Probing Dynamics of Single Molecules: Non-linear Spectroscopy Approach

TL;DR

This paper investigates a non-linear spectroscopy method for single molecules, analyzing photon emission statistics to extract information about spectral diffusion dynamics and stochastic processes.

Contribution

It provides analytical solutions for photon emission probabilities in a two-level molecule model and explores measurement limitations and information content of the technique.

Findings

Photon statistics reveal stochastic process parameters in fast modulation limit.

Selective limit photon statistics depend on spectral shifts and rates, showing oscillations.

Impulsive pulses are necessary in the fast modulation limit to obtain meaningful data.

Abstract

A two level model of a single molecule undergoing spectral diffusion dynamics and interacting with a sequence of two short laser pulses is investigated. Analytical solution for the probability of n=0,1,2 photon emission events for the telegraph and Gaussian processes are obtained. We examine under what circumstances the photon statistics emerging from such pump-probe set up provides new information on the stochastic process parameters, and what are the measurement limitations of this technique. The impulsive and selective limits, the semiclassical approximation, and the fast modulation limit, exhibit general behaviors of this new type of spectroscopy. We show, that in the fast modulation limit, where one has to use impulsive pulses in order to obtain meaningful results, the information on the photon statistics is contained in the molecule's dipole correlation function, equivalently to continuous wave experiments. In contrast, the photon statistics obtained within the selective limit depends on the both spectral shifts and rates and exhibits oscillations, which are not found in the corresponding line-shape.