We present the results of Floquet calculations of rates of photo-detachment from a short-range three-dimensional model atom in an intense high-frequency laser field. We find that beyond a certain intensity the atom becomes progressively more stable against ionisation and that at this intensity the ATI spectrum exhibits a plateau of the kind that has recently been reported in the literature [101]. We also discuss the angular distribution of the photo- electrons and examine the special case of a laser-induced degeneracy in the frequency-intensity plane. In the Floquet method one represents the time-dependent Schrodinger equation by an infinite series of coupled time-independent equations, although in practice one must truncate these to a system of finite size. We study the consequences of this truncation by performing a series of calculations for the rate of (resonant) multiphoton detachment from a one-dimensional model atom in a laser field. We find that if the wavefunction is modified to take full account of the truncation then the number of equations which must be retained in order to obtain accurate results is significantly reduced. In performing a Floquet calculation for a real atomic system it is generally assumed that the atom remains at all times in a single diabatic Floquet state, rather than in a superposition of such states. By constructing a suitable two- state model we investigate the validity of this approximation and discuss the usefulness of the Floquet method in modelling an actual experiment. We present results for the multiphoton ionisation of H(1s) by a monochromatic circularly polarised field and by a linearly polarised bichromatic field of commensurable frequencies. In the monochromatic case we draw qualitative comparisons with the predictions of Keldysh theory and use the concept of a propensity rule to explain why the angular distributions remain essentially perturbative at high intensities. In the bichromatic case we study the structure of the ATI spectrum and in particular the role played by a relative phase. The angular distributions are found to be strongly affected by the low- frequency field even when its intensity is too small to cause any appreciable ionisation of the system.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Includes bibliographical references (p. 177-185).

Cette thèse a pour but de développer et d'utiliser un cadre cohérent permettant de caractériser les phases topologiques dans des milieux spatialement périodiques induites par une perturbation dépendant périodiquement du temps ("phases topologiques de Floquet" ou "isolants topologiques de Floquet"), en présence de symétries. Ces phases sont des généralisation des isolants topologiques apparues lors de l'étude d'isolants topologiques induits par la lumière ainsi que d'analogues ondulatoires des isolants topologiques (en acoustique, mécanique et optique). De nouveaux invariants topologiques caractérisant ces systèmes sont définis, en particulier en présence d'un renversement du temps fermionique. Les cas, déjà connus dans des situations particulières, des classes complexes A et AIII de Cartan-Altland-Zirnbauer sont généralisés à toutes les dimensions, et leur survivance dans les classes réelles est discutée. Les conséquences physiques potentielles dans des systèmes électroniques sont explorées par des simulations de transport résolues en temps, qui concluent à l'existence de conductances différentielles moyennes quantifiées en présence d'un état de bord topologique. / This thesis aims at developing and using a coherent framework to characterize topological states in spatially periodic media stemming from a time-periodic drive (« topological Floquet states » or « Floquet topological insulators »), when symmetries are present. Such states are a generalization of topological insulators, which appeared from the study of the control by light of topological insulators, and from the study of the wave-physics versions of topological insulators (in acoustics, mechanics and optics). New invariants characterizing such systems are defined, in particular when fermionic time-reversal is present. The cases of complex classes A and AIII in the Cartan-Altland-Zirnbauer classification, which are already known in particular cases, are generalized to any space dimension, and their survival in real classes is discussed. Potential physical consequences in electronic systems are explored by time-resolved numerical simulation of transport properties, which show evidence of quantized average differential conductances when a topological edge state is present.

