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Physical Review A

Interaction between a spin-1/2 atom and a strong rf field

T. Yabuzaki, S. Nakayama, Y. Murakami, Toru Ogawa

Published Dec 1, 1974• 52 citations
Publisher

Abstract

Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.

DOI
10.1103/physreva.10.1955

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Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.
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.
The transition probabilities and the shifts of the crossing and anticrossing points of a two-level system (spin-1/2 atom) under the simultaneous influence of a static magnetic field and three orthogonal oscillating rf fields are calculated by using the resolvent formalism in which the rf fields are quantized. A new interference effect, which can be called "crossing of the third kind" in the rf transition, is predicted, and can be interpreted as the interference between different-order transition processes such as single- and two-photon processes, single- and three-photon processes, and so on. Furthermore, for coexistence of the single- and two-photon processes and of the single- and three-photon processes, we can obtain expressions of the transition probabilities (or effective dipole-coupling coefficients) similar to the results obtained in our previous paper, where the interference between single- and two-photon processes were treated by using the time-dependent Schr\"odinger equation.
Energies of the coupled system of a spin 1/2 atom and a strongly oscillating RF field with an arbitrary direction are numerically calculated, and the size and direction of the power shifts of the multiphonon transitions are obtained. The intensity and shape of the multiphoton resonances appearing in optical pumping experiments are also calculated with the semiclassical theory. An optical pumping experiment is performed with caesium vapour to check the validity of the theoretical results, and good agreement is found.
By means of the recursive perturbation method developed by Hioe and Eberly, we present an analytic expression of general fourth-order effects in the frequency shifts of new coherence resonances and multiphoton transitions for the general case that a spin-1/2 atom interacts with an oscillating rf field in optical pumping. Moreover, the validity of the theoretical results is checked by an optical-rf double resonance experiments with cesium vapor, and agreement between observed and calculated results becomes close.
Nonlinear phenomena occurring during interaction between an atom and a strong rf field of resonant or nonresonant frequency are reviewed. The account is given in both semiclassical and consistently quantummechanical languages. The concept of an atom "dressed by the radiation field" in which not only the optical-frequency field but also the radio-frequency field is quantized is presented in detail. The results are summarized of theoretical and experimental studies of multiphoton transitions, radiative shifts of normal magnetic resonance lines, parametric resonance, and coherent resonances under the conditions of optical pumping. The influence of nonresonance rf fields on magnetic properties and the rate of magnetic relaxation of atoms is discussed.
Behavior of the optically pumped atoms in the oscillating rf field is analized classically in terms of the macroscopic magnetization, in the case that the static magnetic field has components both parallel and perpendicular to the rf field. The theory predicts that the g -factor is modified by the rf field when the Hanle effect and the parametric resonance take place, and that the effect makes its appearance in the variation of width and maxima of lines of the Hanle effect and the parametric resonance. The modification of the g -factor is also derived by the quantum mechanical treatment. The theoretical predictions are quantitatively verified by the experiments with cesium vapor.