What is “complex”? A question which stimulates a panoply of often quite diverse associations and answers. While in condensed matter and also (macro-) molecular physics we are used to be forced into effective descriptions of large, multicomponent, interacting quantum systems, complexity is “(re-) constructed” in modern quantum optical experiments. In learning how “complexity” emerges from strongly coupling few degrees of freedom (or particles) we start to contemplate how to control complex systems, and learn to distinguish what is just complicated from what is truly complex. This special issue of Annalen der Physik collects expertise and perspectives on complex (quantum) systems from very diverse areas of research: disordered quantum systems, molecular dynamics and interactions, mesoscopic physics, quantum many body physics, open quantum systems, network and scattering theory, quantum information and control – which all share the same interest in getting a better grasp of complexity on the quantum level. Disorder physics with its long-standing history in the condensed matter context nowadays merges with the physics of ultracold atomic gases in highly controlled potential landscapes, and finds applications in “big data”. Mesoscopic transport theory finds novel playgrounds in graphene or in coupled quantum circuits. The coupling of electronic and nuclear degrees of freedom determines chemical reactions, as well as energy flow and directionality in large molecular complexes, with an intricate interplay of coherent and incoherent effects. Today's “femtochemistry” and “femtobiology” experiments reveal these ultrafast molecular pathways in detail and make the border between quantum and classical regimes directly observable. Indeed, this research area has become a test bed for quantum transport and control theory applied to realistic, truly complex, finite quantum systems. Given the generically highly structured spectral densities which underlie molecular systems, novel strategies are called for to characterize complex open quantum systems exhibiting structured, “active” environments. Well-controlled non- equilibrium many-particle quantum dynamics becomes accessible with ultracold quantum gases loaded into engineered potential landscapes, or in photonic circuitry. This challenges theory to develop novel tools for the efficient characterization of many-particle non-equilibrium dynamics and transport, and possibly for their control, e.g. through robust design principles. Furthermore, controlled many-body quantum systems allow for enhanced sensing, and give room for the creation of highly complex many-particle states. The latter may serve, e.g., as resources for quantum computation – which, in turn, may be used to characterize such states’ complexity. This collection of various contributions either on complex molecular structures which are ever better resolved, or on novel composite quantum systems or materials which are ever better controlled, provide a snapshot of current trends in the science of complex quantum systems. Our authors’ diverse specializations highlight the research field's interdisciplinary appeal, and the broad relevance of many of the unveiled structures – and of those phenomena which remain to be understood. We thus hope that this collection will inspire future work connecting concepts of complexity across disciplines. Irene Burghardt received her Ph.D. in chemistry in 1992 from the University of Lausanne. She carried out postdoctoral research at the Center for Nonlinear Phenomena and Complex Systems in Brussels in 1992–1995, followed by research fellowships at the Universities of Bonn and Heidelberg in 1996–1998. From 1999–2011, she held a CNRS research position at ENS Paris, and was appointed CNRS Research Director in 2007. In 2011, she moved to Goethe University Frankfurt where she holds a full professorship in Theoretical Chemistry. Her research addresses quantum molecular dynamics and nonequilibrium phenomena, with a focus on materials and biological systems. Andreas Buchleitner studied Physics at the Ludwig Maximilians University of Munich and received his diploma in 1989, upon research in experimental quantum optics. In 1993, he obtained his PhD, with theoretical research at Laboratoire de Spectroscopie Hertzienne (today Laboratoire Kastler Brossel) of Universite Pierre et Marie Curie and Ecole Normale Supérieure in Paris. Afterwards, he was a PostDoc at the Max Planck Institute for Quantum Optics, Garching, and a visiting researcher at the Queen's University of Belfast and at the Weizmann Institute of Science, Revohot. In 1999, he received his Habilitation from the Ludwig Maximilians University of Munich. From 1999 to 2007, he led the research group “Nonlinear Dynamics in Quantum Systems” at the Max Planck Institute for the Physics of Complex Systems in Dresden. Since 2007, he holds the Chair for “Quantum Optics and Statistics” at the Albert Ludwigs University of Freiburg. His main research interests are Quantum Chaos, Quantum Information and Quantum Transport. From October 2014 to 2015, he was a Senior Fellow, and Speaker of the Research Focus “Designed Quantum Transport in Complex Materials”, at the Freiburg Institute for Advanced Studies. He serves in different honorary capacities, e.g., for the German Physical Society and for the German National Academic Foundation.
