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Physical Review Letters

Polarization and Collision-Induced Coherence in the Beam-Foil Light Source

C. H. Liu, STANLEY BASHKIN, D. A. Church

Published Oct 21, 1974• 21 citations
Publisher

Abstract

Polarization up to 15% has been detected in the decay of electronic levels in many-electron monatomic systems which were excited by the beam-foil method, the foil being tilted with its plane at 65\ifmmode^\circ\else\textdegree\fi{} to the particle velocity. Quantum beats were found even with an external magnetic field oriented parallel to the particle velocity, indicating that coherence is produced in the beam-foil interaction itself. Results are reported for various levels in He i, O ii, and Ar ii.

DOI
10.1103/physrevlett.33.993

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Physical Review A•Dec 1, 1970•42 citations
Polarization up to 15% has been detected in the decay of electronic levels in many-electron monatomic systems which were excited by the beam-foil method, the foil being tilted with its plane at 65\ifmmode^\circ\else\textdegree\fi{} to the particle velocity. Quantum beats were found even with an external magnetic field oriented parallel to the particle velocity, indicating that coherence is produced in the beam-foil interaction itself. Results are reported for various levels in He i, O ii, and Ar ii.
The preferential population of magnetic quantum levels of atomic states produced in beam-foil collisions is explained using a density-matrix formulation. The density matrix for the beam in the interior of the foil is evolved in time to obtain the density matrix after emergence from the foil. The dependence upon tilt angle of the foil relative to the beam is calculated. The Stokes parameters of the light emitted by decay of the atomic state are given in terms of the density matrix. Formulas which are valid for arbitrary angular momentum of the atomic state are derived. Comparison with experiment shows good agreement with data.
The cylindrically symmetric beam-foil collision produces excitation and alignment of atom and ion levels similar, but not identical, to that resulting at comparable energies from ion-atom or ion-molecule collisions. When the foil is tilted, the macroscopic change acts on the microscopic scale to produce coherent alignment and orientation of the excited levels. The maximum beam energy range bounding this interaction has not yet been defined. The dynamic interaction which produces these effects is currently not predicted by any theory, although the dynamics of the ions subsequent to the collision are well understood. Refinement of current experimental technique can be expected to better define the final foil surface. The beam-tilted-foil collision promises to be useful in the study of ionic structure via quantum beat, radio-frequency and level-crossing spectroscopy techniques, and may provide a useful probe for certain surface interactions. 4 figs, 48 refs.
We have measured the polarization state of the light emitted in the 4He^{4}\mathrm{He}4He I, $2s^{1}S\ensuremath{-}3p^{1}P$ transition after excitation in a beam-foil experiment and find a partial elliptical polarization which depends upon the tilt angle of the carbon foil relative to the beam axis. This indicates that the emergent beam is oriented as well as aligned as a result of an interaction at the foil surface. The relative excitation cross sections and off-diagonal density-matrix elements have been deduced for the angular-momentum sublevels.
The time evolution of alignment and orientation of excited atoms in an electric field is described using a density-matrix treatment. Orientation is produced by applying a tilted static electric field on levels aligned by beam-foil interaction. The modulation of polarization of the light is observed either inside the zone of constant field, by moving along the atomic beam, or downstream, in the field-free zone, by sweeping the field strength. Two different geometries are used for relative directions of ion beam, electric field vector, and foil normal. Tensor polarizabilities and cross sections for excitation of Zeeman sublevels are deduced from frequencies and amplitudes of quantum beat signals. Results are given for n 1{\mathrm{}}^{1}1D2{D}_{2}D2​ levels of 4i(n=3^{4}\phantom{\rule{0ex}{0ex}}\mathrm{i}\phantom{\rule{0ex}{0ex}}(\mathit{n}=34i(n=3, 4, and 5).
Intensity beats in the emission of $\mathrm{L}{\mathrm{y}}_{\ensuremath{\alpha}}$ from beam-foil excited hydrogen in various static electromagnetic field configurations have been studied. The observed beat frequencies agree with the calculated values, which are independent of the field directions. The beat amplitudes, however, show significant dependence on the field directions relative to the beam. The theory for emission of light from the decay of coherently excited states is applied in the sudden perturbation limit. Agreement with experiment can only be obtained under the assumption that the foil excitation generates initial coherent wave functions ${\ensuremath{\Psi}}_{\mathrm{I},\mathrm{I}\mathrm{I}}=\ensuremath{\alpha}|p,\frac{1}{2},\ifmmode\pm\else\textpm\fi{}\frac{1}{2}〉+\ensuremath{\beta}|s,\frac{1}{2},\ensuremath{\mp}\frac{1}{2}〉$, where ∣l,j,mj〉|l,j,{m}_{j}〉∣l,j,mj​〉 notation and the beam as quantization axis are used. The ratio $\frac{\ensuremath{\alpha}}{\ensuremath{\beta}}$ is then determined, which gives the ratio of the excitation cross section of the ppp to that of the sss states as $\frac{{\ensuremath{\sigma}}_{p}}{{\ensuremath{\sigma}}_{s}}>~4\ifmmode\pm\else\textpm\fi{}1$ at a beam energy of 200 (keV) per atom.