Resolution Within the Natural Linewidth

Assume that all other line-broadening effects except the natural linewidth have been eliminated by one of the methods discussed in the previous chapters. The question that arises is whether the natural linewidth represents an insurmountable natural limit to spectral resolution. In this section we give some examples of techniques which allow observation of structures within the 

If molecules are excited into an upper level with spontaneous lifetime T = 1/y by a light pulse ending at t = 0, the time resolved fluorescence amplitude is given by 

If a detection method is used which allows to resolve the natural linewidth Y of the transition (e.g., level crossing spectroscopy or observation of quantum beats), the observed intensity profile of the spectral line becomes 

If the detection probability for I(t) is not constant, but follows a time dependence f(t), the detected intensity Ig(t) is determined by the gate function f(t) 

The Fourier transform of Ig(t) now depends on the form of f(t) and may no longer be a Lorentzian. Let us consider some specific examples [13.27], 

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Level-crossing experiments with time-resolved detection following pulsed excitation may even allow a spectral resolution within the natural linewidth. If only those fluorescence photons are detected which have been emitted at times t > ax after the excitation process (a l) the spectral profile of the signal is narrowed [10.92]. This technique allows one to reach a spectral resolution beyond the natural linewidth (see Sect.13.5). 

Assume that all other line-broadening effects except the natural linewidth have been eliminated by one of the methods discussed in the previous chapters. The question that arises is whether the natural linewidth represents an insurmountable natural limit to spectral resolution. At first, it might seem that Heisenberg s uncertainty relation does not allow outwit the natural linewidth (Vol. 1, Sect. 3.1). In order to demonstrate that this is not true, in this section we give some examples of techniques that do allow observation of structures within the natural linewidth. It is, however, not obvious that all of these methods may realty increase the amount of information about the molecular structure, since the inevitable loss in intensity may outweigh the gain in resolution. We discuss under what conditions spectroscopy within the natural linewidth may be a tool that really helps to improve the quality of spectral information. 

In this chapter we discuss several techniques which can reduce or even completely avoid time-of-flight broadening. Some of these methods have already been realized experimentally while others are only theoretical proposals which could not be proved up to now. These techniques allow ultrahigh resolution, in some cases even within the natural linewidth. This raises the interesting question about the ultimate resolution limit and the experimental or fundamental factors that determine such a limit. 

With this technique the Doppler width could be reduced by two orders of magnitude below the natural linewidth, and spectral structures within the Doppler width could be resolved. Examples are the resolution of hyperfine structure components in an 12-beam using a single-mode argon laser (tunable within a few gigahertz) or the investigation of the upper state hfs-splitting in the atomic... 

As a host crystal a p-terphenyl crystal, with a few micrometers in diameter, has been used, which has been doped with a low concentration (10 ) of ter-rylene molecules. The tip of the optical fiber has been cooled to 1.4 K in order to avoid broadening of the fluorescence line via collective phenomena such as interaction with the phonons of the host crystal. The observed linewidth in fact is the natural linewidth (a few tens of MHz Fig. 9.9). The spectral response of fhese individual molecules can now be used for a local analysis of the surface, albeif with relatively low resolution (180 nm) (Fig. 9.10). Further experimental tricks such as electrical field induced Stark shifts can be applied to determine at least the position of the investigated molecules to within a few 10 nm. 

More detailed information on motion within the Cig chains, at least the timescales that are relevant, are obtained by C NMR relaxation studies [5p]. Several C NMR studies of Cig-derivatized silicas and other n-alkyl analogs have been reported [5n,p,37] Even more detail on the motion can be obtained by wide line H NMR spectroscopy (a technique that does not have high resolution) on Cig-silica samples in which deuterium has been selectively substituted for protons [50]. In this approach, the line-narrowing effects of motion on the broad, quadrupole-based H NMR linewidth of a mechanically static sample is modeled theoretically for specific trial motions to elucidate the detailed nature of the motion. As an example. Figure 34.32 shows experimental H spectra, and the corresponding theoretical simulation for a dry sample of (l-d2)-Ci8-silica as a function of temperature. From the theoretical simulations, based on trial... 

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