What is “complex”? A question which stimulates a panoply of often quite diverse associations and answers. While in condensed matter and also (macro-) molecular physics we are used to be forced into effective descriptions of large, multicomponent, interacting quantum systems, complexity is “(re-) constructed” in modern quantum optical experiments. In learning how “complexity” emerges from strongly coupling few degrees of freedom (or particles) we start to contemplate how to control complex systems, and learn to distinguish what is just complicated from what is truly complex. This special issue of Annalen der Physik collects expertise and perspectives on complex (quantum) systems from very diverse areas of research: disordered quantum systems, molecular dynamics and interactions, mesoscopic physics, quantum many body physics, open quantum systems, network and scattering theory, quantum information and control – which all share the same interest in getting a better grasp of complexity on the quantum level. Disorder physics with its long-standing history in the condensed matter context nowadays merges with the physics of ultracold atomic gases in highly controlled potential landscapes, and finds applications in “big data”. Mesoscopic transport theory finds novel playgrounds in graphene or in coupled quantum circuits. The coupling of electronic and nuclear degrees of freedom determines chemical reactions, as well as energy flow and directionality in large molecular complexes, with an intricate interplay of coherent and incoherent effects. Today's “femtochemistry” and “femtobiology” experiments reveal these ultrafast molecular pathways in detail and make the border between quantum and classical regimes directly observable. Indeed, this research area has become a test bed for quantum transport and control theory applied to realistic, truly complex, finite quantum systems. Given the generically highly structured spectral densities which underlie molecular systems, novel strategies are called for to characterize complex open quantum systems exhibiting structured, “active” environments. Well-controlled non- equilibrium many-particle quantum dynamics becomes accessible with ultracold quantum gases loaded into engineered potential landscapes, or in photonic circuitry. This challenges theory to develop novel tools for the efficient characterization of many-particle non-equilibrium dynamics and transport, and possibly for their control, e.g. through robust design principles. Furthermore, controlled many-body quantum systems allow for enhanced sensing, and give room for the creation of highly complex many-particle states. The latter may serve, e.g., as resources for quantum computation – which, in turn, may be used to characterize such states’ complexity. This collection of various contributions either on complex molecular structures which are ever better resolved, or on novel composite quantum systems or materials which are ever better controlled, provide a snapshot of current trends in the science of complex quantum systems. Our authors’ diverse specializations highlight the research field's interdisciplinary appeal, and the broad relevance of many of the unveiled structures – and of those phenomena which remain to be understood. We thus hope that this collection will inspire future work connecting concepts of complexity across disciplines. Irene Burghardt received her Ph.D. in chemistry in 1992 from the University of Lausanne. She carried out postdoctoral research at the Center for Nonlinear Phenomena and Complex Systems in Brussels in 1992–1995, followed by research fellowships at the Universities of Bonn and Heidelberg in 1996–1998. From 1999–2011, she held a CNRS research position at ENS Paris, and was appointed CNRS Research Director in 2007. In 2011, she moved to Goethe University Frankfurt where she holds a full professorship in Theoretical Chemistry. Her research addresses quantum molecular dynamics and nonequilibrium phenomena, with a focus on materials and biological systems. Andreas Buchleitner studied Physics at the Ludwig Maximilians University of Munich and received his diploma in 1989, upon research in experimental quantum optics. In 1993, he obtained his PhD, with theoretical research at Laboratoire de Spectroscopie Hertzienne (today Laboratoire Kastler Brossel) of Universite Pierre et Marie Curie and Ecole Normale Supérieure in Paris. Afterwards, he was a PostDoc at the Max Planck Institute for Quantum Optics, Garching, and a visiting researcher at the Queen's University of Belfast and at the Weizmann Institute of Science, Revohot. In 1999, he received his Habilitation from the Ludwig Maximilians University of Munich. From 1999 to 2007, he led the research group “Nonlinear Dynamics in Quantum Systems” at the Max Planck Institute for the Physics of Complex Systems in Dresden. Since 2007, he holds the Chair for “Quantum Optics and Statistics” at the Albert Ludwigs University of Freiburg. His main research interests are Quantum Chaos, Quantum Information and Quantum Transport. From October 2014 to 2015, he was a Senior Fellow, and Speaker of the Research Focus “Designed Quantum Transport in Complex Materials”, at the Freiburg Institute for Advanced Studies. He serves in different honorary capacities, e.g., for the German Physical Society and for the German National Academic Foundation.
