Theoretical Description of Correlation Effects in a Single Molecule

Theoretical description of correlation effects in a single molecule 

The time distribution of the fluorescence photons emitted by a single dye molecule reflects its intra- and intermolecular dynamics. One example are the quantum jumps just discussed which lead to stochastic fluctuations of the fluorescence emission caused by singlet-triplet quantum transitions. This effect, however, can only be observed directly in a simple fluorescence counting experiment when a system with suitable photophysical transition rates is available. By recording the fluorescence intensity autocorrelation function, i.e. by measuring the correlation between fluorescence photons at different instants of time, a more versatile and powerful technique is available which allows the determination of dynamical processes of a single molecule from nanoseconds up to hundreds of seconds. It is important to mention that any reliable measurement with this technique requires the dynamics of the system to be stationary for the recording time of the correlation function. 

A thorough description of the correlation properties of classical and nonclassical light fields can be found in the excellent textbook by Loudon [68]. The correlation functions of the field E t) order correlation function) and of the 

When we measure photons emitted by a single molecule using a quantum detector such as a photomultiplier tube, we interpret /(/) to be the photon counting rate (fluorescence intensity at time i) and we can deduce the fluorescence intensity autocorrelation function by counting the number of photon pairs separated by 

At this point we have arrived at the connection between the correlation function and the density matrix elements described in Section 1.2.2.3, because the conditional probability is just proportional to the matrix element (J22 x) corresponding to the transient solution of the optical Bloch equations for our model three-level system in Fig. 6. Then it follows, 

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