Chaotic Ionization Research Articles

Density dynamics in some quantum systems

The quantum domain behavior of classical nonintegrable systems is well-understood by the implementation of quantum fluid dynamics and quantum theory of motion. These approaches properly explain the quantum analogs of the classical Kolmogorov–Arnold–Moser type transitions from regular to chaotic domain in different anharmonic oscillators. Field-induced tunneling and chaotic ionization in Rydberg atoms are also analyzed with the help of these theories. Quantum fluid density functional theory may be used to understand different time-dependent processes like ion-atom/molecule collisions, atom-field interactions, and so forth. Regioselectivity as well as confined atomic/molecular systems and their reactivity dynamics have also been explained. © 2013 Wiley Periodicals, Inc.

Demonstration of Turnstiles as a Chaotic Ionization Mechanism in Rydberg Atoms

We present an experimental and theoretical study of the chaotic ionization of quasi-one-dimensional potassium Rydberg wave packets via a classical phase-space turnstile mechanism. Turnstiles form a general transport mechanism for numerous chaotic systems, and this study explicitly illuminates their relevance to atomic ionization. We create time-dependent Rydberg wave packets, subject them to alternating applied electric-field pulses, and measure the electron survival probability. Ionization depends not only on the initial electron energy, but also on the classical phase-space position of the electron with respect to the turnstile--that part of the electron packet inside the turnstile ionizes after the applied ionization sequence, while that part outside the turnstile does not. The survival data thus encode information on the shape and location of the turnstile, in good agreement with theoretical predictions.

Chaotic ionization of a Rydberg atom subjected to alternating kicks: Role of phase-space turnstiles

We study the ionization of a highly excited Rydberg atom subjected to a periodic sequence of external electric-field pulses. Such systems are important laboratory and theoretical models of classical and quantum chaos. Furthermore, a good theoretical understanding of this chaos is important for controlling electronic states in atoms, as has been demonstrated in a series of recent experiments on the creation and control of electronic wave packets. Here, we present a theoretical analysis of the chaotic ionization of a hydrogen atom subjected to alternating positive and negative impulses. This analysis is based on the observation that the ionization of the atom is due to a turnstile in phase space which promotes the electronic state from negative to positive energy. The geometry of the lobes associated with the turnstile provides a clear picture of how the ionization process proceeds. Using this geometric intuition, we propose two experimental protocols to directly reveal the importance of the turnstile lobes in the laboratory.

Chaotic ionization of a highly excited hydrogen atom in parallel electric and magnetic fields

We present results of our simulations of the ionization of a hydrogen atom excited to a Rydberg wave packet in the presence of external parallel electric and magnetic fields. This is an example of an open, quantum system whose classical counterpart has been shown to display chaos in the time domain. Within the framework of classical mechanics, electrons escape through chaos induced pulse trains. We reproduce such previously observed signatures of classical chaos in the time-dependent current of ionizing electrons and study the interference effects between the outgoing pulse trains which is absent in the classical picture. Our attempts at manipulating the ionization pulse trains and the effect of core scattering coupled with the chaotic ionization are also discussed. We further investigate the onset of chaos as a function of the scaled energy of the system. We find that for relatively high magnetic fields, quantum-mechanical ionization current shows erratic fluctuations in contrast with the classical current which shows transition to regularity. We conclude that the oscillations result from the decrease in the number of the ionization channels for the higher magnetic field strengths. We further study the time-dependent autocorrelation function and its Fourier transform to look for the effects of the Landau quantization in the photoabsorption spectrum. Our results include calculations via the classical trajectory Monte Carlo method to compare our non-perturbative quantum-mechanical results with the underlying chaotic classical dynamics.

Ground‐ and excited‐states reactivity dynamics of hydrogen and helium atoms

AbstractDynamic profiles of various reactivity parameters like hardness, chemical potential, polarizability, phase volume, and electrophilicity index are studied in gaining insights into the ground‐ (n = 1) and excited‐ (n = 15) states dynamics of hydrogen and helium atoms. Pertinent time‐dependent Schrödinger equations are solved for the ground and excited states of hydrogen atom and the Rydberg state of the helium atom while a generalized nonlinear Schrödinger equation is solved for the ground state of the helium atom, all interacting with external electric fields of different frequencies and intensities. For both the atoms ground states are more stable than the corresponding excited states. Hardness and phase volume can be used as diagnostics for the chaotic ionization from the Rydberg states of those atoms. Other quantities like higher‐order harmonics also lend additional support. Dynamic variants of the maximum hardness and minimum polarizability principles are found to be operative. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Quantum localization in the high-frequency limit

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.

