Theoretical Studies of Single Molecule Spectroscopy at Room Temperature

This talk is motivated by recent room-temperature single molecule experiments, which measure the optical spectrum along single molecular trajectories and monitor the molecular dynamics and chemical kinetics of individual reactive systems. These experiments contain new information that requires theoretical models and interpretations. Several aspects of single molecule spectroscopy are analyzed:(1) Event-averaged single molecule quantities are calculated, with the prediction of the echo signal in the joint event probability distribution function^[1]. Similar to the photon echo phenomenon, the single molecule echo signal measures solvent effects on chemical kinetics. (2) The statistics of single molecule blinking events are often correlated to underlying quantum mechanisms. The distribution functions of waiting-time sequences are examined for several quantum processes, including electron transfer, solvent relaxation, laser-induced emission, and single quantum-dot blinking^[2]. (3) Single molecule measurements of heterogeneous diffusion reveal deviations from the Gaussian distribution of Brownian motion. As a quantitative measure, the non-Gaussian indicator decays asymptotically to zero according to 1/t for finite time correlation, but saturates at a plateau value for power-law correlation.