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American Journal of Physics

Optical Pumping Theory and Experiments

Reuben Benumof

Published Feb 1, 1965• 19 citations
Publisher

Abstract

The theory of several experiments involving optical pumping is presented in a simplified form. Vector methods are employed to discuss the hyperfine energy levels of an atom in a weak magnetic field, and, for the purposes of considering relaxation time, the system is assumed to have only two effective levels. The Breit-Rabi equation for the ground-state hyperfine Zeeman energy levels of an alkali atom is derived from the Schrödinger equation to facilitate the interpretation of the quadratic Zeeman effect. A number of suggestions for practical optical pumping experiments are made.

DOI
10.1119/1.1971285

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The distribution of population in the ground-state sublevels of an optically pumped alkali-metal vapor has been found to be strongly dependent on the mechanism assumed responsible for relaxation. Two modes of optical pumping zero mixing and complete mixing in the excited state, and three modes of alkali relaxation, uniform, Zeeman, and electron randomization, are considered. Calculations of the sublevel relative populations are made in terms of experimentally measurable parameters for all six combinations of pumping and relaxation modes. Optical-pumping transient signals are then used to demonstrate that alkali relaxation due to wall collisions is of the low-frequency "Zeeman" variety, while relaxation due to alkali-rare-gas collisions takes place through randomization of the spin of the alkali valence electron. Equations for the rate of change of the electronic spin polarization are derived for all cases, and are found to be nonexponential, in contrast with the case of an alkali of zero nuclear spin.

Physical Review•Jan 7, 1966•30 citations
The theory of several experiments involving optical pumping is presented in a simplified form. Vector methods are employed to discuss the hyperfine energy levels of an atom in a weak magnetic field, and, for the purposes of considering relaxation time, the system is assumed to have only two effective levels. The Breit-Rabi equation for the ground-state hyperfine Zeeman energy levels of an alkali atom is derived from the Schrödinger equation to facilitate the interpretation of the quadratic Zeeman effect. A number of suggestions for practical optical pumping experiments are made.
An extension of a theory of the relaxation, generation, and detection of Zeeman components in the presence of a weak static magnetic field to experiments where hyperfine coherences are also involved is presented. Our study focuses on the geometrical aspects of the optical-microwave double-resonance experiments without considering the transition-profile related phenomena. We determine the coupled evolution equations of the Zeeman and hyperfine components of the atomic density matrix in the irreducible formalism and calculate the stationary solutions to these equations. \textcopyright{} 1996 The American Physical Society.
Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.
Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.
According to the quantum theory of the optical-pumping cycle, one can describe the effect of a nonresonant light beam on the different Zeeman sublevels of an atomic ground state by an effective Hamiltonian He{\mathcal{H}}_{e}He​ which depends on the polarization and spectral profile of the incident light. In order to check the structure of He{\mathcal{H}}_{e}He​, we have performed a detailed experimental study of the ground-state energy sublevels of various kinds of atoms perturbed by different types of nonresonant light beams. Attention is paid to the modification of the Zeeman structure due to He{\mathcal{H}}_{e}He​. We have been able to obtain experimentally in the ground state of 199Hg^{199}\mathrm{Hg}199Hg, 201Hg^{201}\mathrm{Hg}201Hg, and 87Rb^{87}\mathrm{Rb}87Rb, Zeeman light shifts that are larger than the width of the levels due to the thermal relaxation. The removal of the Zeeman degeneracy in zero external field, due to a nonresonant light irradiation, is observed by different optical-pumping techniques; the full Zeeman diagram of the perturbed atoms is also determined when a static field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}}_{0}$ is added. We have checked that the effect of He{\mathcal{H}}_{e}He​ can be described in terms of fictitious static electric or magnetic fields. These fictitious fields can be used to act selectively on a given atomic level.
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.
The distribution of population in the ground-state sublevels of an optically pumped alkali-metal vapor has been found to be strongly dependent on the mechanism assumed responsible for relaxation. Two modes of optical pumping zero mixing and complete mixing in the excited state, and three modes of alkali relaxation, uniform, Zeeman, and electron randomization, are considered. Calculations of the sublevel relative populations are made in terms of experimentally measurable parameters for all six combinations of pumping and relaxation modes. Optical-pumping transient signals are then used to demonstrate that alkali relaxation due to wall collisions is of the low-frequency "Zeeman" variety, while relaxation due to alkali-rare-gas collisions takes place through randomization of the spin of the alkali valence electron. Equations for the rate of change of the electronic spin polarization are derived for all cases, and are found to be nonexponential, in contrast with the case of an alkali of zero nuclear spin.