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AIP conference proceedings

Classical ghosts in quantal microwave ionisation

D. Richards, J G Leopold

Published Jan 1, 1990• 2 citations
Publisher

Abstract

We provide a brief review of the response of an excited hydrogen atom to a microwave field, and a detailed discussion of the behaviour of a one‐dimensional model in a high frequency field. In particular we show that although classical dynamics is incorrect for the parameters of experimental interest an examination of the classical behaviour is helpful in understanding the quantal behaviour. We show further that, for these parameters, the quantal probabilities fluctuate dramatically with the variation of most system parameters and attribute this non‐classical behaviour to the dominant influence of relatively few, about ten, quasi‐resonant states.

DOI
10.1063/1.39267

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 1986•0 citations
We provide a brief review of the response of an excited hydrogen atom to a microwave field, and a detailed discussion of the behaviour of a one‐dimensional model in a high frequency field. In particular we show that although classical dynamics is incorrect for the parameters of experimental interest an examination of the classical behaviour is helpful in understanding the quantal behaviour. We show further that, for these parameters, the quantal probabilities fluctuate dramatically with the variation of most system parameters and attribute this non‐classical behaviour to the dominant influence of relatively few, about ten, quasi‐resonant states.
Quantum transition amplitudes between photonic states for the one-dimensional model of a hydrogenic Rydbcrg atom in a microwave field arc obtained. For this purpose the reduced Hamiltonian and the correspondence principle for transitions between strongly coupled states are used. The result reveals the resonance nature of the atom-har-monic-field interaction. The recently discovered phenomenon of quantum limitation of chaos in classically chaotic systems [1-3] has aroused an additional interest in experimental and theoretical investigations of a hydrogen atom in a microwave field. Much attention has been focused upon the high frequency , regime, when the microwave field frequency to is greater than the classical orbital frequenc [4—8]y . It is just in this case that a quantum limitation of the classical diffusion is observed. The new experimental results [4,5] support the idea that quantum effects suppress classical chaos, however until now there is no evidence for quantum localization by interference effects. The detailed quantum description is complicated and, therefore, is not quite suitable for the interpretation of experimental results. On the other hand, widely used model descriptions and considerable simplifications [1-3] in explaining the phenomena of quantum interference and chaos localization often lack some important features of the system. As a result, there exist various additional explanations on classical chaos limitation by quantum effects [6-8]. From our point of view an adequate quasi-classical theory containing the main quantum effects is needed. Such a theory would be of help in interpreting the experiments and in explaining the existing discrepancies between classical and quantum descriptions. In this paper the analytic quasi-classical expression for amplitudes of transitions between photonic states of the one-dimensional atom in a harmonic field has been obtained. It is believed that this result will be helpful for those engaged in the investigation of quantum chaos. Our consideration is based on a strong coupling correspon-1991 by Allcrton Press, Inc. dence principle [9] which gives the semi-classical transi-tion amplitude. A well-known transformation from an autonomous Hamiltonian in a -dimensional phase space to a new Hamiltonian in a restricted phas e space with dimensions depending periodically on a new effec-tive time parameter [10] has also been used. The Hamil-tonian of the one-dimensional model of a hydrogen atom in an external microwave field of amplitude F and fre-quency is given by [10]
Analytical expressions for dipole matrix elements between high atomic states of nonhydrogenic and perturbed hydrogenic atoms are derived. The theoretical investigation is fulfilled for discrete and continuum atomic states and for the one-dimensional atom. It is shown that the quantal transition probabilities between perturbed atomic states depend on the nature of perturbation, e.g. matrix elements for the hydrogenic atom in an electromagnetic field differ from those of the nonhydrogenic atom. The results obtained generalize and increase the accuracy of some known expressions for the nonhydrogenic atom and extend them for the perturbed hydrogenic atom. Further, the analysis of classical dynamics and the derivation of mapping equations of motion for the one-dimensional atom in a harmonic field is fulfilled. The relationship between the energy change of the classical atom in a harmonic field and expressions for dipole matrix elements is revealed and analysed.
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.
The authors examine the effect of the Coulomb singularity on the classical and semiclassical dynamics of the one-dimensional model for atomic hydrogen, sometimes called the surface-state-electron model, in a periodic electric field and determine a necessary condition, in terms of the field strength, frequency and the initial quantum number, for the violation of the uncertainty principle. They show that when this violation occurs the quantal transition probabilities are significantly less than the equivalent classical probabilities. This criterion is tested numerically and shown to provide a good estimate of the boundary to one of the regions in which classical dynamics fails. The authors also show that when the uncertainty principle is not violated the fluctuations of the quantal about the classical probability spectra can be related to structure in classical phase space. These fluctuations are due to different classical and quantal transport through cantori.
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.