What is 'complex'? A question which stimulates a panoply of often quite diverse associations and answers. While in condensed matter and also macromolecular physics one is used to be forced into effective descriptions of large, multicomponent, interacting quantum systems, complexity is '(re-)constructed' in modern quantum optical experiments. In learning how 'complexity' emerges from strongly coupling few degrees of freedom (or particles) researchers start to contemplate how to control complex systems, and learn to distinguish what is just complicated from what is truly complex. This special issue collects expertise and perspectives from very diverse fields: photonics, quantum information, molecular dynamics, quantum control, quantum many body physics, open/disordered quantum systems -which all share the interest in getting a better grasp of complexity on the quantum level.
Precisely characterizing and controlling the dynamics of realistic open quantum systems has emerged in recent years as a key challenge across contemporary quantum sciences and technologies, with implications ranging from physics, chemistry and applied mathematics to quantum information processing (QIP) and quantum engineering. Quantum control theory aims to provide both a general dynamical-system framework and a constructive toolbox to meet this challenge. The purpose of this special issue of Journal of Physics B: Atomic, Molecular and Optical Physics is to present a state-of-the-art account of recent advances and current trends in the field, as reflected in two international meetings that were held on the subject over the last summer and which motivated in part the compilation of this volume—the Topical Group: Frontiers in Open Quantum Systems and Quantum Control Theory , held at the Institute for Theoretical Atomic, Molecular and Optical Physics (ITAMP) in Cambridge, Massachusetts (USA), from 1–14 August 2010, and the Safed Workshop on Quantum Decoherence and Thermodynamics Control , held in Safed (Israel), from 22–27 August 2010. Initial developments in quantum control theory date back to (at least) the early 1980s, and have been largely inspired by the well-established mathematical framework for classical dynamical systems. As the above-mentioned meetings made clear, and as the burgeoning body of literature on the subject testifies, quantum control has grown since then well beyond its original boundaries, and has by now evolved into a highly cross-disciplinary field which, while still fast-moving, is also entering a new phase of maturity, sophistication, and integration. Two trends deserve special attention: on the one hand, a growing emphasis on control tasks and methodologies that are specifically motivated by QIP, in addition and in parallel to applications in more traditional areas where quantum coherence is nevertheless vital (such as, for instance, quantum control of chemical reactions or high-resolution magnetic resonance spectroscopy); on the other hand, an unprecedented demand for close coupling between theory and experiment , with theoretical developments becoming more and more attuned to and driven by experimental advances as different quantum technologies continue to evolve at an impressive pace in the laboratory. Altogether, these two trends account for several of the recurrent themes in this volume, as well as in the current quantum control literature as a whole: namely, the quest for control strategies that can attain the highest degree of precision and robustness possible, while striving for efficiency and, ultimately, optimality in achieving the intended control task under realistic operational constraints. From a theory standpoint, this makes it imperative to take into account increasingly more realistic control settings; to assess the quantitative impact of limited control resources and/or system knowledge; and to provide a rigorous and general foundation for existing experimental approaches in order to further enhance applicability and performance. From an experimental standpoint, renewed emphasis is in turn placed on validating theoretical predictions and benchmarking performance, so that the limiting constraints can be singled out for additional theoretical analysis and guidance. This ongoing cross-talk is clearly reflected in this collection, which brings together theoreticians and experimentalists, with a significant fraction of