in better agreement with the experimental data.
We derive the moment generating function for photon emissions from a single molecule driven by laser excitation. The frequencies of the fluoresced photons are explicitly considered. Calculations are performed for the case of a two-level dye molecule, showing that measured photon statistics will display a strong and nonintuitive dependence on detector bandwidth. Moreover, it is demonstrated that the antibunching phenomenon, associated with negative values of Mandel's Q parameter, results from correlations between photons with well separated frequencies.
Based on the generating function formalism, we investigate broadband photon statistics of emission for single dimers and trimers driven by a continuous monochromatic laser field. In particular, we study the first and second moments of the emission statistics, which are the fluorescence excitation line shape and Mandel's Q parameter. Numerical results for this line shape and the Q parameter versus laser frequency in the limit of long measurement times are obtained. We show that in the limit of small Rabi frequencies and laser frequencies close to resonance with one of the one-exciton states, the results for the line shape and Q parameter reduce to those of a two-level monomer. For laser frequencies halfway the transition frequency of a two-exciton state, the photon bunching effect associated with two-photon absorption processes is observed. This super-Poissonian peak is characterized in terms of the ratio between the two-photon absorption line shape and the underlying two-level monomer line shapes. Upon increasing the Rabi frequency, the Q parameter shows a transition from super- to sub- to super-Poissonian statistics. Results of broadband photon statistics are also discussed in the context of a transition (frequency) resolved photon detection scheme, photon tracking, which provides a greater insight in the different physical processes that occur in the multi-level systems.