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Journal of Physics B Atomic Molecular and Optical Physics

Multiple resonant photon scattering on the hydrogen atom and the shift of the photon intensity distribution

Leonti N Labzowsky, Dmitry A. Solovyev

Published Jul 24, 2004• 7 citations
Publisher

Abstract

It is shown that the average energy of the emitted photons does not coincide with the average energy of the incident photons in the process of resonant photon scattering on an atom. This happens because of the asymmetry of the natural line profile caused by the nonresonant corrections and by the dependence of the transition rates on the frequency. In the case of the Lyman-α transition in hydrogen, . The effect can be much larger if ‘artificial’ asymmetry of the intensity distribution in the photon source with respect to the resonance frequency takes place. In the latter case, the difference is close to the accuracy of the recent experiments on the Lyman-α frequency measurements.

DOI
10.1088/0953-4075/37/16/005

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It is shown that the average energy of the emitted photons does not coincide with the average energy of the incident photons in the process of resonant photon scattering on an atom. This happens because of the asymmetry of the natural line profile caused by the nonresonant corrections and by the dependence of the transition rates on the frequency. In the case of the Lyman-α transition in hydrogen, . The effect can be much larger if ‘artificial’ asymmetry of the intensity distribution in the photon source with respect to the resonance frequency takes place. In the latter case, the difference is close to the accuracy of the recent experiments on the Lyman-α frequency measurements.
The process of nonresonant photon scattering on a hydrogen atom is considered as a microscopic model for a quantum-mechanical description of the reflection of light on a mirror. Multiple reflections of this kind then can serve as a model for light storage within a system of mirrors. In combination with modern high-precision measurements of atomic transition frequencies, such a storage of light could allow for new information on the time variation of fundamental constants, such as the fine-structure constant. The intensity distribution shift arising due to the inherent asymmetry of the natural line profile sets an ultimate limit for the preservation of the photon light frequency during storage. In the case of a ‘hydrogen mirror’ this shift appears to be much larger than the relative accuracy of about 10 −15 required in measurements of a time dependence of the fine-structure constant. Possibilities of achieving the required accuracy are discussed.
In the present paper, we consider nonresonant corrections to $2s\text{\ensuremath{-}}ns/nd$ transition frequencies in hydrogen for the experiments based on two-photon spectroscopy. A detailed study of angular correlations of quantum interference effects within the framework of rigorous quantum electrodynamics is given. Closed expressions for the resonant two-photon-scattering cross sections on an atomic level with dependence on all atomic quantum numbers including fine and hyperfine structure are derived. These expressions are applied for the description of experiments based on two-photon spectroscopy with fixing of incident (outgoing) photon polarizations. We demonstrate that, for certain experimental geometries, nonresonant corrections could be significant for the determination of Rydberg constant and proton charge radius.
We investigate nonresonant contributions to resonant Rayleigh-scattering cross sections of atoms. The problematic nonresonant contributions set a limit to the accuracy to which atomic spectra determine energy levels. We discuss the off-resonance effects in one-photon transitions. We also show that off-resonance contributions for the 1S–2S two-photon transition in atomic hydrogen are negligible at current and projected levels of experimental accuracy. The possibility of a differential measurement for the detection of off-resonance effects in one-photon transitions in atomic hydrogen is discussed. PACS Nos.: 31.15-p, 12.20Ds
The theory of the nonresonant corrections, defining the limits of accuracy for the frequency measurements in resonance experiments, is generalized to the situation when the excitation of an atomic state is governed by one Hamiltonian Ĥin and the decay of the excited state is governed by another Hamiltonian Ĥout. The description developed here corresponds to the experimental conditions realized in most accurate modern resonance-frequency measurements of the 2s–1s transition in hydrogen. Two different variants of the theoretical description of the resonance experiments, referred to as "statistical" and "coherent" scenarios, are discussed. The criterion of how to define which scenario should be attributed to a particular resonance experiment is shown. The in and (or) out quantum electrodynamic formalism referring to different asymptotic Hamiltonians is applied. A value of 10–5 Hz, obtained for the accuracy limit in the 1s–2s experiment within the "coherent" scenario, is not so far from the accuracy already achieved experimentally (46 Hz). The accuracy limits for the Lyman-alpha frequency measurements for a "coherent" type of experiment are also obtained and shown to be comparable with recent experimental accuracy.PACS Nos.: 06.20.Jr, 31.10.+z, 32.30Bv
The resonantly enhanced multiphoton ionization of atomic hydrogen is studied for the case of four-photon ionization (three-photon resonant). The time-dependent probabilities, the shape of the resonance profile at different intensities, and the nonlinear index are computed for coherent light at frequencies around the resonance (365 nm). The systematic dependence of the cross section as a function of the principal quantum number of the resonant state (as this tends towards the Rydberg states) is investigated at zero detuning. The probabilities of absorption of one photon more than necessary for the four-photon ionization process (resonantly enhanced above-threshold ionization) is computed and the relevant branching ratios are examined. Then it is shown that the effect of the spatio-temporal structures of the laser pulse is to red shift the maximum of the resonance profile, whereas that of an ideal chaotic light is to blue shift and broaden the resonance peak. The shape, shift, and width of the profile resulting from both these effects are in very fair agreement with the experimental ones.