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Physical Review A

Relaxation, generation, and detection of Zeeman coherences in an optically pumped heavy-alkali-metal vapor

Juan Antonio Vallés, J. M. Alvarez

Published Sep 1, 1994• 8 citations
Publisher

Abstract

The relaxation and generation of multipole orientations in a heavy-alkali-metal vapor in the presence of a weak static magnetic field are theoretically studied both for populations and for Zeeman coherences by taking into account the effects on the evolution of the atomic density matrix of the relaxation processes (by alkali-atom--buffer-gas, alkali-atom--alkali-atom with spin exchange and alkali-atom--cell-wall collisions) and of the optical pumping with any light polarization and spectral distribution. The dependence of the stationary-state multipole orientations on the pumping characteristic parameters is numerically analyzed. The detection process of these orientations is also studied.

DOI
10.1103/physreva.50.2490

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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.

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An effect is demonstrated where off-resonant optical pumping is enhanced by spin-exchange collisions, which enables a high degree of spin orientation to be obtained in alkali-metal atoms. The experiment with room-temperature cesium vapor employs radio-frequency spectroscopy under conditions of the nonlinear Zeeman effect that allow the populations of the individual Zeeman sublevels to be determined. The improved efficiency of atomic orientation leads to a significant reduction of population relaxation out of the state with maximum magnetic quantum number $m$ (stretched state), which is observed as a narrowing of radio-frequency resonances. Spin-exchange collisions play a crucial role in this effect although the applied atomic density $\ensuremath{\sim}$10${}^{11}$ cm${}^{\ensuremath{-}3}$ corresponds to collision rates not greater than several tens of Hz. A simplified theoretical model has been developed to reproduce the measurement results numerically.

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Relaxation Mechanisms in Optical Pumping

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Atomic Orientation by Optical Pumping

W. Franzen, A. G. Emslie

A variation of the usual method of atomic orientation of alkali metal vapors by optical pumping is proposed. This variation consists of employing a single circularly polarized ${D}_{1}$ line as pumping radiation, instead of a mixture of the two $D$ lines. Under these conditions, one magnetic substate of the ground state is transparent to the pumping radiation. It is shown that for a sufficiently intense light source and relatively weak relaxation, the entire population of the vapor will tend to be pumped into this single state, resulting in nearly one-hundred percent atomic orientation. The pumping process is analyzed in detail for sodium vapor illuminated with $3{P}_{\frac{1}{2}}\ensuremath{-}3{S}_{\frac{1}{2}}$ radiation, and the time dependence of the populations of the eight magnetic sublevels of the ground state is computed. It is shown that in the steady state, the light absorption by the vapor is linear rather than exponential with distance. A simple method of measuring relaxation times based on this observation is suggested. The conditions under which the imprisonment of resonance radiation limits the size of the oriented sample are discussed, and it is suggested that the proposed technique will allow the alignment of larger samples than is possible by the usual method of optical pumping.

