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Dynamics and Characterization of Composite Quantum Systems Springer Theses Springer Theses Recognizing Outstanding Ph.D. Research Manuel Gessner Dynamics and Characterization of Composite Quantum Systems Springer Theses Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder. • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. More information about this series at http://www.springer.com/series/8790 Manuel Gessner Dynamics and Characterization of Composite Quantum Systems Doctoral Thesis accepted by Albert Ludwigs University of Freiburg, Germany 123 Author Supervisor Dr. Manuel Gessner Prof. Andreas Buchleitner Quantum Science and Technology in Arcetri Institute of Physics (QSTAR) Albert Ludwig University of Freiburg European Laboratory for Non-Linear Freiburg im Breisgau Spectroscopy (LENS) Germany Florence Italy ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-319-44458-1 ISBN 978-3-319-44459-8 (eBook) DOI 10.1007/978-3-319-44459-8 Library of Congress Control Number: 2016949575 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Supervisor’s Foreword Formidable progress in the control and assembly of single constituents of matter has been achieved during the last two decades in quantum optics labs around the world. Experiments with trapped ions and atoms, with tailored states of light, and with metamaterials provide versatile platforms to study and optimize essential building blocks of future quantum computing architectures, to explore the observable dynamical and spectral features of fundamental models of condensed matter theory, and to monitor the emergence of robust macroscopic properties from the micro- scopic dynamics of an increasing number of coupled degrees of freedom. The complexity of such highly engineered, composite quantum systems rapidly increases with the number of interwoven degrees of freedom, and novel tools are required to characterize, monitor and control their dynamical behaviour, in exper- iment and theory, with scalable overhead. The present treatise by Manuel Gessner blends advanced theoretical tools from the theory of open quantum systems, quantum optics, quantum chaos, quantum information theory, and quantum statistics, to provide a fresh perspective on the characterisation and control of “complex” quantum systems such as those now within reach in quantum optics laboratories. Often with specific experimental implementations in mind, this text not only offers a pedagogical introduction to the broader scientific context (together with the relevant literature) and the necessary theoretical machinery, but also elaborates on several innovative applications. Readers with an interest in the efficient probing of collective and spectral properties of composite quantum systems, in their open-system entanglement dynamics, in many-particle dephasing phenomena and in the impact thereon of the particles’ mutual (in)distinguishability will find this text both informative and inspiring. Newcomers to the field will appreciate being able to follow the essential physics issues from their theoretical foundations to cutting-edge research. Freiburg im Breisgau, Germany Prof. Andreas Buchleitner June 2016 v Abstract Due to experimental developments over the past decades on quantum optical and atomic systems, a wealth of composite quantum systems of variable sizes has become accessible under rather well-controlled conditions. Typical systems of tens of trapped ions or thousands of cold neutral atoms are usually too large to fully measure all of their constituents’ microscopic quantum properties, but not large enough to be described completely in terms of thermodynamic quantities. This challenging intermediate regime of controllable quantum few- to many-body sys- tems is particularly interesting, since it combines a variety of different phenomena and applications, ranging from quantum information theory to solid-state physics. The effective characterization of these systems requires flexible and experi- mentally feasible observables, complemented by efficient theoretical methods and models. In this dissertation we employ concepts from the fields of open quantum systems, quantum information theory, quantum many-body theory and physical chemistry, to construct dynamical approaches for the study of various aspects of correlations, and to describe spectral and dynamical features of complex, interacting quantum systems. Some of the developed theoretical ideas are complemented by experimental realizations with trapped ions or photons. To facilitate the scalable analysis of bipartite correlation properties in the context of quantum information theory, we introduce a method which allows to detect and estimate discord-type correlations when only one of the two correlated subsystems can be measured. The method makes use of the influence of the correlations on the local subsystem dynamics, which illustrates the fundamental role of initial corre- lations for the theory of open quantum systems. We present an experimental realization with a single trapped ion, as well as the description of a photonic experiment. Further theoretical studies are presented, including the application to a spin-chain model, which relates the dynamical single-spin signature of the ground-state quantum correlations to a quantum phase transition. Having established this local detection technique for quantum discord, whose information about the state’s correlations is limited, we introduce the correlation rank to assess the degree of total correlations of bipartite quantum states. This allows us to identify strongly correlated states which cannot be generated with local vii viii Abstract operations. Classically correlated noise processes, however, are able to generate strongly correlated, but separable quantum states. This is confirmed in a trapped-ion experiment, where such noise processes occur naturally, and represent one of the dominant sources of error. We further develop a fully analytical description of the generated ensemble-average dynamics, allowing us to de derive conditions that ensure the robustness of entanglement in bipartite and multi-particle systems. Information-theoretic quantifiers of the correlation properties between the con- stituents no longer represent suitable observables for increasingly complex com- posite quantum systems. Hence, we develop a multi-configurational mean-field approach in order to understand the dynamical features and, with it, the role of the energy spectrum in the vicinity of the quantum phase transition in a quantum magnet. Specifically, we study a spin-chain model with variable-range interactions
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