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Journal of Physics B Atomic and Molecular Physics

Time development of resonant multiphoton ionisation of sodium

Stanley L. Haan, S. Geltman

Published Apr 28, 1982• 14 citations
Publisher

Abstract

The time evolution of the ionisation probability of a sodium atom irradiated by linearly polarised light with frequency near the 3s-3p transition frequency is studied theoretically by the following method. The 3s and 3p states are strongly coupled using the rotating-wave approximation and then the resulting strongly coupled wavefunction is used as the lowest-order approximation in applying second-order perturbation theory to obtain the ionisation probability. The photoelectron energy spectrum and total ionisation probability are studied for various laser detunings and turn-on forms. Processes which are forbidden at long times by energy conservation are found to be important at short times (t<or approximately=10 -9 s for a laser intensity of order MW cm -2 ) . The ionisation probability is found to exhibit a plateau behaviour at times much less than the 3s-3p Rabi cycling time and subsequently to oscillate with the 3p population before reaching rate behaviour in the long-time limit.

DOI
10.1088/0022-3700/15/8/015

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Journal of Physics B Atomic and Molecular Physics•May 28, 1978•24 citations
The time evolution of the ionisation probability of a sodium atom irradiated by linearly polarised light with frequency near the 3s-3p transition frequency is studied theoretically by the following method. The 3s and 3p states are strongly coupled using the rotating-wave approximation and then the resulting strongly coupled wavefunction is used as the lowest-order approximation in applying second-order perturbation theory to obtain the ionisation probability. The photoelectron energy spectrum and total ionisation probability are studied for various laser detunings and turn-on forms. Processes which are forbidden at long times by energy conservation are found to be important at short times (t<or approximately=10 -9 s for a laser intensity of order MW cm -2 ) . The ionisation probability is found to exhibit a plateau behaviour at times much less than the 3s-3p Rabi cycling time and subsequently to oscillate with the 3p population before reaching rate behaviour in the long-time limit.
A theoretical procedure is presented for the evaluation of resonant multiphoton ionisation rates for atoms interacting with intense monochromatic lasers. The essence of the procedure is to treat first the strong coupling by solution of the truncated Schrodinger equation to obtain a time-dependent superposition state. This is then used as the lowest order approximation to iterate the full time-dependent Schrodinger equation to obtain the transition amplitude to the continuum. A model-atom study of the time evolution of the ionisation probability is carried out and the approach to rate behaviour in the long-time limit is demonstrated. Ionisation rates are evaluated for a variety of resonant processes in H, Na and Cs involving one or two lasers, as a function of intensities and detunings. Comparison with experiment is still in a fragmentary stage, and some large discrepancies are found to exist.
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.
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 model of multiphoton ionisation is presented which can be used when the turn-on of the atom-field interaction is adiabatic or near adiabatic. It is shown that in the adiabatic limit, the probability of the atom not being ionised is given by a single exponential decaying in time. A time-independent perturbation series is developed which can be used to calculate the adiabatic limit ionisation rate to any desired order. A time-dependent perturbation series is used to calculate the ionisation probability in the near-adiabatic limit. Comparison is made between results obtained with this model and those obtained using the more common sudden approximation to the turn-on.
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.
A theory of two-photon ionisation of atomic systems is developed incorporating into the treatment details of the laser spectrum. A general expression for the time-integrated two-photon ionisation probability is obtained together with general expressions for the induced shifts and widths of the atomic levels. These expressions are valid near resonance, when in the ordinary perturbation treatment the energy denominators vanish. The general expressions are then evaluated for the special case of a Lorentzian laser spectrum, when simple analytic results are obtained. The treatment is not confined to the two-level atom or the rotating-wave approximation.