Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Measurements of the hydrogen 2s-2pcoherence using the quantum-beat technique

Robert DeSerio, Carlos González-Lepera, John P. Gibbons, Joachim Burgdörfer, Ivan A. Sellin

Published Jun 1, 1988• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.37.4111

Related papers

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

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.

Physical Review A•Dec 1, 1997•4 citations

Collisional coherent excitation to the n=2 state of hydrogen

Robert V. Krotkov, J. Stone

This paper presents measurements of the Lyman-$\ensuremath{\alpha}$ photons emitted when target gases He, Ar, ${\mathrm{O}}_{2}$, and ${\mathrm{N}}_{2}$ are bombarded by a beam of ground-state hydrogen atoms. The collisions take place in the presence of an axial electric field and the observed Lyman-$\ensuremath{\alpha}$ brightness depends on field direction. This observation is interpreted as evidence for excitation of hydrogen atoms to states which are linear superpositions of $2s$ and $2p$. Measurements are presented of a "mixed" cross section ${\ensuremath{\sigma}}_{\mathrm{sp}}$ which characterizes the degree of coherent excitation. The real part of ${\ensuremath{\sigma}}_{\mathrm{sp}}$ measures the electric dipole moment created by the collision, while the imaginary part measures the rate at which the moment is changing. It is found that these quantities vary substantially over the energy range 3-30 keV, with maximal values being about as large as permitted theoretically. Coherent excitation should be present to some degree in all inelastic collisions and, when measurable, provides new tests of scattering theory. Some implications are also discussed for precision frequency measurements and searches for weak-interaction effects in atomic physics.

Physical Review A•Aug 1, 1980•26 citations

Measurement of S−P Coherence in the Beam-Foil—Excited n=2 State of Atomic Hydrogen

Andreas Gaupp, H. J. Andrä, J. H. Macek

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.

Physical Review Letters•Feb 11, 1974•69 citations

Coherent Excitation of S and P States of the n=2 Term of Atomic Hydrogen

T. G. Eck

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 $S$ and $P$ 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.

Physical Review Letters•Jul 30, 1973•76 citations

Stark-Induced Quantum Beats in H L Y α Emission

H. J. Andrä

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 $|l,j,{m}_{j}〉$ 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 $p$ to that of the $s$ 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.

Physical Review A•Dec 1, 1970•42 citations

Coherent excitation of the n=3 states in hydrogen

Robert V. Krotkov

This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the $n=3$ state by electron bombardment. By coherence is meant that the density matrix describing the atom after the collision has off-diagonal matrix elements in the field-free basis. The differential cross section for producing Balmer-$\ensuremath{\alpha}$ photons at 90\ifmmode^\circ\else\textdegree\fi{} to the electron beam is calculated as a function of an applied longitudinal electric field. The off-diagonal elements show up as a dependence of the observed light on the directions of the electric field. Theoretical results based on the Born approximation are compared with an experiment at 200 and 500 eV. It is pointed out that this method for measuring relative phases of scattering amplitudes can be generally applied and is not restricted to $n=3$ excitation of hydrogen.

Physical Review A•Nov 1, 1975•19 citations
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.
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 ($\ensuremath{-}200\mathrm{k}\mathrm{V}/\mathrm{m}$ 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.
This paper presents measurements of the Lyman-$\ensuremath{\alpha}$ photons emitted when target gases He, Ar, O2{\mathrm{O}}_{2}O2​, and N2{\mathrm{N}}_{2}N2​ are bombarded by a beam of ground-state hydrogen atoms. The collisions take place in the presence of an axial electric field and the observed Lyman-$\ensuremath{\alpha}$ brightness depends on field direction. This observation is interpreted as evidence for excitation of hydrogen atoms to states which are linear superpositions of 2s2s2s and 2p2p2p. Measurements are presented of a "mixed" cross section ${\ensuremath{\sigma}}_{\mathrm{sp}}$ which characterizes the degree of coherent excitation. The real part of ${\ensuremath{\sigma}}_{\mathrm{sp}}$ measures the electric dipole moment created by the collision, while the imaginary part measures the rate at which the moment is changing. It is found that these quantities vary substantially over the energy range 3-30 keV, with maximal values being about as large as permitted theoretically. Coherent excitation should be present to some degree in all inelastic collisions and, when measurable, provides new tests of scattering theory. Some implications are also discussed for precision frequency measurements and searches for weak-interaction effects in atomic physics.
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.
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.
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.
This paper is a theoretical discussion of a "coherence effect" in the excitation of hydrogen atoms to the n=3n=3n=3 state by electron bombardment. By coherence is meant that the density matrix describing the atom after the collision has off-diagonal matrix elements in the field-free basis. The differential cross section for producing Balmer-$\ensuremath{\alpha}$ photons at 90\ifmmode^\circ\else\textdegree\fi{} to the electron beam is calculated as a function of an applied longitudinal electric field. The off-diagonal elements show up as a dependence of the observed light on the directions of the electric field. Theoretical results based on the Born approximation are compared with an experiment at 200 and 500 eV. It is pointed out that this method for measuring relative phases of scattering amplitudes can be generally applied and is not restricted to n=3n=3n=3 excitation of hydrogen.