Doppler broadening, eliminating

Even in a molecule the size of benzene the resolution achieved in this way is sufficient to investigate the dynamic behavior of individual rotational states. For this it is necessary to eliminate the Doppler broadening of the rovibronic transitions. Two methods have been applied (i) the elimination of Doppler broadening in a Doppler-free two-photon-transition and (ii) the reduction of Doppler broadening in a molecular beam. Measurements of the dynamic behavior have been performed in the frequency [3] and time domain [4]. We will briefly summarize the results from high-resolution measurements and discuss the conclusions on the intramolecular decay mechanism. Then it will be discussed how the intramolecular dynamics is influenced by the attachment of an Ar or Kr atom to the benzene molecule, leading to a weakly bound van der Waals complex. 

The measurements of 2s — Is transitions in magnetically trapped hydrogen have achieved a relative accuracy of one part in 1012 [21] by means of two-photon spectroscopy which eliminates the first-order Doppler broadening. It is hoped that this technique will allow the measurement of the Is — 2s transition with the accuracy limited only by the shape of the transition line dictated by quantum electrodynamics, i.e. to a few parts in 1015. Further, if the center of the Is — 2s line could be determined with the accuracy of a few parts in 103 of its width, the relative accuracy for this transition would increase to a few parts in 1018. 

First order Doppler broadening can be eliminated by using a standing wave geometry (i.e. oppositely running waves) to excite the two-photon transition. The fractional second order Doppler shift, v1 c2, is less than 2 x 10-16 at a temperature of 1 mK. 

Two-photon spectroscopy may also be used to obtain highest-resolution spectra. Doppler broadening, which originates in the random motion of molecules in the gas phase, prevents individual rotational lines of a vibronic transition from being resolved in conventional spectroscopy. However, if two photons of extremely monochromatic light coming from exactly opposite directions are absorbed simultaneously, the Doppler shifts of the two photons just cancel each other and the Doppler broadening is eliminated. As... 

Figure 1.18. Part of the two-photon spectrum of benzene at different resolutions a) vibrational structure of the S - S transition, b) Q branch of the most intense vibrational line (I4i) with a resolution 5v limited by the Doppler broadening, and c) elimination of the Doppler broadening which yields individual rotational lines (by permission from Neusser and Schlag, 1992).

The Doppler-broadened background can be eliminated if the pump beam is chopped and the transmitted probe intensity is monitored through a lock-in amplifier that is tuned to the chopping frequency. According to (2.36), we obtain for a sufficiently weak probe intensity the Doppler-free absorption profile... 

The Doppler-broadened baekground with the residual Doppler width from the divergence of the molecular beam ean completely be eliminated by chopping the two laser beams at two different frequeneies fi, fi, and monitoring the signal at the sum frequency /i -I- /2 (intermodulated fluorescence. Sect. 2.3.1). This is demonstrated by the insert in Fig. 4.25. The linewidth of the Lamb dips in Fig. 4.25 is below 1 MHz and is mainly limited by frequeney fluctuations of the cw single-mode dye laser [453],... 

After the recoil and Doppler broadening have been eliminated, the limiting resolution now is the natural linewidth of the excited nuclear state. This is related to the average lifetime of the excited state before it decays by emitting the y-ray. A Lorentzian line is represented by the relation ... 

The Doppler-broadened background with the residual Doppler width from the divergence of the molecular beam can completely be eliminated by chopping the two laser beams at two different frequencies /i, /2, and monitoring the signal at the sum frequency f + fi (intermodulated fluorescence,... 

The inherent resolution of collinear-beam spectroscopy is still limited by the residual Doppler broadening. In beams with a broad velocity distribution the labeling of one velocity class by optical pumping, probed in a second Doppler-tuning zone, was exploited already before narrow Doppler widths were achieved. The complete elimination of the first-order Doppler effect in resonant two-photon absorption on Ne I has been discussed in Section 3.3, in connection with a precision measurement of the relativistic Doppler effect. A similar experiment was performed on In I, where the 29p Rydberg state was excited from 5p Pi/2 via 6s Si/2 and detected by field ionization. The linewidth caused by the laser jitter can be reduced to the transit-time limit of a few hundred kilohertz. 

Doppler broadening in gases can readily be eliminated by manipulation of experimental conditions. One way to achieve this is to do spectroscopy on supersonic gas jets, in which the translational velocity distribution can be made to resemble a delta function along the jet direction (i.e., the velocity distribution... 

The elimination of Doppler broadening in this experiment allows the clear observation of hyperfine structure that arises from the interaction of electronic and nuclear angular momenta. The total atomic angular momentum is... 

In this section we will describe a number of high-resolution methods, in which the extremely narrow linewidth of single-mode lasers is utilized. Various ways of eliminating Doppler broadening have been investigated during recent years, leading to the development of Doppler-free laser spectroscopic techniques. The effective linewidth that is experimentally obtained is determinated by a number of effects ... 

We have already discussed the two-photon absorption process [9.187] (Sect. 9.1.3c). Normally, the signals are Doppler broadened, and high resolution is not obtained even if narrow-band lasers are used. However, a very important observation was made as early as 1970 by Chebotayev and co-workers [9.188]. The Doppler broadening can be eliminated if the two photons are extracted in such a way that one is supplied from one of two counter-propagating laser beams and one from the other beam. For a certain atom with a velocity component v along one direction of propagation, the energy in-... 

Extremely high laser intensities can be achieved with the pulsed systems discussed in Sect. 8.7.2. Experiments using such systems are surveyed in Sect. 9.6. A further aspect of the extreme performance achievable with laser techniques is the ultra-narrow bandwidth achievable in CW single-mode laser systems as discussed in Sect. 8.5.1. In order to benefit from this, the Doppler broadening must be eliminated. The different techniques of Doppler-free laser spectroscopy arc discussed in Sect. 9.7. Finally, the ultimate resolution achievable by laser cooling and trapping techniques is discussed in Sect. 9.8. 

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