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Physical Review A

Effect of radiation trapping on the polarization of an optically pumped alkali-metal vapor

D. Tupa, L. W. Anderson, David L. Huber, James E. Lawler

Published Feb 1, 1986• 51 citations
Publisher

Abstract

Calculations are presented of the limitations imposed by radiation trapping on the electron spin polarization produced in an alkali-metal vapor by optical pumping in a large magnetic field. It is found that electron spin polarizations of 90% are possible with Na densities up to ${10}^{19}$ atoms/${\mathrm{m}}^{3}$ and ground-level relaxation times of 150 \ensuremath{\mu}s in a large magnetic field using a cylindrical geometry of radius 7.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ m.

DOI
10.1103/physreva.33.1045

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Calculations are presented of the limitations imposed by radiation trapping on the electron spin polarization produced in an alkali-metal vapor by optical pumping in a large magnetic field. It is found that electron spin polarizations of 90% are possible with Na densities up to 1019{10}^{19}1019 atoms/m3{\mathrm{m}}^{3}m3 and ground-level relaxation times of 150 \ensuremath{\mu}s in a large magnetic field using a cylindrical geometry of radius 7.5\ifmmode\times\else\texttimes\fi{}10\ensuremath−3{10}^{\mathrm{\ensuremath{-}}3}10\ensuremath−3 m.
Calculations of the limitations imposed by radiation trapping on the polarization of an alkali-metal atomic beam by optical pumping are presented. In an atomic beam radiation trapping limits the density of alkali-metal atoms that can be highly polarized by optical pumping. This density is about 1/3 the density of an alkali-metal vapor that can be highly polarized by optical pumping. In a low magnetic field the maximum intensity of an atomic beam that can be optically pumped is a few particle milliamperes.
Rate equations for the optical pumping of alkali-metal vapors simultaneously subject to pumping, relaxation in the excited state, and relaxation in the ground state are shown to yield analytic solutions for the alkali-metal electronic and nuclear-spin polarizations in the limit of weak pumping. Nuclear-spin and hyperfine-interaction effects are properly included. Analysis of the double-exponential form of the pumping transient of the ground-state electronic-spin polarization is shown to yield new methods for the measurement of cross sections for collisional relaxation in both the ground and excited states. Formulas are derived that relate relaxation cross sections to experimentally measurable parameters. Formulas describing the influence of nuclear spin on signals obtained from standard depolarization of resonance-radiation experiments also are provided. Ambiguities in earlier optical-pumping experiments and calculations arising from oversimplified descriptions of relaxation processes are discussed.
A variation of the usual method of atomic orientation of alkali metal vapors by optical pumping is proposed. This variation consists of employing a single circularly polarized D1{D}_{1}D1​ line as pumping radiation, instead of a mixture of the two DDD lines. Under these conditions, one magnetic substate of the ground state is transparent to the pumping radiation. It is shown that for a sufficiently intense light source and relatively weak relaxation, the entire population of the vapor will tend to be pumped into this single state, resulting in nearly one-hundred percent atomic orientation. The pumping process is analyzed in detail for sodium vapor illuminated with $3{P}_{\frac{1}{2}}\ensuremath{-}3{S}_{\frac{1}{2}}$ radiation, and the time dependence of the populations of the eight magnetic sublevels of the ground state is computed. It is shown that in the steady state, the light absorption by the vapor is linear rather than exponential with distance. A simple method of measuring relaxation times based on this observation is suggested. The conditions under which the imprisonment of resonance radiation limits the size of the oriented sample are discussed, and it is suggested that the proposed technique will allow the alignment of larger samples than is possible by the usual method of optical pumping.
A vapor of paramagnetic atoms, under conditions in which electronic spin exchange takes place faster than collisional spin relaxation, should acquire a spontaneous spin polarization when illuminated by unpolarized light tuned to excite only certain ground-state atomic hyperfine levels. In magnetic fields above a certain size, the atomic polarization has two stable states, either parallel or antiparallel to the field. Experiments to demonstrate this effect and explore possible applications may be feasible by the use of alkali-metal vapors.