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Journal of Physics B Atomic and Molecular Physics

Bloch-Siegert shifts in resonances between excited states

David A. Andrews, G Newton

Published Jun 21, 1976• 10 citations
Publisher

Abstract

Expressions are presented for the Bloch-Siegert shift appropriate to electric dipole resonance experiments between excited states, when the maximum change in lifetime due to the applied field is used as the criterion for determining the resonance centre. The results differ from those reported by Silverman and Pipkin (1972) in the magnitude of the power shift, and in that the present authors predict an additional power-independent shift. The effect of neighbouring levels on the power shift is calculated, and shown to be substantial in certain cases.

DOI
10.1088/0022-3700/9/9/010

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Expressions are presented for the Bloch-Siegert shift appropriate to electric dipole resonance experiments between excited states, when the maximum change in lifetime due to the applied field is used as the criterion for determining the resonance centre. The results differ from those reported by Silverman and Pipkin (1972) in the magnitude of the power shift, and in that the present authors predict an additional power-independent shift. The effect of neighbouring levels on the power shift is calculated, and shown to be substantial in certain cases.
The two-level rotating wave approximation for two-photon excitations in dipolar molecules is modified to include the effects of the Bloch-Siegert shift in the two-photon resonance energy. The resulting analytical results are used to establish a criterion for when Bloch-Siegert effects are important and the relevance of these effects are compared for fixed laser-molecule configurations versus orientationally averaged results. Two-level model molecules, with parallel permanent and transition dipoles, are used in this work and the effects of Bloch-Siegert shifts are discussed for resonance profiles, time-dependent populations of the excited state, and time-averaged excitation rates. Bloch-Siegert shifts can have pronounced effects on resonance energies and the shape of resonance profiles and, for example, on the magnitudes and the temporal locations of the maxima in the temporal evolution of the time-dependent properties of the system.
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.