the papers reporting on combined quantum control theory–experiment efforts. While a precise categorization would neither be possible nor desirable, contributions to this volume have been loosely grouped into five broad sections. This grouping has been made in the hope that connections between different problems and/or technical approaches will become more transparent, facilitating the transfer of concepts and methods. The special issue opens with a section devoted to open-loop control methods, with special emphasis on dynamical decoupling (DD), which is becoming an increasingly important tool for decoherence control at the physical 'quantum firmware' level. In addition to including original research results, the first two articles, by Brion et al and Biercuk et al , also serve to pedagogically review some background in their respective subjects. In particular, Brion et al revisit one of the conceptually simplest approaches to open-loop manipulation of both closed and open quantum systems, nonholonomic control , motivated by its broad applicability to QIP settings. A special instance of open-loop control based on sequences of (nearly) instantaneous `bang-bang' pulses is addressed by Biercuk et al , who reformulate the simplest DD scenario, suppression of phase decoherence in a single qubit, as a filter-design problem. Peng et al report on the implementation of 'concatenated' DD for arbitrary single-qubit decoherence in the context of nuclear magnetic resonance QIP. A dedicated analysis of the performance of different DD schemes in the presence of realistic pulse errors is given by Wang and Dobrovitski. DD is also one of the strategies used by Lucamarini et al to reduce polarization decoherence in a photon qubit. These authors additionally report on the use of active feedback to counter transmission noise, effectively setting the stage for the second section, which is centered on closed-loop control. Unlike in open-loop control, measurement is an essential ingredient in closed-loop schemes aimed at both reliably identifying features of the target quantum system and further modifying its dynamics. The importance of directly measuring the spectrum of the underlying system-environment coupling is stressed by Almog et al , who show how this knowledge is crucial, in particular, for predicting the performance of DD sequences in experiments and for optimizing performance. Riofrio et al address a weak-measurement protocol for implementing quantum state tomography , which is a necessary 'primitive' for inferring the target quantum state and thereby diagnosing the control performance. Next, the impact of realistic control and system imperfections in continuous-time Markovian feedback strategies for rapid state preparation is analyzed by Combes and Wiseman. A prominent role is played in the special issue by optimal control (OC) approaches, reflecting their central importance for quantum control and QIP. The OC contributions have been divided into two separate sections, depending on whether the target dynamics is modeled as Hamiltonian (section 3) or dissipative (section 4), respectively. The contribution by Beltrani et al deals with `control landscapes', which provide a foundation for analyzing the performance of numerical OC algorithms and their robustness against control errors. Specifically, this paper characterizes geometric properties of the control landscape, relevant to the optimal control of state-to-state transitions. Application of OC theory to the problem of population transfer and coherence enhancement in Λ-systems is studied by Kumar et al , whereas Goerz et al report on the OC-design of a high-fidelity controlled phase-gate in atomic qubits. The robustness of an OC solution is specifically addressed by Negretti et al , along with an approach for identifying easily implementable while still 'close-to-optimal' control pulses. Powerful relaxation-optimized OC schemes (based on so-called opengrape algorithms) for generating unitary target gates in the presence of known dissipation parameters are discussed by Schulte-Herbrüggen et al . Next, Lapert et al report on the problem of time-optimal control of spin-1/2 systems undergoing Bloch relaxation dynamics, highlighting the crucial role played by singular extremals in the control synthesis. Alternative approaches for optimized control of qubits exposed to various decoherence processes