Spectral diffusion trajectory

In fact, single molecule spectroscopy (SMS) experiments have recently become a reality. The first experiments were performed on pentacene (the chromophore) in a p-terphenyl crystal [8-10]. I will focus here on the experiments of Ambrose, Basche, and Moemer [9, 10], which involved repeated fluorescence excitation spectrum scans of the same chromophore. For each chromophore molecule they found an identical (except for its center frequency) Lorentzian line shape whose line width is determined by fast phonon-induced fluctuations (and by the excited state lifetime), as discussed above. However, for each of a number of different chromophore molecules Moemer and coworkers found that the chromophore s center frequency changed from scan to scan, reflecting spectral dynamics on the time scale of many seconds The transition frequencies of each of the chromophores seemed to sample a nearly infinite number of possible values. Plotting the transition frequency as a function of time produces what has been called a spectral diffusion trajectory (although the frequency fluctuations are not necessarily diffusive ). These fascinating and totally... 

In the second type of experiment that measures single molecule spectral dynamics one performs repeated fluorescence excitation scans of the same molecule. In each scan the line shape is described as above, but now there is the possibility that the center frequency of the line will change from scan to scan because of slow fluctuations. Thus one can measure the center frequency as a function of time, producing what has been called a spectral diffusion trajectory. This trajectory can, in principle, be characterized completely by the spectral diffusion kernel of Eqs. (16) and (19), but of course it must be understood that only the slow Kj < 1 /t) TLSs contribute. In fact, the experimental trajectories are really too short to be analyzed with this spectral diffusion kernel. Instead, it is useful [11, 12] to consider three simpler characterizations of the spectral diffusion trajectories the frequency-frequency correlation function in Eq. (14), the distribution of frequencies from Eq. (15), and the distribution of spectral jumps from Eq. (21). For this application of the theoretical results, in all three of these formulas j should be replaced by s, the labels for the slow TLSs. 

Spectral diffusion trajectories due to spontaneous (rather than light-induced) fluctuations have been measured for Tr in PE [14] and for TBT in PIB [15,16]. As in the crystalline case these trajectories reflect dynamics of the slow TLSs. The three published trajectories show that in two cases the chromophore visits a large number of frequencies, and in one case, only four. In this latter case the chromophore is presumably strongly coupled to two TLSs. A correlation function analysis was applied to the PIB system, but for neither the PIB nor the PE system was a temperature-dependent study reported. 

Extremely exciting experimental data for glasses are now beginning to emerge. It has been shown that line shape measurements, fluorescence intensity fluctuations, and spectral diffusion trajectories can all be used to probe TLS dynamics on different time scales. Furthermore, as has been emphasized already, these experiments on individual molecules will provide information complementary to that obtained from more traditional echo and hole burning experiments. At this point what we need is more data. In an ideal world all three of the above experiments would be performed on the same individual molecule at a variety of temperatures, and then would be repeated on many molecules, and all of the above would be repeated for several different systems. Although the basic theoretical apparatus is in place for analyzing these experiments, more refined theoretical results will surely be needed. 

Fig. 2.5. Examples of single-molecule spectral diffusion for pentacene in p-terphenyl at 1.5 K. (A) A series of fluorescence excitation spectra each 2.5 s in duration spaced by 0.25 s showing discontinuous shifts in resonance frequency, with zero detuning = 592.546 nm. (B) Trend or trajectory of the resonance freqnency over a long time scale for the molecule in (a). For details, see [34]...

When the number of perturbing defects in the molecular surroundings is large, either because the molecule is very close to an extended crystal fault, or because the crystal is extremely disordered, the number of preferred frequencies is so large that it becomes impossible to recognize a preferred set. Then, the number of jumps between two scans of the laser is large, and the trajectory looks like a onedimensional random walk, or a spectral diffusion. Such a pattern appears for jumping molecules in strained and disordered crystals at the end of an optical fiber. 

We are beginning to understand chaotic structure in a way not seen before. Numerical methods of measuring chaotic and regular behaviour such as Fast Liapunov Indicators, sup-maps, twist-angles, Frequency Map Analysis, fourier spectal analysis are providing lucid maps of the global dynamical behaviour of multidimensional systems. Fourier spectral analysis of orbits looks to be a powerful tool for the study of Nekhoroshev type stability. Identification of the main resonances and measures of the diffusion of trajectories can be found easily and quickly. Applied to the full N-body problem without simplification, use of these tools is beginning to explain the observed behaviour of real physical systems. 

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