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arXiv:physics/0110053 · Canadian Journal of Physics

Nonresonant effects in one- and two-photon transitions

Ulrich D. Jentschura, Peter J. Mohr

Published Jun 1, 2002• 48 citations
arXivHTMLPDF

Abstract

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

DOI
10.1139/p02-019

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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
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.
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
Theoretical calculations for the 1S → 2S two- photon transition rate in atomic hydrogen are reviewed. They are compared with two experiments via the saturation effects that are observed when three-photon ionization is enhanced by two- photon resonance with the metastable 2S state. There is a significant disagreement between theoretical and experimental results. The disagreement is illustrated by determining the transition rate as a function of intensity for experimental laser profiles: (1) using parameters that give rates in agreement with experimental data, and (2) using theoretical values for the parameters. Finally, experiments that would involve direct observation of the 2S metastable state are considered. It is shown that single-longitudinal-mode laser experiments would provide an accurate measurement of the Rabi frequency for this transition and yield a definitive value for the rate. A Monte Carlo simulation method is used to consider practical effects associated with such an experiment, for example, chirp and ASE noise in the laser. Also, simulations of the multiphoton ionization process in multimode and wide band laser fields are presented.
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 infinite summations over the complete set of unperturbed atomic states appearing in the NNNth-order perturbation theory for multiphoton ionization are performed using the Dalgarno-Lewis method. The relevant transition matrix elements are written in a closed integral form exhibiting all the analytic properties of the amplitude as a function of incident photon energy. The cross sections for two- and three-photon ionization for atomic hydrogen are calculated for both linearly and circularly polarized light with a wide range of photon energy spectrum including the near resonance, and numerical comparison is made with the values obtained by different methods.