are developed by Esher et al and Xue et al , based on a perturbative 'bath-optimized' formalism and on numerical optimization via a genetic algorithm, respectively. Testifying to the richness of the field, the volume concludes with four contributions that address a diverse range of problems. The exploitation of properties of adiabatic quantum evolutions is common to the first two papers. In particular, Legthtas et al offer a rigorous explanation for the robustness of a control protocol, chirped pulsing , that is widely employed in 'adiabatic rapid passage' experiments, while Han et al present a theoretical framework for adiabatic Raman photo-association schemes relevant to ultracold atomic systems. In the context of cavity quantum electrodynamics, Montenegro and Orszag describe how to engineer a system of two atoms coupled to distant lossy cavities so that stable atomic entanglement is generated. Finally, still very little is known about the physical mechanisms that are responsible for and control the experimentally observed 'coherent' features of transport phenomena in biological systems. The last contribution by Alicki and Giraldi analyzes energy transport in dynamical systems that can be modeled as 'quantum networks', and points to this fascinating emerging frontier. It is our hope that the above papers may help readers to gain an overview of some of the main trends in current quantum control efforts, both theoretical and experimental. In closing, we take the opportunity to thank the organizations which sponsored the above-mentioned ITAMP Topical Group (the United States National Science Foundation and Harvard University) and the Safed Workshop (the Israeli Science Foundation, the Safed Scientific Workshop program, CECAM and ACAM). Last but not least our sincere gratitude goes to all of the contributors to the volume and the reviewers as well as the J. Phys. B staff, for their respective efforts in preparing the papers and ensuring the overall quality of this special issue.
Quantum many-body systems, as they appear in different branches of physics and chemistry, are very hard to simulate. The number of parameters defining their quantum states grows exponentially with the number of constituents. This prevents us from exploring and investigating relevant problems involving relatively small numbers of subsystems even with the help of the most powerful supercomputers. Richard Feynman already noticed this difficulty back in 1981 when he wrote his visionary paper “Simulating Physics with Computers” [Int. J. Theor. Phys. 21:6/7, 467 (1982)]. There, he proposed to use quantum systems (as opposed to classical computers) to perform the simulation and in this way to circumvent the need to store and compute a colossal number of parameters, necessary to describe the pertaining superpositions. What was a visionary idea at that time has become a very active field of research in the last few years. The extraordinary progress of both theoretical and experimental research in quantum physics allows us now to tame, control, and manipulate various quantum systems with unprecedented precision. Laser, magnetic, electronic and other technologies enable us to arrange quantum subsystems in different geometries, modify their interactions, and detect them. This allows us to engineer Hamiltonians and emulate systems displaying some of the most intriguing quantum phenomena. This tremendous progress is, to a large extent, due to the pioneering work of many researchers during the last twenty to thirty years. Here, the investigations of basic phenomena with one or few atoms or photons were of particular impact. The degree of control achieved in the experiments has enabled the observation of mind-boggling quantum effects, related to the superposition principle or to entangled states, and their disappearance due to decoherence. In fact, the 2012 Nobel Prize has been awarded to two scientists, S. Haroche and D. Wineland, for such ground-breaking experiments. Such experiments, often in combination with laser cooling of atoms or ions and Bose-Einstein condensation, have formed one of the pillars on which the field of quantum simulations is being established. Quantum simulations with cold atoms, either in magnetic traps or in optical lattices, with trapped ions, with photons, with superconducting devices, with quantum dots, etc., have been theoretically proposed