Bloch-Siegert shifts and multi-quantum transitions in spin-one systems

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Abstract
The Bloch-Siegert-type shifts and multiple-quantum resonance shifts of a spin-one system subjected to an oscillating radio-frequency applied at right angles to a DC field have been calculated to sixth order in V, the amplitude of the oscillating field, for the single-quantum resonance, and to fourth order in V for the higher resonances. The level crossing criterion appropriate to two-level systems cannot be used here, and a resonance condition based on a previously derived analogue of Shirley's equation for spin-one systems is used instead. The calculation uses degenerate continued-fraction perturbation theory. Numerical calculations were performed in order to obtain the shape of the resonances, and partially check the analytic results. The atomic levels were assumed to be completely stable; the corrections due to finite atomic lifetimes are expected to be small.