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Physical Review A

Population, alignment, and coherence of the foil-excited n=2 hydrogen atoms: Polarization observation of the field-dependent quantum beats in the Lyman-α line

Yasuyuki Kimura, Tetsuo Nishida, Keishi Ishii

Published Dec 1, 1997• 4 citations
Publisher

Abstract

We have developed an experimental method for determining the initial density matrix of the foil-excited atoms. The excited hydrogen $(n=2)$ atoms pass through a region of a variable electric field ($\ensuremath{-}200\mathrm{k}\mathrm{V}/\mathrm{m}$ to $+200\mathrm{k}\mathrm{V}/\mathrm{m}$), and the intensity of the Lyman-\ensuremath{\alpha} line (121.6 nm) emitted in a free space downstream is observed. By using a vacuum ultraviolet polarizer, the dependence of the intensities of the polarized components on the electric field, including the field-dependent quantum beats, was measured and it was numerically fitted to a calculation. Thus all the initial density matrix elements were determined in a single measurement. It was found that, in the energy range 100--180 keV, just after the excitation, the electron cloud has higher density in the front side of the ion and the electron probability current is backwards.

DOI
10.1103/physreva.56.4612

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We have developed an experimental method for determining the initial density matrix of the foil-excited atoms. The excited hydrogen (n=2)(n=2)(n=2) atoms pass through a region of a variable electric field (\ensuremath−200kV/m\ensuremath{-}200\mathrm{k}\mathrm{V}/\mathrm{m}\ensuremath−200kV/m to +200kV/m+200\mathrm{k}\mathrm{V}/\mathrm{m}+200kV/m), and the intensity of the Lyman-\ensuremath{\alpha} line (121.6 nm) emitted in a free space downstream is observed. By using a vacuum ultraviolet polarizer, the dependence of the intensities of the polarized components on the electric field, including the field-dependent quantum beats, was measured and it was numerically fitted to a calculation. Thus all the initial density matrix elements were determined in a single measurement. It was found that, in the energy range 100--180 keV, just after the excitation, the electron cloud has higher density in the front side of the ion and the electron probability current is backwards.
Zero-field quantum beats were observed in $\mathrm{L}\mathrm{y}\ensuremath{-}\ensuremath{\beta}$ emission (1026 \AA{}) from hydrogen atoms formed by beam-foil excitation, and the energy dependence of the magnetic-substate cross sections for n=3n=3n=3, l=1l=1l=1 states was determined for beam energies in the range from 230 to 500 keV/atom.
We have measured Lyman-\ensuremath{\alpha} quantum beats from coherently excited hydrogen atoms produced in 85--235-keV proton collisions with a thin helium jet target. Intensity measurements of the radiation emitted at 90\ifmmode^\circ\else\textdegree\fi{} to the beam direction as a function of distance downstream from the target in electric fields both parallel and antiparallel to the beam axis allow extraction of the coherence between the s and p states by Eck's method [Phys. Rev. Lett. 31, 270 (1973)]. Because the jet target allows the collisions to occur in the applied field, we have eliminated the problems associated with field inhomogeneities when gas target cells are used. A strong-intensity peak emitted by excited helium in the target allows a determination of the starting point of the evolution in the field as well as a determination of the effects of experimental averaging. We present the s-p coherence parameters as a function of the projectile energy and compare them with recent theoretical calculations.
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.
The intensity of beam-foil-excited $\mathrm{Ly}\ensuremath{-}\ensuremath{\alpha}$ radiation has been measured in electric fields alternately parallel and antiparallel to the beam. Measurements were made at three energies---110, 165, and 210 keV---and three field strengths. From these data the $S\ensuremath{-}P$ co-herence term ${\ensuremath{\sigma}}_{\mathrm{SP}}$ has been determined. The magnitude of ${\ensuremath{\sigma}}_{\mathrm{SP}}$ is found to be 0.07 at 110 keV, 0.19 at 160 keV, and 0.22 at 210 keV. These results establish that beam-foil-excited hydrogen atoms have a nonzero electric dipole moment.
We have observed second-harmonic generation in atomic hydrogen in the Lyman-α region, with and without an applied dc electric field, Ea. Experiments with a continuous atomic beam were carried out by using a pulsed dye laser tuned to 243 nm for excitation of the n = 2-1 transition. The laser beam was focused 0.4 mm below the H-source nozzle, where the H-atom density was estimated to be 5 × 1013 cm-3. Measurements of second-harmonic generation (SHG) at ~122 nm were made at various electric fields up to ~27 kV/cm. It was shown that the SH signal produced at E a = 0 occurs because of a charge-separation field of ~800 V/cm that is caused by three-photon ionization. Measurements of the SHG and ion current were found to vary as I2 L and I3 L , respectively. At high fields (E a > 10 kV/cm) the SH signal at the center of the Stark-split components decreased somewhat from the peak value, but the ion current (corresponding to photon absorption) approached zero. This observation is a clear demonstration of a similar effect, predicted by Harris et al.1 of efficient nonlinear conversion with induced transparency, and it suggests the possibility of obtaining intense Lyman-a radiation.
An expression is given for the Stark-induced beat signal in the Lyman-$\ensuremath{\alpha}$ radiation from hydrogen atoms in a beam-foil experiment. This expression includes possible contributions to the beat signal from coherent excitation of SSS and PPP states in the beam-foil process. For the case where the electric field is applied parallel to the beam, the coherentexcitation contributions can be separated experimentally from those resulting purely from coherence produced by the electric field, by simply reversing the direction of the electric field.