Experiments with Radiofrequency Transitions

Flguic 1. Apparatus for atomic beam magnetic resonance. 

Finally, optical pumping and double resonance have opened the way to experiments where the species under study can be confined in closed resonance cells, whereas Rabi s technique relied on the spatial separation of atoms or molecules in a beam arrangement. Also, the new methods allowed the investigation of ions that cannot be studied with a Rabi-type apparatus. 

Books on microwave spectroscopy have been published, e.g., by Gordy, Smith, and Trambarulo, by Townes and Schawlow, and by Chantry.  

---

Electron spin resonance spectroscopy is formally similar to NMR if one considers an unpaired electron as taking the role of a spin -1/2 nucleus in an NMR experiment. However, because of the much greater size of the electron magneton (the Bohr magneton) versus the nuclear magneton, much weaker external fields are employed in order to observe transitions with radiofrequency radiation. As a result, coupling interactions between the electron and magnetic nuclei may require a treatment beyond that of first-order perturbation theory. 

With the envisioned higher resolution, it should be possible to determine a better value of the electron/proton mass ratio from a precise measurement of the isotope shift. And a measurement of the absolute frequency or wavelength should provide a new value of the Rydberg constant with an accuracy up to 1 part in 10, as limited by uncertainties in the fine structure constant and the mean square radius of the proton charge distribution. A comparison with one of the Balmer transitions, or with a transition to or between Rydberg states could provide a value for the IS Lamb shift that exceeds the accuracy of the best radiofrequency measurements of the n=2 Lamb shift. Such experiments can clearly provide very stringent tests of quantum electrodynamic calculations, and when pushed to their limits, they may well lead to some surprising fundamental discovery. 

Fig. 6.—Diagrammatic Representation of the Spin-pumping Mechanism for an INDOR Experiment. [Throughout, the observing radiofrequency is centered on the X-2 transition. The upper part depicts the irradiation of the A-1 transition, and the lower, that of A-2. The connectivity relationship for the energy levels corresponding to these transitions is given in the center it is clear that transition X-2 has an energy level in common with both the A-1 and the A-2 transitions.]...

CW ENDOR is considered in this section pulse ENDOR is dealt with below. The instrumentation is usually based around a computer-controlled CW ESR spectrometer and is commercially available. A radiofrequency coil, capable of handling up to 1 kW poweg is used to introduce the NMR frequencies. The coil is contained in a special resonant cavity. Various modulation strategies are employed to improve the signal-to-noise ratio. In order to carry out the ENDOR experiment, the spectrometer is set for a given line in the ESR spectrum. The microwave power is increased to just beyond the saturation level, and then the selected NMR frequency is swept. Two NMR transitions are observed at the frequencies ... 

Recently, HD+ ions have been cooled to 50 mK and trapped in a linear radiofrequency trap [88], This made it possible to measure the rovibrational transition v,N = 0,2 v, N = 4,3 with an absolute accuracy of 0.5 MHz. By making use of the sensitivity coefficient from Ref. [87], one can see that this accuracy translates into a 5 X 10 (5 ppb) accuracy for p.. Note that modern molecular theory of HD+ has achieved a comparable accuracy [89]. Thus, a direct comparison between theory and experiment allows the determination of the absolute value of p. to 5 ppb. 

Spectroscopic experiments in which the species under study interacts with a laser light field and a radiofrequency field can usually be divided into three steps (i) the preparation of an ensemble of particles such that the energy level population becomes noticeably different from thermal equilibrium, (ii) the stimulation of rf transitions, and (iii) the detection of the rf transitions. The steps are mostly carried out subsequently, which... 

Laser-microwave spectroscopy based on nonlinear phenomena developed from the type of experiments on molecules already discussed in Section 3.2 which make use of optical pumping or double resonance. Occasionally, the laser and the rf power were high enough to create the nonlinear phenomena mentioned above, i.e., to saturate the transitions involved and/or to induce multiphoton transitions. The intermediate level in, e.g., two-photon transitions did not have to be a real state but could be virtual as well. Therefore, a drawback often encountered in earlier infared laser-microwave experiments could be avoided if the laser transition frequency did not exactly coincide with the molecular absorption line the Stark or Zeeman effect had to be used for tuning. This results in an undesired line splitting. With laser-microwave multiphoton processes, however, the laser can be operated at its inherent transition frequency. Exact resonance with molecular lines is then achieved by using a nonlinear effect, i.e., a radiofrequency quantum is added to or subtracted from the laser frequency (see Figure 28). 

Pulsed ENDOR. In both the inversion recovery (Fig. 5b) and stimulated echo experiment (Fig. 5c), the echo amplitude is influenced by a radiofrequency pulse applied during the interpulse delay of length T, if this pulse is on-resonance with a nuclear transition. In the former experiment, such a pulse exchanges magnetization between inverted and noninverted transitions, so that echo recovery is enhanced (Davies ENDOR) (32). In the latter experiment the on-resonance radiofrequency pulse induces artificial spectral diffusion, so that the echo amplitude decreases (Mims ENDOR) (33). These pulsed ENDOR experiments exhibit less baseline artifacts and are easier to set up compared with CW ENDOR experiments, as the required mean radiofrequency power is smaller and the ENDOR effect does not depend on a certain balance of relaxation times. Davies ENDOR is better suited for couplings exceeding 1-2 MHz, while Mims ENDOR is better suited for small couplings, for instance matrix ENDOR measurements. 

Figure 7.12 Direct detection of multiple quantum coherences in Yusa et al. experiment. Varying the intensity of the radiofrequency field induces multiple quantum transitions which appear as the oscillations observed in the resistance measured across the split gate. Adapted with permission from [20].

---