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arXiv:0906.5186

Quantum Stabilization by Coherent Population of Scarred Eigenstates: Quantum Suppression of Transport Classically Initiated by Separatrix Band Entry

Luca Perotti

Published Jun 29, 2009• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.0906.5186

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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.
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.
This thesis investigates quantum transport in the energy space of two paradigm systems of quantum chaos theory. These are highly excited hydrogen atoms subject to a microwave field, and kicked atoms which mimic the delta-kicked rotor model. Both of these systems show a complex dynamical evolution arising from the interaction with an external time-periodic driving force. In particular two quantum phenomena, which have no counterpart on the classical level, are studied: the suppression of classical diffusion, known as dynamical localisation, and quantum resonances as a regime of enhanced transport for the delta-kicked rotor. The first part of the thesis provides new support for the quantitative analogy between energy transport in strongly driven highly excited atoms and particle transport in Anderson-localised solids. A comprehensive numerical analysis of the atomic ionisation rates shows that they obey a universal power-law distribution, in agreement with Anderson localisation theory. This is demonstrated for a one-dimensional model as well as for the real three-dimensional atom. We also discuss the implications of the universal decay-rate distributions for the asymptotic time-decay of the survival probability of the atoms. The second part of the thesis clarifies the effect of decoherence, induced by spontaneous emission, on the quantum resonances which have been observed in a recent experiment with delta-kicked atoms. Scaling laws are derived, based on a quasi-classical approximation of the quantum evolution. These laws describe the shape of the resonance peaks in the mean energy of an experimental ensemble of kicked atoms. Our analytical results match perfectly numerical computations and explain the initially surprising experimental observations. Furthermore, they open the door to the study of the competing effects of decoherence and chaos on the stability of the time evolution of kicked atoms. This stability may be characterised by the overlap of two identical initial states which are subject to different time evolutions. This overlap, called fidelity, is investigated in an experimentally accessible situation.
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.
Understanding and coherently controlling the properties of interacting quantum many-body systems is a central challenge in non-equilibrium quantum physics. While in the past decades, a wide range of many-body Hamiltonians have been introduced to study quantum chaos, atypical eigenstates, and quantum resources, systematically engineering and continuously tuning these properties within a single microscopic model remains largely unexplored. Here, we employ a pulse engineering scheme to construct an effective Hamiltonian that continuously interpolates between a chaotic Heisenberg (XXX) chain with a local impurity and the ZX Hamiltonian. Along this interpolation, we identify several families of analytically tractable atypical eigenstates embedded in the excited-state spectrum with distinct entanglement and nonstabilizerness properties. In the XXX limit, these states exhibit exact plateaus in both entanglement and stabilizer Rényi entropy and correspond to coherent superpositions of long-range valence-bond solid (VBS) states. As the pulse strength increases, the effective Hamiltonians exhibit a hierarchy of new set of approximate entanglement plateaus in the low-energy spectrum. Interestingly, in the fully pulse-engineered ZX limit, we uncover a distinct pair of long-range entangled stabilizer eigenstates, corresponding to rainbow scar states. We further show that pulse engineering preserves the distinct chaotic and non-chaotic regimes of the original model, while that is largely absent in the dynamical generation of entanglement and nonstabilizerness. The pulse-engineered models generate nearly identical quantum resources in both regimes, revealing a partial decoupling between quantum chaos and quantum-resource generation. Our results establish pulse engineering as a versatile framework for generating many-body Hamiltonians with structured eigenstates and tunable quantum resources.
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.