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Physical Review

Frequency Shifts in Atomic Beam Experiments

L. Evans

Published Feb 5, 1969• 0 citations
Publisher

Abstract

In certain triple-loop atomic beam experiments reported in the literature, a shift in the resonance frequency was observed on reversing the direction of the $C$ field. This shift is explained by assuming that the rf field changes in direction along the transition region, which causes the moving atom to experience a frequency different from that of the basic oscillatory frequency. All the observed properties of the shift can be accounted for by the explanation given.

DOI
10.1103/physrev.178.430

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In certain triple-loop atomic beam experiments reported in the literature, a shift in the resonance frequency was observed on reversing the direction of the CCC field. This shift is explained by assuming that the rf field changes in direction along the transition region, which causes the moving atom to experience a frequency different from that of the basic oscillatory frequency. All the observed properties of the shift can be accounted for by the explanation given.
In radio frequency (RF) experiments on aligned atoms (e.g. optical double resonance) new phenomena can be found in the case of longitudinal excitation if a strong oscillating RF field is used: both the positions of the RF resonances (RF shift) and the widths (power broadening) depend on the direction of the light observed and on the state of its (linear) polarisation. This applies to the main (single-quantum) transitions as well as the (odd) multi-quanta transitions. These effects have been observed in an experiment on aligned mercury atoms in the metastable 6 3 P 2 state and have been confirmed by numerical calculations based on the semiclassical approach.
Resonance transition probabilities for a system in the presence of oscillatory perturbations at two or more different frequencies are discussed. It is shown that if resonance transitions are induced by a perturbation at one frequency, then the presence of the other perturbations at nonresonant frequencies alters the resonance frequency for the first perturbation. Theoretical expressions for the alteration of the resonance frequency are derived. Various applications of the derived formulas are discussed, including resonance experiments with more than one oscillatory field, molecular beam experiments in a nonuniform constant field, evaluation of "collision-narrowing" effects in nuclear paramagnetic resonance, etc. The effects of the extraneous oscillatory perturbations are shown to be especially important if their frequencies are close to Bohr frequencies for the perturbation.
Cs and Rb atomic vapors have been optically pumped in their ground states. The optical/rf-field configuration used allowed for the optical detection of magnetic resonance spectra with subkilohertz resolution by a pump–probe beam technique, in which the free-precessional motion of spins is recorded in the time domain. A six-level system serves as a model to describe the dependence of the observed spectra on the optical frequencies involved. With an intense laser beam applied during the free-precession period, Zeeman light-shift effects are observed. The spatial electric-field distribution of the laser beams and particle diffusion have to be taken into account to let us explain the observed magnetic resonance line shapes adequately.
We have proposed to use the sensitivity function to account for frequency shifts in atomic spectroscopy. This method applies to all interrogation schemes and is of particular interest when the atomic evolution cannot be calculated analytically. We have proposed a simple method to experimentally measure the sensitivity function and tested it in the case of a multi-Rabi interrogation (TE/sub 013/ cavity). The results, in good agreement with numerical simulations, give a clear explanation of the frequency shift observed on our frequency standard.
By means of the dressed atom concept examined theoretically by Cohen-Tannoudji and Haroche, the misalignment effects of an oscillating rf-field in optical-rf double resonances are investigated. We present a fully quantum mechanical calculation of higher-order effects in the frequency shifts of new coherence resonance for the general case that a spin-1/2 atom interacts with the oscillating rf-field in optical-pumping. It is analytically shown that the new type resonances can occur even by taking account of higher-order effects in the perturbation theory for the oscillating rf-field whose direction makes a special angle from that of a static field, and that the direction of the shift of the resonance field is not along that of the static field but perpendicular to that of the oscillating field. Theoretical results are compared with optical-pumping experiments of cesium vapor.