Chaotic ionization of non-classical alkali Rydberg states—computational physics beats experiment

We report on a novel numerical treatment of highly excited alkali Rydberg states strongly driven by a coherent microwave field. Our approach establishes particularly clean experimental conditions which remain to be realized by the traditional experimentalist in the laboratory. First results obtained on the largest currently available parallel supercomputers resolve a long-standing problem in the theoretical analysis of the ionization process of nonhydrogenic alkali Rydberg states.

Chaotic Ionization of Nonhydrogenic Alkali Rydberg States

We report the first ab initio quantum treatment of microwave driven alkali Rydberg states. We find that nonhydrogenic atomic initial states exhibit fingerprints of classically chaotic excitation, and identify the cause of their experimentally observed enhanced ionization, as compared to Rydberg states of atomic hydrogen.

Direct and Chaotic Ionization in the Presence of External Fields: the Transition-State Theory Point of View

The transition state is fundamental to modern theories of reaction dynamics. Although transition-state theory (TST) has been used mainly in chemical physics, it can be applied to any problem that involves some form of transformation, including half-scattering events such as ionization. In this paper, we use TST to investigate the competition between direct and chaotic mechanisms in the ionization of Rydberg atoms in external electric fields.

Transition state theory without time-reversal symmetry: chaotic ionization of the hydrogen atom

We present the first application of transition state theory to a system that evolves from an initial to a final state without time-reversal symmetry. The problem studied is the chaotic ionization of a hydrogen atom in crossed electric and magnetic fields. The stable manifolds of the transition state reveal a fractal tiling which connects the geometrical properties of the tiling to the ionization rate, leading to a theoretical explanation for the computational and experimental observation of "prompt" and "delayed" electrons in this problem.

Kepler Map

We present a consecutive derivation of mapping equations of motionfor the one-dimensional classical hydrogenic atom in a monochromaticfield of any frequency. We analyze this map in the case of high andlow relative frequency of the field and transition from regular tochaotic behavior. We show that the map at aphelion is suitable forinvestigation of transition to chaotic behavior also in the lowfrequency field and even for adiabatic ionization when the strength ofthe external field is comparable with the Coulomb field. Moreover, theapproximate analytical criterion (taking into account theelectron’s energy increase by the influence of the field) yieldsa threshold field strength quite close to the numerical results. Wereveal that transition from adiabatic to chaotic ionization takesplace when the ratio of the field frequency to the electron Keplerfrequency approximately equals 0.1. For the dynamics and ionization ina very low frequency field the Kepler map can be converted to adifferential equation and solved analytically. The threshold field ofthe adiabatic ionization obtained from the map is only 1.5% lower thanthe exact field strength of static field ionization.

Classical theory of the chaotic ionization of highly excited helium atoms

In this paper, we introduce a classical model for the behavior of the outer electron of a Rydberg helium atom in both static and time-dependent electric fields; we contrast the behavior of this dynamical system with the behavior of the classical model for highly excited hydrogen atoms in similar fields; and we show that these classical models recover many features of the system that would seem to be purely quantal in origin. Perhaps the most surprising of these is the apparent presence of ‘‘classical avoided crossings’’ in the Stark energy level structure of the classical helium model. Finally, we compare the behavior of our helium model to experimental data obtained by Koch, Mariani, and co-workers in their investigations of the ionization of highly excited helium atoms in a microwave field, and we note the agreement between experiment and theory.

Classical theory of the chaotic ionization of highly excited hydrogen atoms

Over the past decade, classical mechanics has been transformed from an historical relic into a contemporary model for certain problems in atomic and molecular physics. This transformation has been brought about by recent interest in the study of chaotic dynamics in nonlinear classical systems. A good example is the behavior of highly excited atoms in microwave fields. In the language of classical mechanics a hydrogen atom in a microwave field is a periodically perturbed nonlinear oscillator. Depending on the strength of the perturbing microwave field, the equations of motion can become chaotic. The chaotic electron dynamics results in rapid ionization above a threshold microwave field strength. This paper presents the basic components of the classical models that we have introduced to describe this chaotic ionization of highly excited hydrogen atoms.

