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Physical Review A

Superelastic scattering with imperfect laser polarization

Robert E Scholten, V. Karaganov, P. J. O. Teubner, Peter M. Farrell

Published Jul 1, 1999• 3 citations
Publisher

Abstract

The formalism applied to superelastic electron scattering from laser-excited atoms has to date assumed perfect polarization of the laser light. We consider the effects of imperfect polarization, deriving an expression for the superelastic scattering rate from target atoms optically pumped with elliptically polarized light, and show how imperfect polarization effects can be measured and minimized under experimental conditions. In particular, we find that in measuring the scattering for linearly polarized light with a small circular component, the errors are proportional to the undesired circular polarization component and to ${P}_{3}$, the scattering sensitivity to circular light. We also present in detail a polarizer design which generates both linear and circular polarizations, allowing measurement of all scattering polarization sensitivities without requiring interchange of optical elements.

DOI
10.1103/physreva.60.330

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The formalism applied to superelastic electron scattering from laser-excited atoms has to date assumed perfect polarization of the laser light. We consider the effects of imperfect polarization, deriving an expression for the superelastic scattering rate from target atoms optically pumped with elliptically polarized light, and show how imperfect polarization effects can be measured and minimized under experimental conditions. In particular, we find that in measuring the scattering for linearly polarized light with a small circular component, the errors are proportional to the undesired circular polarization component and to P3{P}_{3}P3​, the scattering sensitivity to circular light. We also present in detail a polarizer design which generates both linear and circular polarizations, allowing measurement of all scattering polarization sensitivities without requiring interchange of optical elements.
An expression is derived for the intensity of electrons inelastically scattered from an atomic state prepared by optical pumping. The expression is a sum of state multipoles, the coefficient of each multipole being a spherical harmonic in the polar coordinates of the light direction for circularly polarized light, or the direction of the electric vector for linearly polarized light times a weight function depending on the population of the initial state. These weight functions are given in closed form for both linearly and circularly polarized light.
This thesis presents the results of a series of experiments in which electrons are superelastically scattered from various laser excited states of sodium. The atoms, once in the optically prepared state, are forced to relax via the superelastic collision with an electron. The rate of detection of superelastically scattered electrons was measured as a function of the laser polarisation which enabled pseudo Stokes parameters to be determined. These pseudo Stokes parameters are functions of both optical pumping parameters and atomic collision parameters. The optical pumping parameters describe the laser-atom interaction and the atomic collision parameters describe the electron-atom collision process. Three different laser excitation mechanisms were used to optically pump the atoms into various excited states. The first of these used a single laser tuned to the 32S 112(F'=2 hyperfine state)-~32P312 transition. The excited atoms underwent a superelastic collision with an electron leaving the atom in the ground state and pseudo Stokes parameters were measured as a function of both scattering angle and incident electron energy. The second superelastic experiment, utilised a folded step excitation mechanism which employed two lasers tuned from the two hypethne states of the 32S112 ground state respectively to the 32P312 excited state. Power broadening effects in the single laser experiment cause the atoms to be optically pumped into the F= 1 hyperfine ground state. The laser powers used were not great enough to power broaden the hyperfine ground states and as such the F'= 1 sublevel effectively acted as a sink. The folded step excitation method enabled the excited state population to be increased so that data at larger scattering angles could be obtained. Stokes parameters from both of these experiments which had an incident energy range of 10eV to 30eV and an angular range of 5°-25° were compared to three current electron-atom scattering theories and previous experimental data. Overall, fair to good agreement was found between theory and experiments for the individual Stokes parameters. Losses of coherence was observed at small scattering angles (50.200) at 20eV and 25eV incident electron energies which were poorly modelled by the three different theories. The third superelastic experiment involved the use of two lasers of specified polarisation to stepwise excite the atoms to the 32D512 excited state. Superelastic collisions with incident electron energies of 20eV from the 32D512-*32P312~312 collision were studied at three different scattering angles and pseudo Stokes parameters for the case where the polarisations of the radiation from the lasers were parallel were measured. The single step and folded step laser-atom interactions for it excitation were modelled using a full quantum electrodynamical treatment so that the optical pumping parameters from the single and folded step experiments could be investigated. Equations of motion were derived in the Heisenberg picture and it is shown that for the single laser case 59 equations of motion are required to fully model the interaction and for the folded step ease 78 equations of motion are required. The results of calculations demonstrated that the optical pumping parameters were sensitive to laser intensity, laser detuning and the Doppler width of the atomic beam. The theoretical quantum electrodynamical calculation results were in good agreement with the experimental results.
The optical pumping parameters that modify the pure-state pseudo-Stokes parameters in an electron-superelastic-scattering experiment are calculated for the 3 2^{2}2S1/2{\mathit{S}}_{1/2}S1/2​(F=2)--32{3}^{2}32P3/2{\mathit{P}}_{3/2}P3/2​(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.
Optically pumped alkali metal atoms currently provide a sensitive solution for magnetic microscopic measurements. As the most practicable plan, Faraday rotation of linearly polarized light is extensively used in spin polarization measurements of alkali metal atoms. In some cases, near-resonant Faraday rotation is applied to improve the sensitivity. However, the near-resonant linearly polarized probe light is elliptically polarized after passing through optically pumped alkali metal vapor. The ellipticity of transmitted near-resonant probe light is numerically calculated and experimentally measured. In addition, we also analyze the negative impact of elliptical polarization on Faraday rotation measurements. From our theoretical estimate and experimental results, the elliptical polarization forms an inevitable error in spin polarization measurements.
Collisions studies using optically state selected beams is discussed. Measurements of spin resolved differential cross sections for superelastic scattering of electrons from excited sodium atoms (3P) are reported. The excited states are prepared by laser optical pumping with circularly polarized light thus giving a pure atomic state before the collision. A crossed beam arrangement of sodium atoms and electrons is used with a scattered electron detector. Scattered electron intensity as a function of scattering angle, incident electron energy, and relative orientation of the incident electronic and atomic spins is measured. 8 refs., 10 figs.
Measurements of superelastic scattering of electrons by laser-excited 138Ba^{138}\mathrm{Ba}138Ba(. . .6s6p 1P1^{1}P_{1}1P1​) atoms were carried out. An asymmetry observed by us and previously by Register et al. [Phys. Rev. A 28, 151 (1983)] has been explained using a model of scattering from a target with finite dimensions. This model employed coherence parameters which we calculated in the distorted-wave approximation. The results indicated that the interpretation of coherence experiments in terms of scattering from a pointlike target can lead to serious errors in the deduction of coherence parameters at low scattering angles.