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Journal of Physics B Atomic Molecular and Optical Physics

Near-threshold behaviour of multiphoton ionisation probabilities

H. Gratl, G. Alber, P. Zoller

Published Oct 14, 1989• 12 citations
Publisher

Abstract

The near-threshold behaviour of four-photon ionisation is studied in an energy region where the third laser photon crosses the Rydberg threshold. Particular emphasis is given to the role played by the Stark shift (raising of the ionisation potential) in a Gaussian laser pulse. As a function of the laser frequency the ionisation probability shows (i) a region where individual Rydberg resonances are well resolved, followed by (ii) a smoothly decreasing ionisation probability in the bound-state region, and (iii) an almost energy-independent above-threshold ionisation signal.

DOI
10.1088/0953-4075/22/19/002

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Journal of Physics B Atomic and Molecular Physics•Oct 14, 1979•6 citations
The near-threshold behaviour of four-photon ionisation is studied in an energy region where the third laser photon crosses the Rydberg threshold. Particular emphasis is given to the role played by the Stark shift (raising of the ionisation potential) in a Gaussian laser pulse. As a function of the laser frequency the ionisation probability shows (i) a region where individual Rydberg resonances are well resolved, followed by (ii) a smoothly decreasing ionisation probability in the bound-state region, and (iii) an almost energy-independent above-threshold ionisation signal.
The author presents a theory of resonant multiphoton ionisation by multimode laser light. He investigates N photon resonant N+1 photon ionisation for a high order bound-bound transition with the resonance dominated by the Stark shift. Two aspects of the problem are considered. He studies the bandwidth dependence for the resonant ionisation probability, approximating the multimode laser light by a chaotic field. Secondly, he investigates the effects of finite mode numbers of the multimode laser. Finally, the theory is compared with the recent experimental results of Lompre et al (1981).
Previous results for the shift of the ionisation potential of an atom in a laser field are used to investigate the kinematics of multiphoton ionisation in either a laser beam or a laser pulse. Previous results for a laser beam show essentially no shifts of the 'above-threshold ionisation' peaks in the electron energy distribution and only small widths. Results for a laser pulse show the possibility of large shifts and widths growing as the pulse becomes shorter. Electrons which absorb a larger number of photons are predicted to show less shifted and narrower peaks.
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 authors treat a model for photoionisation in which the atom has many bound atomic levels and the laser may be either monochromatic or possess a finite bandwidth. The treatment is restricted to the case where the laser is not sufficiently intense to cause Stark splitting of the atomic energy levels. They obtain an expression for the two-photon ionisation probability as a function of time which covers both resonant and non-resonant excitation. They identify several time regimes where the probability takes on a particularly simple form. In particular they discuss the short time behaviour and the conditions under which a time-independent transition rate exists. Numerical plots of the ionisation probability against laser frequency for a wide range of pulse durations are given for the two-level model.
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.