Dynamical theory for photon and photoelectric pulse distributions in single molecule fluorescence

A single two-level molecule driven by CW-laser field and a photomultiplier tube (PMT) are considered as two parts of the united dynamical system connected with each other by photons of molecular fluorescence. Each PMT is characterized by a rate α of photo-effect and by a rate β of PMT recovery. A theory for the photon distribution function w_N(t) and for the photoelectric pulse distribution function f_n(t) for such a system is built up. If times 1/ α and 1/ β characterizing PMT are much shorter as compared to the average time interval 1/ k between two successively emitted photons of fluorescence, the photon and the photoelectron distribution functions coincide with each other, i.e. f_n(t) ≅ w_N(t). A relation between w_N(t) and f_n(t) is studied in detail for the case in which PMT works slower as compared to the rate k of photon emission, i.e. at 1/ α, 1/ β ≥ 1/ k.