2004/11/14 by Yong He, Eli Barkai
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Advanced Fluorescence Microscopy Techniques #Continuous wave #Excitation #Excited state #Motional narrowing #Photon #Quantum #Quantum Information and Cryptography #Quantum optics and atomic interactions #Rabi frequency #Semiclassical physics #Spectral line #Spectroscopy #Stochastic process #cond-mat.mes-hall #cond-mat.stat-mech #physics.chem-ph #quant-ph
paper · pdf · doi:10.1063/1.1888388
published as J. of Chemical Physics Vol. 122 p. 184703 (2005) · 14 Phys. Rev style pages, 10 figures
arxiv created 2004/11/14 · openalex publication_date 2005/05/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 Q 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 Q 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.