Results are presented for Floquet calculations of photodetachment rates from a one-dimensional model atom irradiated by intense laser light. Light-induced quasibound states are found to originate from the movement of poles of the multichannel scattering matrix on the Riemann energy surface. The appearance of new bound states of the negative Hydrogen ion, recently predicted, is related to the motion of resonance poles that correspond to autoionising states in the absence of the field. A number of pole trajectories, leading to light-induced states, are discussed for the one-dimensional model atom. The Floquet method allows one to represent the wave function of a quantum system in a laser field, as an infinite sum of harmonic basis functions. In any practical calculation this infinite sum must be truncated. The consequences of representing the wave function, via the Floquet method, by a finite sum of harmonics is addressed. An illustration of these consequences is made by way of a number of representative calculations performed on a one-dimensional model atom. Results are presented of calculations performed to determine the influence of a laser field, of low to moderate intensity, upon the partial and total photodetachment rates of the negative Hydrogen ion, H(^-). Using the R-matrix Floquet method, a study is undertaken into the detachment of an electron from the ion, via multiphoton transitions through one of several autodetaching resonances of the ion. The discussion focuses on the influence of the laser field upon auto detaching pathways. It is found that the laser may induce structure into the continuum that does not exist in the absence of the laser field, or, conversely, may suppress field-free structure. In the latter case, the suppression of structure is related to the appearance of laser-induced degeneracies.

The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically. / Die vorliegende Arbeit behandelt Quantensimulationen von stark wechselwirkenden Systemen ultrakalter Atome in optischen Gittern. Dabei fokussiert sich diese theoretische Arbeit auf die Möglichkeit, diese Systeme mit Hilfe eines hochfrequenten Antriebs kohärent zu kontrollieren. Diese Form des Quantenengineering nennt man Floquet-Engineering. Experimentell wurden mit Hilfe eines zeitperiodischen Antriebs des optischen Gitters bereits viele physikalische Phänomene und Modelle realisiert, insbesondere im Bereich geringer Wechselwirkungen. Hier beschreiben wir zwei neue Vorschläge für interessante Phänomene im Bereich starker Wechselwirkungen, welche durch zeitperiodisches Gitterschütteln ermöglicht werden: Das Schmelzen eines Mott-Isolators in einen angeregte suprafluiden Zustand durch kohärentes Koppeln von Bloch-Bändern, sowie die Erzeugung von eindimensionalen Gitter-Anyonen. Außerdem wird die Rolle von Multiphoton-Übergängen in angetriebenen Gittern untersucht, da diese Prozesse zu ungewolltem Heizen und damit zur Verhinderung von erfolgreichem Floquet-Engineering führen können. Das einleitende Kapitel 1 gibt einen Überblick über das Feld der Quantensimulationen mit ultrakalten Atomen und beschreibt den experimentellen Fortschritt der letzten Jahre auf diesem Gebiet. In Kapitel 2 wird die Floquet-Theorie eingeführt, die einen exzellenten Rahmen dafür bietet zeitperiodische Hamiltonians zu behandeln und die Grundlage für die folgenden Kapitel ist. Kapitel 3 stellt den Vorschlag vor, Bloch-Bänder in optischen Gittern durch das Schütteln des Gitters kohärent miteinander zu koppeln. Insbesondere wird im Detail gezeigt, wie dieses Bandkoppeln zu einem orbital getriebenen Phasenübergang von einem Mott-Isolator zu einem Suprafluid führen kann. In Kapitel 4 wird der Vorschlag erläutert, wie eindimensionale Anyonen durch stark wechselwirkende Bosonen erzeugt werden können, indem das Gitter gekippt und geschüttelt wird. Außerdem wird vorgeschlagen, Friedel-Oszillationen im Ortsraum als im Experiment messbare Signatur für die Anyonisierung zu nutzen. Schließlich werden in Kapitel 5 Multiphoton-Übergänge in höhere Bloch-Bänder untersucht, im Falle eines geschüttelten und eines Amplitudenmodulierten Gitters. Die Stärke und die Lage der Resonanzen, welche zu Heizen führen, werden hierbei theoretisch und numerisch beschrieben.

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(理学) / 甲第23693号 / 理博第4783号 / 新制||理||1685(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐藤 昌利, 教授 柳瀬 陽一, 教授 川上 則雄 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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Thesis (Ph. D.)--University of Texas at Austin, 2003. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--University of Missouri-Columbia, 1996. / Typescript. Vita. Includes bibliographical references (leaves 94-95). Also available on the Internet.