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Journal of Physics B Atomic and Molecular Physics

An adiabatic and near-adiabatic model of multiphoton ionisation

L Armstrong, Howard C. Baker

Published Dec 28, 1980• 11 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/13/24/007

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Journal of Physics B Atomic and Molecular Physics•Jul 14, 1980•57 citations
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.
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.
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.
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.