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Journal of Physics B Atomic and Molecular Physics

Use of the Green's function formalism in resonant two-photon ionisation of alkali-metal atoms. I. Formal theory

M. Jaouen, G Laplanche, A. Rachman

Published Dec 14, 1984• 12 citations
Publisher

Abstract

The resonant two-photon ionisation of alkali-metal atoms is analysed in the dressed-atom picture using the resolvent formalism. The authors define a ladder approximation which is explained with the help of a diagrammatic representation. They show that it is then possible to perform the infinite summations related to perturbation theory which are involved in the matrix elements of the shift operator. The theoretical framework used is the Green's function formalism extended to the spin-orbit scheme adopting the quantum defect method for the atomic model. A numerical example of such a procedure is presented in the case of the caesium atom.

DOI
10.1088/0022-3700/17/23/010

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For pt.I see ibid., vol. 17, p.4643 (1984). The authors apply the theoretical results obtained in a previous paper in order to study the two-photon resonant ionisation of atomic caesium in the neighbourhood of the fine-structure doublet 7P 1/2 -7P 3/2 when the incident light is right-hand circularly polarised. This formalism allows one to consider these two resonant states on an equal footing and it includes the effects of the infinite summations involved in higher-order perturbation theory. The numerical results show that the two-photon resonant ionisation of caesium takes place through an anticrossing of levels, at least in the intensity range studied. The temporal behaviour of the probability exhibits two distinct temporal regimes: linear for long interaction times and cubic for the shorter ones. The intermediate regime is characterised by quantum beats. At high intensity values, it is found that the induced light shift of the resonances is time dependent. It is also shown that the contribution of the higher-order effects may explain the slight departures between the theoretical and experimental results in the off-resonant two-photon ionisation of atomic caesium.

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Non-perturbative completely analytic calculations of the spin polarisation of photoelectrons produced in resonant two-photon ionisation of alkali atoms with exciting and ionising light beams are presented. A well justified alkali atom model composed of four discrete states and the continuum is applied. Contrary to simpler models it enabled one to obtain results valid when the effective resonance Rabi frequency exceeds the frequency separation between the two components forming a given fine-structure energy doublet at resonance. It is shown that in this limit the photoelectron polarisation depends critically on whether a light or heavy alkali atom is ionised. In the former case the photoelectron polarisation is proved to be a copy of the electronic polarisation of the atom, whereas in the case of heavier alkalis it departs appreciably from that of the ionised atom due entirely to spin-orbit perturbation of radial wavefunctions of P discrete states. It is also shown how the author's present results go over into those previously obtained for weaker exciting fields.

Journal of Physics B Atomic and Molecular Physics•Dec 28, 1983•2 citations
The resonant two-photon ionisation of alkali-metal atoms is analysed in the dressed-atom picture using the resolvent formalism. The authors define a ladder approximation which is explained with the help of a diagrammatic representation. They show that it is then possible to perform the infinite summations related to perturbation theory which are involved in the matrix elements of the shift operator. The theoretical framework used is the Green's function formalism extended to the spin-orbit scheme adopting the quantum defect method for the atomic model. A numerical example of such a procedure is presented in the case of the caesium atom.
For pt.I see ibid., vol. 17, p.4643 (1984). The authors apply the theoretical results obtained in a previous paper in order to study the two-photon resonant ionisation of atomic caesium in the neighbourhood of the fine-structure doublet 7P 1/2 -7P 3/2 when the incident light is right-hand circularly polarised. This formalism allows one to consider these two resonant states on an equal footing and it includes the effects of the infinite summations involved in higher-order perturbation theory. The numerical results show that the two-photon resonant ionisation of caesium takes place through an anticrossing of levels, at least in the intensity range studied. The temporal behaviour of the probability exhibits two distinct temporal regimes: linear for long interaction times and cubic for the shorter ones. The intermediate regime is characterised by quantum beats. At high intensity values, it is found that the induced light shift of the resonances is time dependent. It is also shown that the contribution of the higher-order effects may explain the slight departures between the theoretical and experimental results in the off-resonant two-photon ionisation of atomic caesium.
A theoretical method previously developed for the two-photon ionization of alkali-metal atoms is extended to the spin-orbit coupling scheme. We have obtained the Green's function of this problem in the framework of quantum-defect theory and so we have been able to perform the infinite summations related to perturbation theory. The generalized transition probability rates are calculated in the off-resonant and resonant regions, respectively, for polarized incident radiation. Destructive interference effects between the unperturbed atomic states in the infinite summations producing a finite deep minimum in the off-resonant region, are predicted by our theory, both for linearly and circularly polarized incident radiation. A detailed calculation of electron-spin polarization is given. Comparisons of values predicted by the present work with experiment and other theoretical calculations are made for the case of atomic cesium initially in the ground 6S6S6S state.
For the last ten years, the production of polarised electrons has been of increasing interest in different fields of physics. One of the methods used to obtain polarised electron beams is based on the multiphoton ionisation of heavy alkali-metal atoms. The authors give a systematic analysis of the theoretical tools necessary for the study of the experimental quantities which can be measured in multiphoton ionisation experiments for moderate intensities in the non-resonant region. They use a description of the problem based on the density operator. The expansion of this density operator over the complete set of irreducible spherical tensor operators enables them to describe the different parameters attainable by experiments and so to construct the density matrix. This formalism allows the authors to study the total transition probabilities, the angular distributions and the differential polarisation degrees along any direction. They use the quantum defect theory as an atomic model. The atomic core polarisation is fully taken into account. The infinite summations running over the whole unperturbed atomic spectrum (discrete plus continuum) related to time dependent perturbation theory are performed using the Green's function formalism.
The infinite summations over the complete set of unperturbed atomic states appearing in the Nth-order time-dependent perturbation theory are performed using the Green's function formalism. In order to test the method extended calculations of the cross section for two- and three-photon ionization for atomic hydrogen are made and numerical comparison is shown with the values obtained by different methods. The resonant character of the process is made evident since the poles of the radial part of the Green's function represent the actual energy spectrum of the atom. The relevant transition matrix elements are written in closed form and then computed exactly without averaging over the intermediate states. The cross sections vanish for circularly polarized light near some energies which explains the form of the cross sections for circularly and linearly polarized light.
Three-photon ionisation probability rates have been calculated for circularly and linearly polarised incident radiation applying time-dependent perturbation theory to the lowest non-vanishing order in the framework of the quantum defect method generalised to the spin-orbit coupling scheme. The infinite summations over the unperturbed atomic states have been performed on the basis of the Green's function formalism. Electron spin polarisation has been evaluated and the possibility of obtaining ejected polarised electrons in the direction of the incident radiation wavevector through three-photon ionisation by circularly polarised radiation is shown.
Non-perturbative completely analytic calculations of the spin polarisation of photoelectrons produced in resonant two-photon ionisation of alkali atoms with exciting and ionising light beams are presented. A well justified alkali atom model composed of four discrete states and the continuum is applied. Contrary to simpler models it enabled one to obtain results valid when the effective resonance Rabi frequency exceeds the frequency separation between the two components forming a given fine-structure energy doublet at resonance. It is shown that in this limit the photoelectron polarisation depends critically on whether a light or heavy alkali atom is ionised. In the former case the photoelectron polarisation is proved to be a copy of the electronic polarisation of the atom, whereas in the case of heavier alkalis it departs appreciably from that of the ionised atom due entirely to spin-orbit perturbation of radial wavefunctions of P discrete states. It is also shown how the author's present results go over into those previously obtained for weaker exciting fields.