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Physical Review Letters

Excited Atoms in Strong Microwaves: Classical Resonances and Localization in Experimental Final-State Distributions

J. E. Bayfield, David W. Sokol

Published Oct 31, 1988• 59 citations
Publisher

Abstract

Highly excited hydrogen atoms have been exposed to an intense pulse of microwaves with frequency near the initial classical electron orbit frequency. Measurements were made of the probability distribution for different bound states after the pulse. Structure in such distributions is found to be near classical, and arises from the presence of a classical resonance island in action-angle space. The measured distributions also yield values of electron localization length in action space that are in agreement with quantum localization theory and with numerical values based on quantum mechanics.

DOI
10.1103/physrevlett.61.2007

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Highly excited hydrogen atoms have been exposed to an intense pulse of microwaves with frequency near the initial classical electron orbit frequency. Measurements were made of the probability distribution for different bound states after the pulse. Structure in such distributions is found to be near classical, and arises from the presence of a classical resonance island in action-angle space. The measured distributions also yield values of electron localization length in action space that are in agreement with quantum localization theory and with numerical values based on quantum mechanics.
Excited hydrogen atoms in pulsed microwave electric fields exhibit a nonclassical increase of stability over a relatively wide range of frequencies even around and below the classical Kepler frequency 1/n3 where Anderson-like localization due to quantum interference plays no role. I show here that the increased stability for microwave frequencies in the whole frequency range 0.7/n3–0.85/n3 is due to selective population of long-lived 'scarred' states that are associated with the chaotic separatrix band surrounding the principal classical resonance zone in phase space. A quantum explanation is given in terms of adiabatic evolution of Floquet states and the destabilizing effect of two-level quantum resonances is investigated. The role of neighbouring classical resonance zones in defining the frequency range of stabilization is revealed both by quasienergy curves and by Husimi functions for the instantaneous quantum states. Nonclassical stability peaks as a function of microwave frequency are thus explained as transition points from one classical resonance to another.
We have studied the ionization of lithium Rydberg atoms by pulsed microwave fields in the regime in which the microwave frequency is equal to or a subharmonic of the classical Kepler frequency of the two-body Coulomb problem. We have observed a series of resonances where the atom is relatively stable against ionization. The resonances are similar to those seen previously in hydrogen, but with significant quantitative differences. We also present measurements of the distribution of states that remain bound after the microwave interaction for initial states near one of the classical subharmonic resonances.
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.
Excitation/ionization probabilities have been measured as a function of microwave electric amplitude F at three different microwave frequencies {omega}/2{pi} = 26.43, 30.36, 36.02 GHz for a wide range of initial no states of hydrogen Rydberg atoms. Using classically scaled variables n{sub 0}{sup 3}{omega}, n{sub 0}{sup 4}F, we discuss the scaling properties of these data. In particular, we note the scaling properties of nonclassical stability observed near n{sub 0}{sup 3}{omega} = 1.3. Our data support the assertion that this stability is due to the presence of a {open_quote}scarred{close_quote} wavefunction.