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Canadian Journal of Physics

Optical pumping as a relaxation process

Jacques Vanier

Published Jul 15, 1969• 17 citations
Publisher

Abstract

A theory of optical pumping is given in which the interaction between the radiation and the ensemble of atoms is treated as a random perturbation. The theory gives the pumping rate and the light shift magnitude. The results are compared with those already published.
DOI
10.1139/p69-188

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Physical Review•Nov 5, 1967•249 citations
A theory is derived for the relaxation of hyperfine-level populations, which is caused by an interaction of atoms with solid surfaces during steady-state optical pumping. The relaxation rate is found through a joint solution of the optical-pumping equation and the transport equation for the optical radiation. Disorienting surfaces of various geometric configurations are considered: (a) two parallel planes; (b) the lateral surface of a cylinder; and (c) the entire surface of a cylinder: with weak pumping. Numerical values are found for the relaxation rates for Rb--He and Rb--Ar systems under various conditions. Analytic expressions are derived for the limiting cases of strong and weak pumping. The relaxation rate with steady-state pumping differs in most cases of practical importance from the rate given by the Franzen expression (W. Happer, Rev. Mod. Phys. 44, 169 (1972)); the differences are in magnitude, in the pressure dependence, and in the dependence on the size of the system.
After the brief discussion of the internal degrees of freedom of atomic systems, we give an overview of how these variables can acquire nonvanishing average values in an ensemble of atoms. Optical pumping was one of the first experimental schemes that allowed physical systems to be pushed far from equilibrium through the interaction with light, a direct consequence of angular momentum conservation and the symmetry properties of the interaction between atoms and radiation. Principle and overview Phenomenology Optical pumping (Happer 1972) is one of the earliest examples wherein optical radiation qualitatively modifies the properties of a material system. In its original implementation, it corresponds to a selective population of specific angular momentum states, starting from thermal equilibrium. In the idealised process depicted in Figure 5.1, the light brings the atomic system from the initially disordered state, in which the populations of degenerate levels are equal, into an ordered state where the internal state of all atoms is the same. If we consider only the material system, it appears as if the evolution from the initially disordered state into an ordered state, where the population of one level is higher than that of another level, violated the second law of thermodynamics. This process does not proceed spontaneously, however. It is the interaction with polarised light that drives the system and increased disorder in the radiation field compensates for the increase in the population difference in the material system (Enk and Nienhuis 1992).
Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.
Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.
Real and virtual absorption of weak monochromatic light is analyzed with semiclassical radiation theory. The influence of the light on the atoms is described by an effective ground-state Hamiltonian operator, and the effect of the atoms on the light is described by a dielectric susceptibility operator. These operators are expressed explicitly in terms of familiar ground-state observables, angular factors, oscillator strengths, and plasma dispersion functions. The theory gives a comprehensive description of optical pumping, light shifts, and light modulation due to real and virtual absorption of light, and several new effects are predicted. Repopulation of the atomic ground state from a polarized excited state is not considered in this paper.