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Journal of Physics B Atomic and Molecular Physics

Non-resonant multiphoton ionisation of caesium in strong fields

Michele Crance, M Aymar

Published Nov 14, 1980• 13 citations
Publisher

Abstract

Non-resonant k-photon ionisation cross sections may be calculated by kth order perturbative treatment. This method is generally considered to be good when the detuning from the closest resonance is much larger than the expected shift and width of this resonance. The aim of this paper is to discuss the validity of this criterion for several realistic cases. By diagonalising an effective Hamiltonian built on a few quasi-resonant states, we have calculated multiphoton ionisation cross sections for ground state caesium by linearly polarised light in frequency ranges containing the tuning range of the ruby laser, the Nd glass laser and its first harmonic. The study is carried out up to an intensity of 10 11 W cm -2 .

DOI
10.1088/0022-3700/13/21/008

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Critical discussion of an absolute measurement of multiphoton ionisation cross sections in caesium

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Four-photon ionisation of caesium requires strong electromagnetic fields and the usual interpretation in terms of generalised cross sections has to be questioned. A theoretical calculation in the experimental conditions of a recent measurement provides a new interpretation of the results of Morellec and Normand (1979): the effect of light shifts masks the effect of saturation and leads one to overestimate the multiphoton ionisation cross section. The expected overestimation is only 25 per cent for the quoted experiment, but could be larger in some other physical cases.

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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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The multiphoton ionization of caesium and the perturbation of bound states

R. G. Evans, Peter C. Thonemann

Orer a small range of light intensity the three-photon ionization rate of caesium atoms by ruby laser light decreases when the incident photon flux is increased. This result may be quantitatively explained by an induced energy shift of the 913 levels of the caesium atom proportional to the square of the light intensity. Thus perturbations of bound electron states by an intense light beam can be of importance in determining the multiphoton ionization rate. In this paper the functional dependence of the ionization rate on the photon flux is calculated for caesium, using a perturbation theory somewhat different from that usually employed.

Philosophical magazine•Jun 1, 1973•6 citations
Non-resonant k-photon ionisation cross sections may be calculated by kth order perturbative treatment. This method is generally considered to be good when the detuning from the closest resonance is much larger than the expected shift and width of this resonance. The aim of this paper is to discuss the validity of this criterion for several realistic cases. By diagonalising an effective Hamiltonian built on a few quasi-resonant states, we have calculated multiphoton ionisation cross sections for ground state caesium by linearly polarised light in frequency ranges containing the tuning range of the ruby laser, the Nd glass laser and its first harmonic. The study is carried out up to an intensity of 10 11 W cm -2 .
Four-photon ionisation of caesium requires strong electromagnetic fields and the usual interpretation in terms of generalised cross sections has to be questioned. A theoretical calculation in the experimental conditions of a recent measurement provides a new interpretation of the results of Morellec and Normand (1979): the effect of light shifts masks the effect of saturation and leads one to overestimate the multiphoton ionisation cross section. The expected overestimation is only 25 per cent for the quoted experiment, but could be larger in some other physical cases.
For pt.I see ibid., vol.19, p.79 (1986). The authors study the two-photon ionisation of unpolarised target atoms of caesium in their ground state or in one of the two first excited states 6P 1/2 or 6P 3/2 in the non-resonant region. Circularly, linearly and unpolarised light are considered. For each case they give a systematic analysis of generalised transition probabilities, angular distributions and polarisation phenomena. In particular, it is shown that polarised electrons can be obtained even with linearly or unpolarised light.
By using a perturbative treatment based on the central field approximation, the authors have calculated multiphoton ionisation probabilities in several cases of experimental interest (two-, three- and four-photon ionisation of the caesium and potassium ground states at the doubled Nd glass laser frequency and one-, two- and three-photon ionisation of some s, p, d and caesium Rydberg states). Some of these probabilities have been calculated beyond the minimum non-vanishing order. They have also performed some calculations for hydrogen. The comparison of their results with previous ones obtained by analytical methods provides a good test of the numerical techniques involved in the calculations.
Perturbation theory of multiphoton ionisation due to a classical electromagnetic field is modified to allow for intermediate resonances with bound states. Complex energies, generally associated with resonances, do not enter into this formalism. For a monochromatic field of frequency u, a constant ionisation rate can then be defined unambiguously and only such continuum states are excited which correspond to the absorption of energy in integral multiples of hu. As an application, differential and total cross sections for the two-photon ionisation of hydrogen, for frequencies below the n = 3 resonance region, are obtained in closed form. Existing data for generalised cross sections, calculated numerically using the complex coordinate method, are in good agreement with the present results. Finally, the mean fractional ionisation resulting from a pulse of finite duration is estimated on the basis of the associated power spectrum. For short pulses, the time dependence of ionisation exhibits a departure from that expected of a time-independent rate.
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.
Orer a small range of light intensity the three-photon ionization rate of caesium atoms by ruby laser light decreases when the incident photon flux is increased. This result may be quantitatively explained by an induced energy shift of the 913 levels of the caesium atom proportional to the square of the light intensity. Thus perturbations of bound electron states by an intense light beam can be of importance in determining the multiphoton ionization rate. In this paper the functional dependence of the ionization rate on the photon flux is calculated for caesium, using a perturbation theory somewhat different from that usually employed.