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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Scaling Of Classically Stochastic Many-Photon Absorption Processes From The Microwave Region To Higher Frequencies

J. E. Bayfield

Published Oct 21, 1986• 0 citations
Publisher

Abstract

Both experiments and quantum calculations have revealed some validity of classical predictions for the classically stochastic or "diffusive" many-photon excitation and ionization of hydrogen atoms with principal quantum number n near 60 in an intense microwave field. These processes partially arise from the relatively dense number of excited atomic states present near the continuum, and from the large radiative couplings between these states. The classical scaling relations are supplemented to predict approximate threshold conditions for "diffusion" and ionization. Diffusion occurs when an electron orbit changes during one orbit time, while ionization requires adequate energy absorption from the the external field. Indicated are interesting experiments at ten micron wavelengths, intensities of tens of gigawatts per square cm, and bound electrons such as in the helium ion with n=6. These values are similar to those predicted for n=1 electrons in quantum well structures, where the situation is somewhat different because of the inverted anharmonicity of the ladders of field-free atom energy levels.

DOI
10.1117/12.938693

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Both experiments and quantum calculations have revealed some validity of classical predictions for the classically stochastic or "diffusive" many-photon excitation and ionization of hydrogen atoms with principal quantum number n near 60 in an intense microwave field. These processes partially arise from the relatively dense number of excited atomic states present near the continuum, and from the large radiative couplings between these states. The classical scaling relations are supplemented to predict approximate threshold conditions for "diffusion" and ionization. Diffusion occurs when an electron orbit changes during one orbit time, while ionization requires adequate energy absorption from the the external field. Indicated are interesting experiments at ten micron wavelengths, intensities of tens of gigawatts per square cm, and bound electrons such as in the helium ion with n=6. These values are similar to those predicted for n=1 electrons in quantum well structures, where the situation is somewhat different because of the inverted anharmonicity of the ladders of field-free atom energy levels.
New experimental results are presented for short-pulse microwave ionization of highly excited hydrogen atoms. A comparison of these results with quantum numerical computations and analytical predictions provides for the first time experimentally grounded evidence of the localization phenomenon that leads to the suppression of the quantum version of the chaotic diffusion in action space occurring in the classical limit. The onset of chaotic motion in externally driven classical systems is a key problem in nonlinear dynamics that is now well understood in its essential aspects. In many physically interesting cases, as the perturbation strength increases beyond some critical value, the system starts absorbing energy in a diffusive way. The question whether “diffusive” excitation processes can take place also in externally driven quantum systems is then a very interesting one for the physics of atoms and molecules in external electromagnetic fields. This is a deep question involving the nature and the validity of the quasiclassical approximation when the underlying classical dynamics is chaotic. The question of “quantum diffusion” was first addressed in a simple model system, the kicked rotator. It was chosen because the features of classical chaos in it were relatively clean and well understood. Besides that, the numerical simulation of its quantum dynamics could be easily accomplished. The major indication of this model was that quantum mechanics suppresses the classical chaotic diffusion in action via a destructive interference effect similar to that responsible for the Anderson localization well known in condensed matter physics.
We have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains concerning their widths.
When a hydrogen atom in a state with principal quantum number ni{n}_{i}ni​ is irradiated simultaneously with light of frequency ${\ensuremath{\omega}}_{L}$, nearly that required to produce a transition to a higher state with principal quantum number nf{n}_{f}nf​ and with microwave radiation of frequency $\ensuremath{\omega}$, the transition is very probable when the resonance condition ${\ensuremath{\omega}}_{L}+k\ensuremath{\omega}={E}_{f}\ensuremath{-}{E}_{i}$ is satisfied, the emission or absorption of the net number kkk of microwave photons just compensating for the detuning of the light from the resonance. This process is analyzed with the use of a forward scattering method and the results are used to discuss the experiments of Bayfield et al. on the excitation of hydrogen.
Continuum–continuum, bound–bound, bound–free, and free–bound atomic field-induced transitions are investigated. The initial atomic state is supposed to be given by a wave packet of coherently populated levels of continuous or discrete spectra. Interference effects were found to increase the probabilities of these types of transition and to change their dependence on the pulse duration τ. Interference is shown to occur also in the two-photon ionization probability with highly excited Rydberg levels as intermediate states. Criteria of applicability of the energy diffusion model are formulated. The different diffusion criteria are shown to be incompatible with each other, owing particularly to described interference effects. An alternative picture of multiphoton excitation is suggested. This picture is similar to the above-threshold ionization and predicts the appearance of some maxima in the spectrum of excited electrons below the ionization threshold.
The behavior of Rydberg atoms in a recent experiment involving selective excitation in combined ac and dc electric fields is shown to be consistent with the predictions of a one-dimensional model incorporating only the extreme level of each Stark manifold. For low microwave powers, the excitation is resonant and is described qualitatively by multiphoton perturbation theory. For higher powers, an alternative stochastic theory predicts rapid ionization at all frequencies, as observed experimentally.
An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.