Physical Review•Dec 15, 1957•88 citations
The relaxation and generation of multipole orientations in a heavy-alkali-metal vapor in the presence of a weak static magnetic field are theoretically studied both for populations and for Zeeman coherences by taking into account the effects on the evolution of the atomic density matrix of the relaxation processes (by alkali-atom--buffer-gas, alkali-atom--alkali-atom with spin exchange and alkali-atom--cell-wall collisions) and of the optical pumping with any light polarization and spectral distribution. The dependence of the stationary-state multipole orientations on the pumping characteristic parameters is numerically analyzed. The detection process of these orientations is also studied.
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.
An effect is demonstrated where off-resonant optical pumping is enhanced by spin-exchange collisions, which enables a high degree of spin orientation to be obtained in alkali-metal atoms. The experiment with room-temperature cesium vapor employs radio-frequency spectroscopy under conditions of the nonlinear Zeeman effect that allow the populations of the individual Zeeman sublevels to be determined. The improved efficiency of atomic orientation leads to a significant reduction of population relaxation out of the state with maximum magnetic quantum number mmm (stretched state), which is observed as a narrowing of radio-frequency resonances. Spin-exchange collisions play a crucial role in this effect although the applied atomic density $\ensuremath{\sim}101010{}^{11}$ cm${}^{\ensuremath{-}3}$ corresponds to collision rates not greater than several tens of Hz. A simplified theoretical model has been developed to reproduce the measurement results numerically.
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.
We present a comprehensive theory of nuclear spin polarization of 3He{}^{3}\mathrm{He}3He and 129Xe{}^{129}\mathrm{Xe}129Xe gases by spin-exchange collisions with optically pumped alkali-metal vapors. The most important physical processes considered are (1) spin-conserving spin-exchange collisions between like or unlike alkali-metal atoms; (2) spin-destroying collisions of the alkali-metal atoms with each other and with buffer-gas atoms; (3) electron-nuclear spin-exchange collisions between alkali-metal atoms and 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe atoms; (4) spin interactions in van der Waals molecules consisting of a Xe atom bound to an alkali-metal atom; (5) optical pumping by laser photons; (6) spatial diffusion. The static magnetic field is assumed to be small enough that the nuclear spin of the alkali-metal atom is well coupled to the electron spin and the total spin is very nearly a good quantum number. Conditions appropriate for the production of large quantities of spin-polarized 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe gas are assumed, namely, atmospheres of gas pressure and nearly complete quenching of the optically excited alkali-metal atoms by collisions with N2{\mathrm{N}}_{2}N2​ or H2{\mathrm{H}}_{2}H2​ gas. Some of the more important results of this work are as follows: (1) Most of the pumping and relaxation processes are sudden with respect to the nuclear polarization. Consequently, the steady-state population distribution of alkali-metal atoms is well described by a spin temperature, whether the rate of spin-exchange collisions between alkali-metal atoms is large or small compared to the optical pumping rate or the collisional spin-relaxation rates. (2) The population distributions that characterize the response to sudden changes in the intensity of the pumping light are not described by a spin temperature, except in the limit of very rapid spin exchange. (3) Expressions given for the radio-frequency (rf) resonance linewidths and areas can be used to make reliable estimates of the local spin polarization of the alkali-metal atoms. (4) Diffusion effects for these high-pressure conditions are mainly limited to thin layers at the cell surface and at internal resonant surfaces generated by radio-frequency magnetic fields when the static magnetic field has substantial spatial inhomogeneities. The highly localized effects of diffusion at these surfaces are described with closed-form analytic functions instead of the spatial eigenmode expansions that are appropriate for lower-pressure cells.
Alkali-metal-vapor magnetometers, using coherent precession of polarized atomic spins for magnetic field measurement, have become one of the most sensitive magnetic field detectors. Their application areas range from practical uses such as detections of NMR signals to fundamental physics research such as searches for permanent electric dipole moments. One of the main noise sources of atomic magnetometers comes from the light shift that depends on the frequency of the pump laser. In this work, we theoretically study the light shift, taking into account the relaxation due to the optical pumping and the collision between alkali atoms and between alkali atoms and the buffer gas. Starting from a full master equation containing both the ground and excited states, we adiabatically eliminate the excited states and obtain an effective master equation in the ground-state subspace that shows an intuitive picture and dramatically accelerates the numerical simulation. Solving this effective master equation, we find that in the light-narrowing regime, where the line width is reduced while the coherent precession signal is enhanced, the frequency-dependence of the light shift is largely reduced, which agrees with experimental observations in cesium magnetometers. Since this effective master equation is general and is easily solved, it can be applied to an extensive parameter regime, and also to study other physical problems in alkali-metal-vapor magnetometers, such as heading errors.
A variation of the usual method of atomic orientation of alkali metal vapors by optical pumping is proposed. This variation consists of employing a single circularly polarized D1{D}_{1}D1​ line as pumping radiation, instead of a mixture of the two DDD lines. Under these conditions, one magnetic substate of the ground state is transparent to the pumping radiation. It is shown that for a sufficiently intense light source and relatively weak relaxation, the entire population of the vapor will tend to be pumped into this single state, resulting in nearly one-hundred percent atomic orientation. The pumping process is analyzed in detail for sodium vapor illuminated with $3{P}_{\frac{1}{2}}\ensuremath{-}3{S}_{\frac{1}{2}}$ radiation, and the time dependence of the populations of the eight magnetic sublevels of the ground state is computed. It is shown that in the steady state, the light absorption by the vapor is linear rather than exponential with distance. A simple method of measuring relaxation times based on this observation is suggested. The conditions under which the imprisonment of resonance radiation limits the size of the oriented sample are discussed, and it is suggested that the proposed technique will allow the alignment of larger samples than is possible by the usual method of optical pumping.