We investigate the distribution of the number of photons emitted by a single molecule undergoing a spectral diffusion process and interacting with a continuous wave laser field. The spectral diffusion is modeled based on a stochastic approach, in the spirit of the Anderson–Kubo line shape theory. Using a generating function formalism we solve the generalized optical Bloch equations and obtain an exact analytical formula for the line shape and Mandel’s parameter. The line shape exhibits well-known behaviors, including motional narrowing when the stochastic modulation is fast and power broadening. The Mandel parameter, describing the line shape fluctuations, exhibits a transition from a quantum sub-Poissonian behavior in the fast modulation limit to a classical super-Poissonian behavior found in the slow modulation limit. Our result is applicable for weak and strong laser fields, namely, for arbitrary Rabi frequency. We show how to choose the Rabi frequency in such a way so that the quantum sub-Poissonian nature of the emission process becomes strongest. A lower bound on is found and simple limiting behaviors are investigated. A nontrivial behavior is obtained in the intermediate modulation limit, when the time scales for spectral diffusion and the lifetime of the excited state become similar. A comparison is made between our results and previous ones derived, based on the semiclassical generalized Wiener–Khintchine formula.
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8 May 2005
Research Article|
May 06 2005
Super- and sub-Poissonian photon statistics for single molecule spectroscopy
Yong He;
Yong He
Department of Chemistry and Biochemistry,
Notre Dame University
, Notre Dame, Indiana 46556
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Eli Barkai
Eli Barkai
Department of Chemistry and Biochemistry,
Notre Dame University
, Notre Dame, Indiana 46556 and Department of Physics, Bar Ilan University
, Ramat Gan 52900, Israel
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J. Chem. Phys. 122, 184703 (2005)
Article history
Received:
November 16 2004
Accepted:
February 16 2005
Citation
Yong He, Eli Barkai; Super- and sub-Poissonian photon statistics for single molecule spectroscopy. J. Chem. Phys. 8 May 2005; 122 (18): 184703. https://doi.org/10.1063/1.1888388
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