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Physical Review A

Power-series analysis of light shifts in optical pumping experiments

W. Happer, Sune R. Svanberg

Published Jan 1, 1974• 10 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.9.508

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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.
Cs and Rb atomic vapors have been optically pumped in their ground states. The optical/rf-field configuration used allowed for the optical detection of magnetic resonance spectra with subkilohertz resolution by a pump–probe beam technique, in which the free-precessional motion of spins is recorded in the time domain. A six-level system serves as a model to describe the dependence of the observed spectra on the optical frequencies involved. With an intense laser beam applied during the free-precession period, Zeeman light-shift effects are observed. The spatial electric-field distribution of the laser beams and particle diffusion have to be taken into account to let us explain the observed magnetic resonance line shapes adequately.
The optical pumping of Cs atoms with light of the D 1 line under magnetic resonance conditions is numerically calculated. This calculation is done to check the suggestion that an unexpectedly strong influence of the polarization of the pumping light on the resonance signals of transverse alignment, which we observed experimentally, is caused by the coupling between orientation and alignment by means of the magnetic field and/or the pumping light. This suggestion has been confirmed: upon circularly polarized pumping, the shape of the signal line of transverse alignment proved to be similar, as well as in the experiment, to the shape of the signal line of transverse orientation and was sharply different from the shape of the line of alignment observed upon linearly polarized pumping. For metastable 23 S 1 4He atoms, in accordance with the experimental data, the calculated shape of the signal line of transverse alignment is found to be independent of the polarization of the pumping light. The calculations also confirm the possibility of a reverse effect: the influence of alignment on orientation, which manifests itself in the occurrence of orientation upon pumping with unpolarized light under magnetic resonance conditions. For Cs atoms exposed to a field of ∼0.6 Oe, the largest contribution to this effect is yielded by the field coupling of orientation and alignment, whereas, for metastable 23 S 1 4He atoms, the largest contribution is made by the light coupling of these polarization moments.
We observe very narrow (\ensuremath{\sim}200 Hz) magnetic resonance lines in alkali vapors with atomic densities much greater than usual and with cell dimensions much smaller than usual. The Zeeman resonance frequency is shifted downward by a large factor, but the spin-exchange broadening vanishes in the high-density limit. This new regime affords important new possibilities for investigating basic interactions in dense alkali vapors, and it also opens the way to miniaturized optically pumped devices.
In an experiment with an optical pumping of 133Cs atoms in the 62 S 1/2 ground state, the line shape of the D 2f magnetic resonance signal for the transverse alignment component oscillating at a double frequency f of a radio-frequency (RF) magnetic field is found to strongly depend on the polarization of pumping radiation. On passage from a linearly polarized pumping light to a circularly polarized (CP) light with a sufficiently strong RF field the ordinary three-peak line with the highest central peak transforms into a two-peak line with a minimum at the center, so that the D 2f signal line resembles the M f signal line of a transverse orientation oscillating at the RF field frequency f. This suggests that the orientation (the first-rank polarization moment (PM)) arising upon CP pumping affects the alignment (the second-rank PM); i.e., the PMs of Cs atoms with different parities of their ranks become coupled. No influence of the polarization of a pumping radiation on the line shape of the D 2f signal is observed in a similar experiment with the 4He atoms in the 23 S 1 metastable state.
A density matrix description of magnetic resonance is constructed, with detailed application to spin J = 1 (or greater) particles. Different types of “monitoring” or “measurement” operators employed in atomic beam, induction, and optical experiments are constructed, and used as a compact introductory basis for the description of resonance line shapes and other characteristics of these experiments. Of particular interest are the similarities and unique differences between the optical experiments known by the names “optical pumping,” “double resonance,” and “light beats” on the one hand, and magnetic induction and atomic beam experiments on the other.
The spectroscopic characteristics of the polarization of 129Xe nuclei in Xe gas by spin exchange with optically pumped Rb atoms is examined in high magnetic field. The high field Zeeman effect provides the spectral dispersion necessary to separate the effects of different light polarizations and incident wavelengths on the pumping cycle. Indirect detection of the D1 line in Rb using 129Xe nuclear magnetic resonance in combination with direct optical detection indicates that conventional container construction significantly decreases the efficiency of the 129Xe polarization. The decreased pumping efficiency is due to randomly polarized photons that can be eliminated by using containers with good optical quality windows. Study of these effects is facilitated by the large Zeeman shifts obtained with multi-tesla fields which resolve the D1 multiplet structure even in the presence of the significant pressure-broadening incells with typical gas pressures of 0⋅1-1 atm.