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Journal of Physics B Atomic and Molecular Physics

Semi-classical theory of radiofrequency transitions in a dressed atom

David Thomas Pegg

Published Jan 1, 1972• 4 citations
Publisher

Abstract

The interaction of an atom with two radiofrequency fields was recently examined theoretically by Allegrini and Arimondo (see abstr. A60907 of 1971) in terms of the dressed atom concept. This letter indicates how the same problem can be easily solved by the semi-classical approach of Pegg and Series (see abstr. A36273 of 1970).
DOI
10.1088/0022-3700/5/1/002

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The theoretical behaviour of radiofrequency transitions with Delta m>or=1 in an atomic vapour under the simultaneous action of a longitudinal optical pumping, a static field introducing small decoupling between I and J and a relaxation mechanism is investigated. It is shown that the information contained in the eigenvalues and eigenvectors of the Hamiltonian of the atom 'dressed' by the RF field can be used to simplify significantly the equations of the time evolution of the atomic density matrix. Although an analytical solution is obtained only in a few simple cases a numerical solution is possible for any RF polarization. Several previous treatments are shown to be limiting cases of the general equations presented here. From the analysis of the recent experimental results of Arimondo and Corbalan (1974) on the ground state of 87 Rb, it turns out that the observable quantities are strongly dependent on all the parameters describing the simultaneous action of the pumping cycle, relaxation and the RF interaction. Thus accurate descriptions of the pumping cycle and the relaxation mechanism are required for any comparison with theory of experimental results for the widths and shifts of multiple-quantum transitions.
A semi-classical approach developed by Pegg and Series (1970, 1973) is used to study higher order effects in magnetic resonance produced by an oscillating magnetic field perpendicular to a static field as the oscillating field strength is increased. It is shown that the well-known 'multiple quantum' transitions arise from a semi-classical theory, being transformed into 'single quantum' transitions induced by field harmonics in the most appropriate reference frame for treating the problem. Higher order terms in the Bloch-Siegert shift support those derived by Shirley (1965) by means of Floquet theory, and are in gross disagreement with those derived by Chang and Stehle (1971) from quantum electrodynamics, particularly at very high field intensities where the results are not even qualitatively similar. It should be possible to decide easily between the two approaches by experiment.