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Single Molecules

Photon Statistics in Single Molecule Experiments

Michel Orrit

Published Nov 1, 2002• 35 citations
Publisher

Abstract

Single molecule fluorescence experiments yield a stream of photocounts, whose statistical properties contain valuable information about processes within the molecule and in its microscopic environment. The photon statistics display features specific of single quantum systems and are therefore best discussed in the frame of a quantum mechanical theory of radiation. The present summary of a lecture given in April 2002 at the Hofgeismar Spring School on single molecules presents the main concepts used in quantum theory of light, together with a few useful references, and discusses some illustrations and applications to single molecule measurements drawn from the recent literature.

DOI
10.1002/1438-5171(200211)3:5/6<255::aid-simo255>3.0.co;2-8

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Single molecule fluorescence experiments yield a stream of photocounts, whose statistical properties contain valuable information about processes within the molecule and in its microscopic environment. The photon statistics display features specific of single quantum systems and are therefore best discussed in the frame of a quantum mechanical theory of radiation. The present summary of a lecture given in April 2002 at the Hofgeismar Spring School on single molecules presents the main concepts used in quantum theory of light, together with a few useful references, and discusses some illustrations and applications to single molecule measurements drawn from the recent literature.
The subject of the investigation are single atoms, for instance isolated in a Paul trap, which are driven by laser fields while their resonance radiation is measured by photon counters. For a rather wide class of experimental setups or theoretical models, a method is developed to determine the statistics of the photons observed. In contrast to other approaches it avoids referring to 'continuous measurements' or similar concepts, but tries to stay as far as possible within the framework of ordinary quantum mechanics. The method is illustrated by application to simple models.
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.
We investigate theory of single-photon control from a two-level single-molecule source irradiated by laser pulses of various shapes and pulse durations in terms of quantum trajectories which link stochastic dynamics of the radiating source with quantum measurement theory. Using Monte Carlo wave function simulation, we analyze the detailed dissipative dynamics of the single-molecule source and the photon statistics as revealed by repeated Gedanken photon measurement on the single radiating source. We show that much of the photon statistics from the two-level single-molecule single-photon sources, including few-photon emission probability, waiting time distribution, and two-time correlation function of the fluorescent light, can be understood qualitatively from the simple picture of Rabi nutation and pi pulse in terms of pulse areas.
Quantitative information is key to unravel molecular processes in all fields of research. Counting by Photon Statistics (CoPS) is a single molecule technique that provides such quantification for fluorescent species. CoPS exploits the photon antibunching effect to infer \nthe number of independent emitters and their molecular brightness from multiple photon detection events. I laid the foundation for high quality results by improving the microscope detection efficiency more than threefold compared to earlier measurements. Using both simulations \nand experiments with defined, DNA-based probes, I investigated the critical interplay of fluorophore properties and analysis parameters. I discovered that measurements at high molecular brightness can be ten times faster than previously established which opens new possibilities for time resolved quantification. The findings stress that the choice of analysis parameters is vital and provide an objective measure of fluorophore eligibility for CoPS. I characterized sixteen \norganic dyes across the visible spectrum based on their molecular brightness and photostability. This study accomplished the transition of CoPS from a proof of concept technique to a widely applicable quantification method. Experiments demonstrated that CoPS can reveal \nthe label number distribution of fluorescent markers, a prerequisite for quantitative investigations in biology. Moreover, I showed that CoPS offers new perspectives for characterization of photophysical processes in photoluminescent materials.