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Europhysics Letters (EPL)

Manifestation of Localization in Noise-Induced Ionization and Dissociation

Shmuel Fishman, Dima L. Shepelyansky

Published Oct 14, 1991• 17 citations
Publisher

Abstract

The manifestation of quantal localization for classically chaotic systems in disintegration processes such as ionization and dissociation is investigated. It is assumed that these processes are induced by noise. The effects of a nonperturbative mechanism that was recently introduced by D. Cohen are explored. The relation between these effects and noise-induced ionization of Rydberg atoms in the presence of microwave driving is discussed.

DOI
10.1209/0295-5075/16/7/006

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The manifestation of quantal localization for classically chaotic systems in disintegration processes such as ionization and dissociation is investigated. It is assumed that these processes are induced by noise. The effects of a nonperturbative mechanism that was recently introduced by D. Cohen are explored. The relation between these effects and noise-induced ionization of Rydberg atoms in the presence of microwave driving is discussed.
Localization in the quantum kicked rotator (QKR) problem leads to nontrivial dynamical correlations that are absent in the classical limit. These correlations are related to the spectral properties of the model. The effect of noise on coherence is studied. Also, its effect on the dynamical correlations is investigated, and thus one is able to determine analytically the diffusion that is induced. If the noise is white, then coherence time is the same as that for the undriven system. For colored noise it is essential to take into account the nature of the dynamical correlations. It follows that a Markovian treatment of the dynamics for a system that is coupled to a low-temperature heat bath is not valid even if the system is classically chaotic. The formalism applies also to the problem of QKR with kicks that are not strictly periodic in time, and also to the quantum kicked particle problem, where a nonperturbative mechanism for destruction of coherence has been found.
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 quantum localization of the periodically kicked Rydberg atom in the limit of high frequencies $\ensuremath{\nu}$ is studied. We show that the quantum suppression of fast chaotic ionization as predicted by classical dynamics persists as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\nu}}\ensuremath{\infty}.$ Properties of localization in the regime of strong coupling to the continuum due to one-photon transitions are discussed. For the unidirectionally kicked atom, the high-frequency limit of localization is determined by the zero-frequency Stark Hamiltonian. The persistence of quantum localization due to interference of classical trajectories can be understood in terms of smearing out of the instabilities at finite $\ensuremath{\Elzxh}.$ Unstable trajectories whose action differs from each other and from Stark orbits in less than $\ensuremath{\Elzxh}$ contribute to quantum localization rather than to chaotic ionization.
We study theoretically and experimentally the effect of noise on Rydberg atoms passing through a strong coherent microwave field. We derive a master equation containing the coherent field exactly. Its solution reveals the presence of four universal dynamical regimes: (i) an initial classical regime, (ii) a subsequent coherent localized regime, (iii) a transition, induced by the noise, in which coherence and localization are destroyed, and (iv) the final regime, where equidistribution over the quasienergy states is reached.
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.