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Applied Optics

Overhauser and Jeffries-Abragam Effect in a Four-Level System

M. L. Narchal, William A. Barker

Published Aug 1, 1963• 7 citations
Publisher

Abstract

The method of partial distributions is used to compute the normalized population distribution in an electron-nuclear coupled spin system in which I = S = 1/2. The expressions obtained are more general than those reported previously in that they include the effects of competitive relaxation and competitive radiative induced transition probabilities. It is clear that positive and negative enhancement may be obtained either by the Overhauser or the Jeffries-Abragam effect irrespective of the relative magnitudes of the nuclear Zeeman and hyperfine interaction energies. A small enhancement is not necessarily due to incomplete saturation, but may well be the result of compensating emission and absorption.

DOI
10.1364/ao.2.000787

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The method of partial distributions is used to compute the normalized population distribution in an electron-nuclear coupled spin system in which I = S = 1/2. The expressions obtained are more general than those reported previously in that they include the effects of competitive relaxation and competitive radiative induced transition probabilities. It is clear that positive and negative enhancement may be obtained either by the Overhauser or the Jeffries-Abragam effect irrespective of the relative magnitudes of the nuclear Zeeman and hyperfine interaction energies. A small enhancement is not necessarily due to incomplete saturation, but may well be the result of compensating emission and absorption.
The effect of the hyperfine interaction on collisional relaxation among Zeeman sublevels is evaluated for a J=32J=\frac{3}{2}J=23​ state coupled to nuclear spins of 32\frac{3}{2}23​, 52\frac{5}{2}25​, and 72\frac{7}{2}27​. Standard depolarization experiments, performed on atoms with hyperfine structure, are discussed in terms of relaxation-probability matrices parametrized in terms of the relative collisional-transition probabilities for a nuclear-spin-zero atom. Experimental results involving D2{D}_{2}D2​ optical pumping of 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb are shown to support the approximation of nuclear decoupling in collisional relaxation. The cross sections for electronic collisional relaxation, assuming a van der Waals model for the collisional interaction, are, in units of ${10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2, 1.19 (85Rb^{85}\mathrm{Rb}85Rb-He), 1.09 (85Rb^{85}\mathrm{Rb}85Rb-Ne), 2.44 (85Rb^{85}\mathrm{Rb}85Rb-Ar), 1.13 (87Rb^{87}\mathrm{Rb}87Rb-He), 1.03 (87Rb^{87}\mathrm{Rb}87Rb-Ne), and 2.26 (87Rb^{87}\mathrm{Rb}87Rb-Ar).
The method of partial distributions is used to calculate the population distribution of three level maser systems in which spontaneous emission and cross relaxation as well as thermal relaxation and induced absorption processes are included. The results obtained are in agreement with the solution of the relevant rate equations. The method has the advantage of speed and suggestiveness. Two examples are presented: (1) A three level optical maser is analyzed in which one spontaneous emission transition probability is included. The solution in this example does not make the linear approximation to the Boltzmann factor. (2) A three level microwave maser is analyzed in which one cross relaxation mechanism is included. The solution to this problem by the method of partial distributions does require use of the linear approximation to the Boltzmann factor.
The method of partial distributions is used to calculate the population distribution of three level maser systems in which spontaneous emission and cross relaxation as well as thermal relaxation and induced absorption processes are included. The results obtained are in agreement with the solution of the relevant rate equations. The method has the advantage of speed and suggestiveness. Two examples are presented: (1) A three level optical maser is analyzed in which one spontaneous emission transition probability is included. The solution in this example does not make the linear approximation to the Boltzmann factor. (2). A three level microwave maser is analyzed in which one cross relaxation mechanism is included. The solution to this problem by the method of partial distributions does require use of the linear approximation to the Boltzmann factor.