and experimentally considered by many researchers. Most of the proposals so far deal with problems in condensed matter physics that are either difficult to tackle with modern supercomputers or are difficult to observe in solid state systems. This has established a very close link between different disciplines, like atomic, molecular, and optical (AMO) physics, and condensed matter physics. Although some of the experiments are still in their infancy, and a lot of research is still needed, the extraordinary progress made in all these research areas during the last few years makes us feel confident that in the not too distant future quantum simulators will provide a key tool to investigate many-body quantum systems. Furthermore, we also expect that quantum simulators will help quantum physicists to establish new and fruitful links to other scientific communities, like high-energy physics or quantum chemistry. The present special issue contains various review papers as well as research papers on quantum simulations. It starts out with two papers written by last year's Nobel Prize winners describing their foundational work (Wineland, p. 739 and Haroche, p. 763). The issue continues with three thorough, invited review papers covering different topics on quantum simulations. The first one reviews recent theoretical proposals to use cold atoms in optical lattices to simulate lattice gauge theories of the sort that appear in high-energy physics (U.-J. Wiese, p. 783). The second covers both theoretical proposals and experimental demonstrations of cold-atom systems to simulate the physics of matter in the presence of gauge fields, displaying so-called topological phenomena, which so far have only been observed in solid-state systems (I. Spielman, p. 794). The third one contains an extensive overview and new proposals to perform a broad range of quantum simulations using quantum dot systems (P. Barthelmy et al., p. 813). The issue also includes six original papers with a variety of theoretical proposals as well as the introduction of novel theoretical techniques related to the field of quantum simulation. The field of quantum simulations is just starting, but we are confident that it will soon generate an even larger plethora of new ideas and discoveries, trigger interdisciplinary research, and lead us to the adventure of describing and understanding the quantum world. We hope that this special issue will help future researchers in such an exciting adventure. Rainer Blatt received his PhD degree in physics from the University of Mainz in 1981. As a postdoctoral fellow he worked on atomic beam cooling in Boulder, CO and later as a research assistant in Hamburg with single trapped ions. In 1995 he accepted a chair in experimental physics at the University of Innsbruck working on quantum information processing with trapped ions. Since 2003 he is also scientific director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences. Immanuel Bloch received his PhD degree in physics from the Ludwig Maximilians University of Munich in 2000. As a junior group leader, he continued in Munich starting his work on ultracold quantum gases in optical lattices. In 2008 he was appointed scientific director of the newly founded division on Quantum Many-Body Systems at the Max Planck Institute of Quantum Optics. Since 2009 he also holds a chair in quantum optics at the Ludwig-Maximilians University of Munich. Ignacio Cirac received his PhD degree in physics from the Universidad Complutense de Madrid in 1991. He was professor at the Universities of Castilla-La Mancha and Innsbruck from 1991–1996 and 1996–2001, respectively. In 2001 he joined the Max-Planck Institute of Quantum Optics, where he leads the Theory Division. His current research interests include quantum information theory and quantum optics. Peter Zoller obtained his doctorate from the University of Innsbruck in 1977. He was Max Kade Fellow at the University of Southern California from 1978/79, and was JILA visiting Fellow 1981/82 and 1988. In 1990 he became JILA Fellow and professor of physics at the University of Colorado. At the end of 1994, he accepted a chair at the University of Innsbruck, where he has worked ever since. Since 2003, he has also held the position of Scientific Director at the Institute for Quantum Optics and Quantum Information (IQOQI) of the Austrian Academy of Sciences.
