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Journal of Physics B Atomic and Molecular Physics

Power shifts of multiphoton transitions in a spin1/2system

T. Yabuzaki, Y Murakami, T Ogawa

Published Jan 11, 1976• 24 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/9/1/002

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Physical Review A•Jan 1, 1974•10 citations
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.
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 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.
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.
For pt.I see Chem. Phys. Lett. vol.96, p.464 (1983). The non-linear multiphoton excitation dynamics of two-level systems under the influence of two strong linearly polarised monochromatic fields is studied exactly for the first time along the semiclassical many-mode Floquet theory. The present approach relaxes the restrictions of the conventional generalised rotating-wave approximation (GRWA) and allows correct treatment of various non-linear features such as power broadening, resonance shift, asymmetry in absorption lineshape, etc. By extending the nearly degenerate perturbative method of Salwen (1955), approximate analytical expressions for transition probabilities are obtained for multiphoton resonance processes for which (n+1) photons of one field are absorbed, whereas n photons of the other field are emitted, where n is an arbitrary integer. Detailed comparison of the analytical, the GRWA and the numerically exact results is given. Also presented is a case study of the time evolution of spin 1/2 systems in multi-quantum NMR transitions driven by pulsed bichromatic radiofrequency fields.
By expanding the atomic density matrix in powers of the light intensity, it is possible to derive simple formulas for the light shifts and optical broadening of magnetic-resonance lines in optical pumping experiments. Thus, we have obtained for the first time approximate analytic formulas for the light shifts in Zeeman multiplets with spins greater than 1/2. The predicted light shifts for a high-spin atom are similar to those for a spin-1/2 atom, and shifts due to real and virtual transitions can be identified. However, in contrast to the situation with a spin-1/2 atom, the light shifts for a high-spin atom depend on the magnitude of the rf field, and the shifts for the longitudinal and transverse components of orientation and alignment are not necessarily the same.