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Zeitschrift für Naturforschung A

Methoden zur Bestimmung von Wirkungsquerschnitten für Spinaustausch und Depolarisation indirekt optisch gepumpter Atome

A. Assfalg, Jochen Fricke, J. Haas, E. Lüscher

Published Oct 1, 1971• 0 citations
Publisher

Abstract

Abstract Two methods are described to derive cross sections for spin exchange and spin depolarization of an indirectly pumped alkali vapor with zero nuclear spin. Either pulsed or sinusoidally modulated radiofrequency can be used to destroy the polarization of the indirectly pumped (secondary) system, while the intensity of the transmitted pumping light is observed. Cross sections follow from the indirectly produced depolarization of the primary system i. e. from the change in pumping light transmission or from the phase angle between the rf modulation and the intensity oscillations of the transmitted light. The quality of the two methods is tested by deriving cross sections for spin exchange between Cs and Rb and for depolarization of Rb in Argon buffer gas.

DOI
10.1515/zna-1971-1004

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Theory of spin-exchange optical pumping of 3 He and 129 Xe

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Importance of Nuclear-Spin Effects in Extracting Alkali Spin-Exchange Cross Sections from Zeeman Optical-Pumping Signals

Hyatt M. Gibbs

The importance of the nuclear spins in the analysis of alkali spin-exchange experiments employing optical pumping by circularly polarized light and performed in low magnetic fields is demonstrated. Since the exchange interaction is an electronic process, the spin-exchange cross section is expected to be essentially independent of the nuclear spins. However, the hyperfine coupling is sufficient to make the expressions for the signals depend upon the nuclear spins. Failure to include the nuclear-spin effects in the analysis can lead to errors as large as several hundred percent in the deduced cross sections. The signal for general nuclear spin is found for the Franzen-type transient experiment and for the Dehmelt-type steady-state experiment in the limit of low light intensity. The results are quite sensitive to the process assumed for the relaxation of the ground-state populations. The solutions are given for a general process in which randomly oriented disorientation fields interact with the spins of the alkali atom only through the electron spin. The steady-state-signal expression includes the effects of self spin exchange and partial disorientation in the excited state. Only the diagonal elements of the density matrix are included.

Physical Review•Aug 30, 1965•36 citations
Abstract Two methods are described to derive cross sections for spin exchange and spin depolarization of an indirectly pumped alkali vapor with zero nuclear spin. Either pulsed or sinusoidally modulated radiofrequency can be used to destroy the polarization of the indirectly pumped (secondary) system, while the intensity of the transmitted pumping light is observed. Cross sections follow from the indirectly produced depolarization of the primary system i. e. from the change in pumping light transmission or from the phase angle between the rf modulation and the intensity oscillations of the transmitted light. The quality of the two methods is tested by deriving cross sections for spin exchange between Cs and Rb and for depolarization of Rb in Argon buffer gas.
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.
It has been demonstrated that optical pumping of alkali atoms (rubidium and cesium) results to a highly efficient indirect optical orientation of metastable He (2 3 S 1 ) atoms. However, in an attempt to perform the inverse experiment (i.e. to receive spin-polarization of alkali atoms upon optical pumping of metastable helium atoms) the result was quite unexpected: the magnetic resonance signal of Cs or Rb atoms was very weak (several hundred times weaker compared to conventional optical pumping of helium in the presence of cesium (rubidium)). We propose an explanation for the unusually small ratio of the magnetic resonance signals from Cs (Rb) and metastable He atoms under condition of optical orientation of He atoms. Except of Cs atoms we are the first to have observed magnetic resonance signals from atoms of 85 Rb and 87 Rb isotopes when using the indirect optical orientation in conditions of helium-rubidium gas discharge plasma. It is shown that the anomaly in the amplitude ratios of the observed MR signals can be explained by the unidirectional action of three different factors (the presence of a large nuclear spin of alkali atoms, depolarization of alkali atoms between collisions, and spin exchange between atoms of rubidium isotopes (for the He-Rb system).
We present a comprehensive theory of nuclear spin polarization of 3He{}^{3}\mathrm{He}3He and 129Xe{}^{129}\mathrm{Xe}129Xe gases by spin-exchange collisions with optically pumped alkali-metal vapors. The most important physical processes considered are (1) spin-conserving spin-exchange collisions between like or unlike alkali-metal atoms; (2) spin-destroying collisions of the alkali-metal atoms with each other and with buffer-gas atoms; (3) electron-nuclear spin-exchange collisions between alkali-metal atoms and 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe atoms; (4) spin interactions in van der Waals molecules consisting of a Xe atom bound to an alkali-metal atom; (5) optical pumping by laser photons; (6) spatial diffusion. The static magnetic field is assumed to be small enough that the nuclear spin of the alkali-metal atom is well coupled to the electron spin and the total spin is very nearly a good quantum number. Conditions appropriate for the production of large quantities of spin-polarized 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe gas are assumed, namely, atmospheres of gas pressure and nearly complete quenching of the optically excited alkali-metal atoms by collisions with N2{\mathrm{N}}_{2}N2​ or H2{\mathrm{H}}_{2}H2​ gas. Some of the more important results of this work are as follows: (1) Most of the pumping and relaxation processes are sudden with respect to the nuclear polarization. Consequently, the steady-state population distribution of alkali-metal atoms is well described by a spin temperature, whether the rate of spin-exchange collisions between alkali-metal atoms is large or small compared to the optical pumping rate or the collisional spin-relaxation rates. (2) The population distributions that characterize the response to sudden changes in the intensity of the pumping light are not described by a spin temperature, except in the limit of very rapid spin exchange. (3) Expressions given for the radio-frequency (rf) resonance linewidths and areas can be used to make reliable estimates of the local spin polarization of the alkali-metal atoms. (4) Diffusion effects for these high-pressure conditions are mainly limited to thin layers at the cell surface and at internal resonant surfaces generated by radio-frequency magnetic fields when the static magnetic field has substantial spatial inhomogeneities. The highly localized effects of diffusion at these surfaces are described with closed-form analytic functions instead of the spatial eigenmode expansions that are appropriate for lower-pressure cells.
Optical pumping of an optically thick atomic vapor typically requires a quenching buffer gas, such as N2, to prevent radiation trapping of unpolarized photons which would depolarize the atoms. We show that optical pumping of a trace contamination of Rb present in K metal results in a 4.5 times higher polarization of K than direct optical pumping of K in the absence of N2. Such spin-exchange polarization transfer from optically thin species is useful in a variety of areas, including spin-polarized nuclear scattering targets and electron beams, quantum-nondemolition spin measurements, and ultrasensitive magnetometry.
The importance of the nuclear spins in the analysis of alkali spin-exchange experiments employing optical pumping by circularly polarized light and performed in low magnetic fields is demonstrated. Since the exchange interaction is an electronic process, the spin-exchange cross section is expected to be essentially independent of the nuclear spins. However, the hyperfine coupling is sufficient to make the expressions for the signals depend upon the nuclear spins. Failure to include the nuclear-spin effects in the analysis can lead to errors as large as several hundred percent in the deduced cross sections. The signal for general nuclear spin is found for the Franzen-type transient experiment and for the Dehmelt-type steady-state experiment in the limit of low light intensity. The results are quite sensitive to the process assumed for the relaxation of the ground-state populations. The solutions are given for a general process in which randomly oriented disorientation fields interact with the spins of the alkali atom only through the electron spin. The steady-state-signal expression includes the effects of self spin exchange and partial disorientation in the excited state. Only the diagonal elements of the density matrix are included.