Ionization mechanism of Rydberg atoms in a circularly polarized microwave field.

Placing a hydrogen atom in a circularly polarized microwave field exposes it to velocity-dependent forces that open new routes to chaotic ionization, access to which is controlled by the details of state preparation.

Autocorrelation functions in the photoionization of hydrogen in electric and magnetic fields.

The photoionization (PI) cross section of hydrogen in external electric and magnetic fields was studied by a direct version of the recursive residue generation method, combined with complex dilation and discretization. The PI cross section was computed for three different combinations of fields: an electric field only, perpendicular electric and magnetic fields, and, finally, an electric field with an angle of 80\ifmmode^\circ\else\textdegree\fi{} to the magnetic field. The field-induced resonances were shown to have Fano-type profiles, with a shape depending on the field combination. The fluctuations of the base line were studied using an autocorrelation function C(\ensuremath{\epsilon}). For the field combinations studied here, C(\ensuremath{\epsilon}) has for small \ensuremath{\epsilon} an initial Lorentzian shape. With increasing \ensuremath{\epsilon} different oscillatory structures in C(\ensuremath{\epsilon}) were observed. The correlation functions were studied for several energy ranges, achieving a common Lorentzian shape for the highest range, independent of the field combinations. A simple interpretation of the behavior for all cases in terms of chaotic ionization is possible.

Fractal dimensions in the phase space of two-electron atoms.

In chaotic ionization of the classical s-wave model of two-electron atoms, initial conditions of bound nonionizing trajectories form Cantor sets in phase space. The fractal dimensions of these sets are noninteger and increase with increasing nuclear charge, i.e., with decreasing importance of the electron-electron interaction.

Ericson fluctuations in the chaotic ionization of the hydrogen atom in crossed magnetic and electric fields.

We report exact quantum calculations for the hydrogen atom in crossed magnetic and electric fields. Employing the complex-coordinate-rotation method we are able to extend the calculations of eigenstates far into the continuum region. Calculated photoionization cross sections are found to exhibit strong Ericson fluctuations, a characteristic feature of chaotic scattering. This interpretation is supported by classical trajectory calculations which reveal a fractal dependence of the classical ionization time on the initial conditions.

Deterministic onset of chaos in a gas discharge

Sequences of bifurcations in the radiation intensity of a discharge plasma on the boundary between regular and chaotic ionization waves regions were observed by varying the discharge current at a constant gas flow velocity and pressure. Fundamental constants of the Feigenbaum scenario were measured in the experiment as δ = 4.6±0.1 and α = 2.6±0.6 by means of recording succeeding period doublings.

Chaotic ionization of highly excited hydrogen atoms: Comparison of classical and quantum theory with experiment

The experimental and theoretical studies of the microwave ionization of highly excited hydrogen atoms provide a unique opportunity to explore two new frontiers of modern physics simultaneously. Since the Coulomb binding fields decrease rapidly with increasing quantum number, these atoms can be easily perturbed by external fields that are comparable or even greater than the atomic fields, which permits a thorough investigation of a variety of interesting, non-perturbative processes involved in the interaction of intense electromagnetic radiation with matter. In addition, since the classical description of the Bohr atom in a strong, oscillating electric field has been shown to exhibit “chaotic” behavior, this physical system serves as an important paradigm for the study of the quantum manifestations and modifications of classical chaos. This review describes a number of surprising phenomena that have emerged from these detailed experimental and theoretical studies of this strongly perturbed quantum system throughout the entire range of the experimentally accessible parameters - from the low-frequency regime of tunnelling ionization, to the high-frequency regime of multiphoton ionization, and to the complex intermediate-frequency regime of “chaotic” ionization. Particular emphasis will be placed on both the striking quantum-classical correspondence in the intermediate-frequency regime where the experimental onset of ionization is well described by the onset of classical chaos, as well as the remarkable quantum suppression of the chaotic ionization in the high-frequency regime because of quantum interference effects closely related to the process of Anderson localization in solid-state physics.

Inhibition of quantum transport due to ‘‘scars’’ of unstable periodic orbits

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.