Theory of single-molecule spectroscopy: Beyond the ensemble average

Single-molecule spectroscopy (SMS) is a powerful experimental technique used to investigate a wide range of physical, chemical, and biophysical phenomena. The merit of SMS is that it does not require ensemble averaging, which is found in standard spectroscopic techniques. Thus SMS yields insight into complex fluctuation phenomena that cannot be observed using standard ensemble techniques. We investigate theoretical aspects of SMS, emphasizing (a) dynamical fluctuations (e.g., spectral diffusion, photon-counting statistics, antibunching, quantum jumps, triplet blinking, and nonergodic blinking) and (b) single-molecule fluctuations in disordered systems, specifically distribution of line shapes of single molecules in low-temperature glasses. Special emphasis is given to single-molecule systems that reveal surprising connections to Lévy statistics (i.e., blinking of quantum dots and single molecules in glasses). We compare theory with experiment and mention open problems. Our work demonstrates that the theory of SMS is a complementary field of research for describing optical spectroscopy in the condensed phase.