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Journal of Physics B Atomic and Molecular Physics

Multiple quantum transitions in optically oriented87Rb vapour

E. Arimondo, R. Corbalán

Published Dec 1, 1974• 8 citations
Publisher

Abstract

In an optically pumped 87 Rb vapour, multiple quantum transitions in the ground state Zeeman sublevels are examined as a function of the radiofrequency field intensity. The experimental results are compared with existing theoretical approaches. Good agreement is found, for the resonance shifts, with the theoretical analysis based on the Hamiltonian solution for the atom plus RF field system. A more refined theory must be developed for interpreting line broadening results.

DOI
10.1088/0022-3700/7/17/022

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In an optically pumped 87 Rb vapour, multiple quantum transitions in the ground state Zeeman sublevels are examined as a function of the radiofrequency field intensity. The experimental results are compared with existing theoretical approaches. Good agreement is found, for the resonance shifts, with the theoretical analysis based on the Hamiltonian solution for the atom plus RF field system. A more refined theory must be developed for interpreting line broadening results.
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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.
We study both theoretically and experimentally three-photon electromagnetically induced transparency and electromagnetically induced absorption resonances in inhomogeneously broadened 85 Rb atomic vapour driven by probe and drive laser radiations. We observe narrow Doppler-free absorption as well as transmission resonances for the probe field when the driving laser field is redshifted from the D1 or D2 lines of 85Rb; the frequency difference between the drive and probe fields is equal to the hyperfine splitting of the ground state of the atoms, and the probe field is tuned to the centre of the Doppler broadened atomic transition. We theoretically study the spectroscopic effect in both homogeneously and inhomogeneously broadened media. Our numerical simulations are in good agreement with the experimental results.
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.
Subnatural-width resonances due to coherent effects in optical pumping at hyperfine (hf) transitions of Rb are investigated using a linearly or circularly polarized single-frequency diode laser beam. The sign and amplitude of the resonances in the fluorescence are measured by scanning the laser frequency over the hf transitions of the Rb D 1 and D 2 lines. The fluorescence perpendicular to the laser beam is detected as a function of magnetic field parallel to the beam propagation and scanned around zero value. In the case of linear polarization of the field, dark resonances are observed for hf transitions with F g → F e = F g -1 and F g → F e = F g , and bright resonances are observed for transitions with F g → F e = F g + 1. This is in agreement with the recently developed theories. For all (except F g = 2→ F e = 3, 85 Rb, D 1 line) hf transitions the sign of the resonances reverses when the polarization of the field changes to circular. The amplitudes of the resonances correspond to the probability of the hf transitions and to the calculated loss rate of the population to the ground hf level not excited by the laser field. The observed narrow resonances (FWHM: few tens of kHz) and their sensitivity to weak magnetic fields are interesting for high-resolution spectroscopy and for development of simple and precise magnetometers.