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Canadian Journal of Physics

The Expected Performance of an Optical Pumping Light Source, and the Kinetics of Optical Pumping of 23S13He

J. M. Daniels, Roland S. Timsit

Published Mar 1, 1971• 19 citations

Abstract

A practical light source for optical pumping necessarily excites transitions other than those which it is desired should be excited. It is shown that a pumping light source for 23S13He may be characterized by three parameters, which describe the transition rates for Δm = ±1, and 0, transitions under standard conditions. Expressions are derived relating these parameters to the geometry of the light source. The equation which describes the flow of angular momentum into 3He is formulated, using these parameters, the light flux, the lifetime of the metastable atoms, and collisional mixing in the 23P states. This equation is solved to give the polarization which may be attained, and the rate at which the polarization is built up. A modification of this equation is also given, which takes into account moderate trapping of resonance radiation. An expression is also derived which relates the polarization of 3He to the intensity of the scattered pumping light.

DOI: 10.1139/p71-070

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A practical light source for optical pumping necessarily excites transitions other than those which it is desired should be excited. It is shown that a pumping light source for 23S13He may be characterized by three parameters, which describe the transition rates for Δm = ±1, and 0, transitions under standard conditions. Expressions are derived relating these parameters to the geometry of the light source. The equation which describes the flow of angular momentum into 3He is formulated, using these parameters, the light flux, the lifetime of the metastable atoms, and collisional mixing in the 23P states. This equation is solved to give the polarization which may be attained, and the rate at which the polarization is built up. A modification of this equation is also given, which takes into account moderate trapping of resonance radiation. An expression is also derived which relates the polarization of 3He to the intensity of the scattered pumping light.

Abstract The features of fluorescence and transmission signals in optical pumping of dilute gases with non‐coherent light sources are discussed in terms of a generalized signal function. Using the spherical tensor operator formalism kinetic equations for the atomic state multipoles as well as rate equations for spontaneous emission and absorption are derived. In these rate equations the kinetics of the atomic system expressed by the, generally, time dependent state multipoles of the atomic distribution in the ground or excited state is weighted by the optical signal parameters to give a signal function, which is explicitly adapted to the experimental conditions of observation.

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 optical pumping parameters that modify the pure-state pseudo-Stokes parameters in an electron-superelastic-scattering experiment are calculated for the 3

^{2}

{\mathit{S}}_{1/2}

(F=2)--

{3}^{2}

{\mathit{P}}_{3/2}

(F) transitions of Na. A QED model is used to describe the laser excitation. It is found, that while the magnitude of the pumping parameter K' associated with circularly polarized excitation is close to unity for other than weak laser intensities, the value of the parameter K, associated with linearly polarized light, differs significantly from unity and is dependent on such experimental conditions as laser intensity, laser detuning, laser beam profile, and the Doppler width of the atomic transition. Methods for measuring K are suggested.

We derive quantum-mechanical kinetic equations for the matter density $\ensuremath{\rho}$ and radiation density matrix

{\mathit{S}}_{1/2}

, which describe optical pumping phenomena. The resultant kinetic equations are a set of coupled nonlinear equations for $\ensuremath{\rho}$ and

R

. With appropriate linearizations, we can obtain the present theories of optical pumping. The nonlinear equations describe multiple scattering and line narrowing due to imprisonment of resonant radiation. We show that the coupled equations for $\ensuremath{\rho}$ and

R

are equivalent to coupled equations for $\ensuremath{\rho}$ and a generalized polarization matrix II, whose matrix elements are the second moments of

R

. The polarization matrix II constitutes a complete description of linear phenomena in the same manner as present theories describe optical pumping phenomena by using the matter density matrix $\ensuremath{\rho}$ alone. As a consequence of our nonphenomenological treatment of radiation, we can provide a completely microscopic treatment of the externally modulated light-beam experiment of Bell and Bloom. We show that the atom absorbs the modulation envelope directly from the external thermal light beam in the same way that the atom absorbs transverse polarization directly from the light beam in optical pumping experiments.