Theory for Frequency-Resolved Photon Emission Statistics in Single-Molecule Fluorescence Spectroscopy

We derive the moment generating function for photon emission from a single molecule driven by laser excitation. The frequencies of the fluoresced photons are explicitly considered. Calculations were performed for the case of a two level dye molecule, showing that measured photon statistics will display a strong and nonintuitive dependence of detector bandwidth. Moreover it is demonstrated that the anti-bunching phenomenon associated with negative values of Mandel's Q parameter, results from correlations between photons with well separated frequencies.