Theory and experiment have not fully resolved the apparent dichotomy , which has agonized physics for the past eighty years: on the one hand, the description of microsystems by quantum mechanics and, on the other, the description of macrosystems by classical dynamics or statistical mechanics. Derivations of the time-irreversible Liouville equation for an open quantum system, based on projecting out its environment, have narrowed the gap between the quantum and classical descriptions. Yet our `classical' intuition continues to be confronted by quantum-mechanical results like the Einstein--Podolsky--Rosen paradox that challenges the classical notion of locality, or the quantum Zeno effect which suggests that the isolation of a system is not the only way to preserve its quantum state. There are two key concepts in any discussion of such issues. The first, which is responsible for the most salient nonclassical properties, is entanglement , that is partial or complete correlation or, more generally, inseparability of the elements comprising a quantum ensemble . Even after their interaction has ceased, this inseparability, originating from their past interaction, can affect the state of one element when another element is subject to a nonunitary action, such as its measurement, tracing- out, or thermalization. The second key concept is decoherence of open quantum systems, which is the consequence of their entanglement with their environment, a `meter' or a thermal `reservoir', followed by the tracing-out of the latter. Despite new insights into entanglement and decoherence, there are still no complete, unequivocal answers to the fundamental questions of the transition from quantal to classical behaviour: how do irreversibility and classicality emerge from unitarity as systems and their environments become increasingly complex ? At what stage does system--meter entanglement give rise to a classical readout of the meter? Is there an upper limit on the size or complexity of systems displaying entanglement? Major developments have opened new vistas into controlled entanglement , which is the resource of quantum information processing. However, these developments have mainly focused on ensembles of simple two- and three-level systems that are thoroughly isolated from their environments. Treatments of coherence in quantum computing have mostly assumed that only a single or a few the elements of the quantum ensemble may simultaneously undergo an uncontrolled intervention---a quantum error. Decoherence-control protocols for more general types of errors are still incomplete. In order to resolve the outstanding issues of the quantum--classical transition, and study the control of entanglement and decoherence without the foregoing restrictions, we must venture into the domain of Quantum Complex Systems (QUACS), either consisting of a large number of inseparable elements or having many coupled degrees of freedom. Our conviction is that fundamental understanding and manipulation of entanglement within QUACS or their entanglement with the environment or a meter, call for the creation of a new conceptual framework or paradigm, that would encompass phenomena common to cold atoms in laser fields, large molecules, Josephson junctions, quantum gases and solids, with the view of employing these systems for quantum information processing and computing. Progress within this paradigm should allow us to answer the questions: does entanglement play an essential role in the evolution of large collections of complex systems? What are the size and complexity limits of systems and ensembles still controllable by an external intervention? What are the most appropriate decoherence protection schemes and control algorithms? This special issue addresses the challenge of understanding in depth and manipulating the basic quantum properties of optical, atomic, molecular and condensed-matter QUACS, and large ensembles thereof. In view of the interdisciplinary character of this issue, we find it expedient to look at the presented articles not only according to the physical objects they describe, but also from a unifying standpoint. Several unifying themes may be discerned: memory effects in dephasing and relaxation; protection of quantum information by its distribution throughout the ensemble; control of decoherence and entanglement by time-dependent interventions or measurements; manifestations of entanglement in scattering off statistical ensembles; measurment-induced dynamics. The concerted discussion of the topics outlined above should help us advance the new paradigm that addresses our abilities to diagnose and manipulate the entangled states of complex quantum objects and their robustness against decoherence. These abilities are required for quantum information (QI) applications in matter--wave interferometry in molecular, semiconducting or superconducting systems. On the fundamental level, this book may help establish the notion of dynamical information exchange between quantum systems and chart in detail the route from unitarity to classicality. Further developments within the outlined paradigm should yield novel, advantageous QI processing schemes and high-sensitivity interferometers, owing to decoherence suppression and effective control of many degrees of freedom. In the long run, these strategies may prove to be the first step towards the (hitherto unattempted) use of entanglement in nanotechnology, metrology and chemistry, with potentially remarkable novel applications.
