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Journal of Physics B Atomic Molecular and Optical Physics

Low frequency quantum stabilization of the hydrogen atom in a microwave field: scarred states and classical stability island overlap

Luca Perotti

Published Nov 30, 2011• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/44/24/245002

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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.
Comparisons of experimental data with numerical predictions of a classical model indicate that an excited hydrogen atom in a pulsed microwave electric field exhibits a nonclassical increase of stability over a relatively wide range of frequencies. I show here that this 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.
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.
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.
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]
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.
The effect of parametric perturbations on the quantum dynamics of a system with nonintegrable classical limit and a mixed phase space is shown to depend crucially on the local invariant phase space structures sampled by the evolution. Using a probe coherent state four distinct scenarios are considered: (i) large regular regions surrounding primary fixed points; (ii) smaller regular regions corresponding to higher order orbits; (iii) scarred states on hyperbolic fixed points; (iv) chaotic regions. The result that scarring stabilizes quantum dynamics against fluctuations is discussed in the general context of instability in the quantum evolution as well as in relation to recent experiments on microwave ionization of Rydberg atoms.