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Journal of Physics B Atomic Molecular and Optical Physics

On the effect of the orientation of the optical pump beam in magnetic resonance experiments

Wilhelmus M. Ruyten

Published Jun 14, 1990• 4 citations
Publisher

Abstract

Using a novel semiclassical approach, the authors analyse the resonance behaviour of spin-1/2 atoms subjected to static and oscillating magnetic fields. Unlike a number of previous calculations, the orientation of the pump beam is taken into account explicitly. Thus it is shown that much previous work is valid only if the pump beam is along the static magnetic field. They also show how one such previous calculation can be generalised, namely that based on diagonalisation of the Floquet Hamiltonian.

DOI
10.1088/0953-4075/23/11/004

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Journal of the Physical Society of Japan•Sep 15, 1976•2 citations
Using a novel semiclassical approach, the authors analyse the resonance behaviour of spin-1/2 atoms subjected to static and oscillating magnetic fields. Unlike a number of previous calculations, the orientation of the pump beam is taken into account explicitly. Thus it is shown that much previous work is valid only if the pump beam is along the static magnetic field. They also show how one such previous calculation can be generalised, namely that based on diagonalisation of the Floquet Hamiltonian.
It is shown that, in modulated magnetic resonance on spin-1/2 systems, the time-averaged absorption signal of the optical pump beam can be obtained directly from the dressed-atom energy eigenvalues of the Floquet Hamiltonian for arbitrary orientations of the optical pump beam, namely, by a straightforward generalization of Shirley's well-known result [Phys. Rev. 138, B979 (1965)]. Analytical and numerical results derived from this generalized diagonalization technique are compared with the vanishing damping solution of the Bloch equations from the preceding paper [W. M. Ruyten, Phys. Rev. A 42, 4226 (1990)] and are shown to be in complete agreement with the latter.
The resonance behavior of magnetic and optical two-level systems under the influence of strong modulated fields is studied in detail by solving the Bloch equations in the limit of vanishing damping, namely, in terms of matrix continued fractions. Thus both analytical and numerical results are obtained for the positions of the various multiple quantum resonances in the time-averaged as well as modulated interaction components. Specifically, the role of the orientation of the optical pump beam in magnetic-resonance configurations is investigated, and it is shown that there are several classes of resonances for which the behavior of the system is independent of the orientation of the pump beam. These are the geometries in which the static and oscillating magnetic fields are either orthogonal or parallel, the geometries leading to Haroche-like resonances (which, however, play a special role in modulated interaction components also), and a previously unknown class, labeled saddle-point resonances. However, other than for these special classes, the behavior of the system depends generally on the orientation of the optical pump beam, unlike as implied in some previous work on this problem. As in the recently studied case of a fully amplitude-modulated optical interaction [W. M. Ruyten, Phys. Rev. A 40, 1447 (1989)], it is found that the resonances in modulated interaction components are generally doubly branched, with one branch duplicating the resonances found in the time-averaged component. A new feature found for not-fully-amplitude-modulated and phase-modulated, off-resonance optical excitation (or magnetic resonance with nonparallel or nonorthogonal static and oscillating magnetic fields) is the occurrence of an extra type of resonance in modulated components of the interaction that cannot, like all other resonances of the system, be classified as power-shifted multiple quantum transitions.
This article reviews the early investigations of Series on the resonance absorption and fluorescence of light by samples of oriented atoms dagger subjected to static and oscillatory magnetic fields. These investigations include experiments on optical-radiofrequency double resonance, light beats in double resonance, circulation of coherence in optical pumping, and time-biasing in level-crossing spectroscopy. It then describes some selected laser spectroscopy experiments involving the interaction of optically oriented atoms with static magnetic fields that were stimulated by the earlier work of Series, including experiments on hyperfine structure quantum beats, cascade quantum beats, ground-state quantum beats in transmission, and optogalvanic detection of atomic coherences. Finally, it describes some current work which uses static magnetic fields to manipulate the external variables (momentum and position) of laser-cooled oriented atoms, with applications in the rapidly developing field of atom optics and atom interferometry.
The optical pumping of Cs atoms with light of the D 1 line under magnetic resonance conditions is numerically calculated. This calculation is done to check the suggestion that an unexpectedly strong influence of the polarization of the pumping light on the resonance signals of transverse alignment, which we observed experimentally, is caused by the coupling between orientation and alignment by means of the magnetic field and/or the pumping light. This suggestion has been confirmed: upon circularly polarized pumping, the shape of the signal line of transverse alignment proved to be similar, as well as in the experiment, to the shape of the signal line of transverse orientation and was sharply different from the shape of the line of alignment observed upon linearly polarized pumping. For metastable 23 S 1 4He atoms, in accordance with the experimental data, the calculated shape of the signal line of transverse alignment is found to be independent of the polarization of the pumping light. The calculations also confirm the possibility of a reverse effect: the influence of alignment on orientation, which manifests itself in the occurrence of orientation upon pumping with unpolarized light under magnetic resonance conditions. For Cs atoms exposed to a field of ∼0.6 Oe, the largest contribution to this effect is yielded by the field coupling of orientation and alignment, whereas, for metastable 23 S 1 4He atoms, the largest contribution is made by the light coupling of these polarization moments.
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.