In the past decades, rapid advances in the experimental control of quantum systems have opened up unparalleled capabilities of engineering exotic quantum states. Nowadays, we may consider ourselves witnesses of a second quantum revolution as strongly correlated quantum matter is regularly created, on a daily basis, within the most diverse platforms, e.g. arrays of Rydberg atoms, ultra-cold atoms in optical lattices, superconducting qubits, trapped ions, and quantum dots. In this era, dubbed Noisy-Intermediate Scale Quantum (NISQ) era, the effort in pursuing research for realizing quantum technologies with practical purposes, such as quantum computing, simulations, communication and metrology, has greatly accelerated, and we are just starting to experience the immense progress that could be achieved. The remarkable breakthrough we are facing builds upon seminal theoretical and experimental advances in quantum physics. The key achievements in atomic, molecular, and optical (AMO) physics have opened up the possibility of controlling, trapping, and measuring single atoms, one by one, with high accuracy and reliability. In parallel, from a theoretical point of view, the study of quantum entanglement and correlations has bridged AMO physics and quantum information with crucial proposals for the realization of universal quantum computers. In this context, entanglement has emerged as one of the key tools to characterize and to exploit quantum many-body systems for quantum information purposes. We will study quantum entanglement in several scenarios to investigate and probe complex quantum many-body systems. We will consider examples ranging from generic mixed states in equilibrium to out-of-equilibrium dynamics, with and without dissipation, and topologically non-trivial systems. The leitmotif of this work will be how entanglement and correlations can be exploited to characterize the many-body quantum state describing a physical system and how entanglement can be detected in an experimentally efficient manner.
Many outstanding problems in quantum physics, such as high-Tc superconductivity or quark confinement, are still - after decades of research - awaiting commonly accepted explanations. One reason is that such systems are often difficult to control, show an intermingling of several effects, or are not easily accessible to measurement. To arrive at a deeper understanding of the physics at work, researchers typically derive simplified models designed to capture the most striking phenomena of the system under consideration. However, due to the exponential complexity of Hilbert space, even some of the simplest of such models pose formidable challenges to analytical and numerical calculations. In 1982, Feynman proposed to solve such quantum models with experimental simulation on a physically distinct, specifically engineered quantum system [Int. J. Theor.Phys. 21, 467]. Designed to be governed by the same underlying equations as the original model, it is hoped that direct measurements on these so called quantum simulators (QSs) will allow to gather deep insights into outstanding problems of physics and beyond. In this thesis, we identify four requirements that a useful QS has to fulfill, relevance, control, reliability, and efficiency. Focusing on these, we review the state of the art of two popular approaches, digital QSs (i.e., special purpose quantum computers) and analog QSs (devices with always-on interactions). Further, focusing on possibilities to increase control over QSs, we discuss a scheme to engineer quantum correlations between mesoscopic numbers of spinful particles in optical lattices. This technique, based on quantum polarization spectroscopy, may be useful for state preparation and quantum information protocols. Additionally, employing several analytical and numerical methods for the calculation of many-body ground states, we demonstrate the variety of condensed-matter problems that can be attacked with QSs consisting of ultracold ions or neutral atoms in optical lattices. The chosen examples, some of which have already been realized in experiment, include such diverse settings as frustrated antiferromagnetism, quantum phase transitions in exotic lattice geometries, topological insulators, non-Abelian gauge-fields, orbital order of ultracold Fermions, and systems with long-range interactions. The experimental realization of all of these models requires techniques which go beyond standard optical lattices, e.g., time-periodic driving of lattices with exotic geometry, loading ultracold atoms into higher bands, or immersing trapped ions into an optical lattice. The chosen models, motivated by important open questions of quantum physics, pose difficult problems for classical computers, but they may be amenable in the near future to quantum simulation with ultracold atoms or ions. While the experimental control over relevant models has increased dramatically in the last years, the reliability and efficiency of QSs has received considerably less attention. As a second important part of this thesis, we emphasize the need to consider these aspects under realistic experimental conditions. We discuss specific situations where terms that have typically been neglected in the description of the QS introduce systematic errors and even lead to novel physics. Further, we characterize in a generic example the influence of quenched disorder on an analog QS. Its performance for simulating universal behavior near a quantum phase transition seems satisfactory for low disorder. Moreover, our results suggest a connection between the reliability and efficiency of a QS: it works less reliable exactly in those interesting regimes where classical calculations are less efficient. If QSs fulfill all of our four requirements, they may revolutionize our approach to quantum-mechanical problems, allowing to solve the behavior of complex Hamiltonians, and to design nano-scale materials and chemical compounds from the ground up.