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Journal of Physics B Atomic Molecular and Optical Physics

Laser-assisted electron - atom resonance scattering and laser-induced resonance interference

Lars Bojer Madsen, Knud Taulbjerg

Published Mar 28, 1997• 6 citations
Publisher

Abstract

The weak-field soft-photon theory for free - free transitions is generalized to include atomic potentials which support resonances. The present formulation is not restricted by geometrical constraints. In particular, it may be applied in situations where the laser polarization is perpendicular to the electron momentum transfer. In this special geometry, former theories have predicted that laser-assisted electron - atom scattering resonances should appear as pure Breit - Wigner peaks on a vanishingly small background. The present theory includes higher-order terms and shows that the background amplitude may compete with the resonance part to produce characteristic Fano-type resonance signals. Considering tunable radiation fields it is shown that the laser may induce resonance-interference effects. The shapes of overlapping resonances are in general determined by an interplay between resonance scattering amplitudes and a laser-controlled contrast parameter. Characteristic spectral features in the laser-induced overlap between fine-structure components are uniquely related to the distinctly different interference properties of direct and spin-flip amplitudes.

DOI
10.1088/0953-4075/30/6/024

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The weak-field soft-photon theory for free - free transitions is generalized to include atomic potentials which support resonances. The present formulation is not restricted by geometrical constraints. In particular, it may be applied in situations where the laser polarization is perpendicular to the electron momentum transfer. In this special geometry, former theories have predicted that laser-assisted electron - atom scattering resonances should appear as pure Breit - Wigner peaks on a vanishingly small background. The present theory includes higher-order terms and shows that the background amplitude may compete with the resonance part to produce characteristic Fano-type resonance signals. Considering tunable radiation fields it is shown that the laser may induce resonance-interference effects. The shapes of overlapping resonances are in general determined by an interplay between resonance scattering amplitudes and a laser-controlled contrast parameter. Characteristic spectral features in the laser-induced overlap between fine-structure components are uniquely related to the distinctly different interference properties of direct and spin-flip amplitudes.
A modified perturbation theory is developed for the calculation of the time-dependent wave function describing the propagation of an atom in a two-mode laser field. With the mode frequencies nearly equal, a first approximation is obtained that reproduces and extends known results, for both resonant and nonresonant transitions. This lowest-order solution sums terms that describe the absorption of a photon from one mode and emission into the other, leaving the total number of photons unchanged and shifting the momentum of the atom accordingly. Corrections are generated by expansion of a resolvent from which the nearly degenerate states have been projected out. These approximate solutions are used to construct asymptotic states in a formulation of atom-atom scattering in the two-mode field. In close analogy with the soft-photon approximation, a ``soft-pair'' approximation is developed based on the dominance of those asymptotic interactions in which the transfer of energy from the field to the atom is small, allowing one to relate the scattering amplitude in the presence of the field to the field-free amplitude. When the atomic ground state and an excited state are closely coupled by the field, the asymptotic wave function can have mixed parity allowing for long-range contributions to the effective potential. In addition to an enhancement of forward-scattering probabilities, this leads to a threshold anomaly that is analyzed here, in the resonant case, with the aid of a modified effective-range theory.
A quantum statistical theory of resonant optical phenomena is developed for the case when the fluctuations of the laser, used for exciting transitions, are important. The general equations describing the dynamics of a relaxing two-level atom (TLA) are solved exactly for different types of mean values and the two-time amplitude and intensity correlations. The phase-diffusion model is adopted for laser fluctuations. The exact results are used to analyze the effect of laser fluctuations on a number of optical effects-optical free-induction decay, adiabatic following, the spectrum of the scattered light from a relaxing TLA, the energy-absorption spectrum from a weak field, Hanle resonances, etc. In each case, the laser fluctuations are found to affect in an important way the characteristics of the above optical-resonance phenomena. For example, the spectrum of scattered radiation from a TLA has the usual three-peak structure for fields at resonance and with strengths $\ensuremath{\alpha}$ above the threshold and for $\ensuremath{\alpha}\ensuremath{\gg}{\ensuremath{\gamma}}_{c}$; however, now the peak heights (widths) are in the ratio 3x3x3x (23x\frac{2}{3x}3x2​), $x=\frac{[{\ensuremath{\gamma}}_{c}+\frac{({T}_{1}^{\ensuremath{-}1}+{T}_{2}^{\ensuremath{-}1})}{3}]}{[2{\ensuremath{\gamma}}_{c}+{T}_{2}^{\ensuremath{-}1}]}$, where ${\ensuremath{\gamma}}_{c}^{\ensuremath{-}1}$ is the correlation time for laser phase fluctuations. For ${\ensuremath{\gamma}}_{c}\ensuremath{\gg}\ensuremath{\alpha}$, one gets a single-peak spectrum. The laser field is treated as a second-quantized field with excitation in either a coherent state or a Fock state. The results, obtained by straightforward perturbation theory, but valid for arbitrary values of the relaxation parameters, detuning, and the laser correlation time, are also presented.
We have extended our previous analysis of diatom laser-induced excitation transfer, illustrated by several examples, to include modifications due to laser-induced resonances. Compact and rigorous final results have been obtained through the use of a projection-operator scheme in combination with the ``symmetric-top'' basis set and a full quantal treatment of the radiation field. The principal limitations on our analysis are a neglect of fine-structure coupling and a simplifying assumption that the ground electronic manifold supports no bound nuclear states. Simple order-of-magnitude estimates of the predicted resonant cross sections also are provided.
Coherent effects in the interference of overlapping laser-induced resonances in helium atoms are considered. The simultaneous action of single-mode radiation of the 294-nm second harmonic of a cw dye laser and a 1064-nm Nd:YAG laser on helium atoms provides the overlap of two resonances induced by transitions from the 1 s 2 s 1 S and 1 s 4 s 1 S helium levels. The shape of the overlapping laser-induced resonances in the rotating-wave approximation is described by analytic expressions, which depend on the laser radiation intensities and the ratio of laser frequencies.
States behaving like autoionizing states can be selectively induced by laser radiation into one of the continuum spin channels in the photoionization of polarized excited alkaki atoms. As a result of destructive or constructive interference between the direct ionization channel and those introduced by the dressing laser radiation, the cross section of this specific spin component is completely suppressed or enhanced, while leaving the other spin channel unaffected. The qqq parameter which determines the line shape of the Fano-type resonance can be resonantly tuned as a function of the dressing laser frequency.
Steady electric and magnetic fields can stimulate frequency mixing of two laser waves in ensemble of free atoms. In addition to coherence conditions, the steady fields may induce additional resonance singularities essentially enhancing the cross section for scattering the sum-frequency wave. Interference between different components of the electric- and magnetic-field induced frequency summation amplitudes may cause significant effects on the efficiency of conversion. The dependence on the incident wave polarization and the atomic resonance structure is calculated analytically for the frequency mixing in atoms with a singlet structure of the ground and resonance states. Numerical estimates for the quantitative characteristics of the effect are presented for helium, alkali-earth and mercury atoms in their groundn1S0-state in the case of the two-photon resonance on excited singlet states with angular momentum 0, 1, and 2.