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Physical Review Letters

rf Spectroscopy on Coherent Populations Using Quantum Beats

Peter B. Kramer

Published May 2, 1977• 2 citations
Publisher

Abstract

The resonant interaction between an rf electric field and a coherent atomic state is studied by monitoring the field-induced changes in the quantum beats after a beam-foil collision. A theory for the interaction is discussed and a preliminary measurement of the fine-structure interval $J=\frac{3}{2}$ to $J=\frac{5}{2}$ in the $n=4$ state of hydrogen is presented.

DOI
10.1103/physrevlett.38.1021

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Physical Review Letters•Mar 28, 1983•17 citations
The resonant interaction between an rf electric field and a coherent atomic state is studied by monitoring the field-induced changes in the quantum beats after a beam-foil collision. A theory for the interaction is discussed and a preliminary measurement of the fine-structure interval J=32J=\frac{3}{2}J=23​ to J=52J=\frac{5}{2}J=25​ in the n=4n=4n=4 state of hydrogen is presented.
This series of articles will describe a novel method of utilizing optical detection of RF-induced fine structure transitions to investigate the population of excited states of fast hydrogen atoms produced by charge exchange collisions between an initial proton beam and various gas or foil targets. In Part I a model of the charge exchange collision and the interaction of the hydrogen beam with an external oscillatory field are considered within the framework of the density matrix formalism and expressions are obtained for the RF lineshapes in terms of the initial atomic density matrix elements.
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.
The strong field-induced quantum beats observed in beam-foil studies of Ly- alpha radiation are obtained in a conventional metastable-hydrogen quenching experiment. The phase relation between the Stark shifted 2s 1/2 -2p 1/2 Lamb-shift oscillations and the much more rapid 2s 1 -2p 3/2 fine-structure oscillations depends on the detailed way in which the quenching field is switched on. Apart from a phaseshift, the results agree with a non-perturbative theoretical calculation which assumes that the field is applied suddenly. Various frequency components of the time-dependent radiation intensity are identified with specific hyperfine transitions or groups of transitions. No adjustable parameters are used for the initial state amplitudes.
Hydrogen atoms are excited into high Rydberg states following fast proton impact on a thin carbon foil. The effects of various electromagnetic fields on these atoms are observed by measuring the integral ionization yield in an additional constant electric field. These experiments reveal oscillations in that yield, regularly spaced as a function of electric field. A model is outlined that quantitatively describes the observed field dependence. This new phenomenon indicates selective excitation of the Stark substates.