Exact Solution for the Influence of Spectral Diffusion on SingleMolecule PhotonStatistics.pdfVIP

Exact Solution for the Influence of Spectral Diffusion on Single-Molecule Photon-Statistics Y. He, E. Barkai Department of Chemistry and Biochemistry, Notre Dame University, Notre Dame, IN 46556. 3 (Dated: February 2, 2008) 0 0 We investigate the distribution of number of photons emitted by a single molecule undergoing a 2 spectral diffusion process and interacting with a continuous wave field. Using a generating function formalism an exact analytical formula for Mandel’s Q parameter is obtained. The solution exhibits c transitions between: (i) Quantum sub-Poissonian and Classical super-Poissonian behaviors, and (ii) e fast to slow modulation limits. Our solution yields the conditions on the magnitude of the spectral D diffusion time scales on which these transitions are observed. We show how to choose the Rabi frequency in such a way that the Quantum sub-Poissonian nature of the emission process becomes 9 strongest, we find Ω2 = ΓSD+Γ where ΓSD (Γ) is the spectral diffusion (radiative) contribution to Γ 2 ] the width of the line shape. h c PACS numbers: 82.37.-j, 05.10.Gg, 33.80.-b, 42.50.Ar e m - Physical, Chemical, and Biological systems are inves- molecule undergoing a stochastic spectral diffusion pro- t a tigated in many laboratories using single molecule spec- cess. For that aim we use the powerful generating func- t troscopy [1]. The investigation of the distribution of num-