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Fortschritte der Physik

Signal Parameters in Optical Pumping Experiments

L. Dellit

Published Jan 1, 1979• 0 citations
Publisher

Abstract

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.

DOI
10.1002/prop.19790270102

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Physical Review•Nov 5, 1967•249 citations
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.
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.
The response of a system of coherently pumped atoms to weak electromagnetic perturbing fields is discussed in general terms. The pump field is prescribed, and is assumed to propagate unattenuated through the medium which the (identical) atoms comprise, exciting a particular transition through either electric or magnetic dipole coupling. The perturbing field, which is assumed to act through electric dipole coupling, is allowed to be the (resonant) field emitted by the atoms, a weak external field absorbed by the atoms under resonant conditions, or a resonant or nonresonant wave propagating through the pumped medium. All of these cases are conveniently described within the same general framework, based on an analysis of the (single-atom) two-time dipole-moment correlation function. This function contains nonstationary components as well as stationary ones, owing to the time dependence imposed by the pump field. We are accordingly led to introduce a time-dependent linear susceptibility, which is inhomogeneous and anisotropic, due, respectively, to the variation of the pump phase within the medium and the preferred direction established by the pump-field polarization. Such disparate effects as parametric frequency conversion, emission- and absorption-line splitting, and time-dependent modulation of resonant emission and absorption functions in optical-pumping experiments emerge naturally from a single unified formalism.
The rate of absorption of energy from a weak signal field by an atom driven by a strong pump field is evaluated. The pump field and the signal field are assumed to induce transitions between the same pair of states, and their frequencies are both assumed to lie near the atomic resonance frequency for the transition in question. We find that the signal-field absorption line-shape function takes on negative values, representing stimulated emission rather than absorption, even though population inversion does not occur. This amplification of the signal field, which is most pronounced at high pump intensities, is shown to occur primarily at the expense of the pump field, which suffers an increased rate of attenuation. The results are discussed in the context of a theorem which expresses the absorption line-shape function for general atomic systems in terms of a suitable atomic correlation function.
Description of detailed temporal excitation dyanmics for coherent excitation, such as is produced by idealized laser radiation, contrasts with evaluation of rate coefficients by means of generalized Golden Rule procedures; it requires an appropriate time-dependent Schroedinger equation. When the atom undergoing excitation is also affected by incoherent processes, such as collisions, this equation no longer suffices. The Heisenberg equations, or equivalent density-matrix equations, permit treatment in which coherence and incoherence play comparable roles in the excitation dynamics. Unlike rate equations, such equations must incorporate complexities that originate in the orientation degeneracy expressed by magnetic quantum numbers. In simple cases of coherent excitation, both for single-photon and multiphoton excitation, the sublevels merely require an average of 2J+1 independent Schroedinger equations. Relaxation couples the independent equations. It has been known for some time that appropriate state-multipole operators can simplify the description of many phenomena connected with optical pumping. This memo discusses application of these multipole operators to the description of Raman (or more general multiphoton) coherent excitation. In some simple limiting cases the equations simplify, but in general one has a hierarchy of coupled multipole polarizations and coherences in place of the populations and coherences that occur as variables in nondegenerate systems. 28 refs., 4 figs.
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.