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.
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.
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.
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.
The rapid growth of quantum information sciences over the past few decades has fueled a corresponding rise in high profile applications in fields such as metrology, sensors, spintronics, and attosecond dynamics, in addition to quantum information processing. Realizing this potential of today's quantum science and the novel technologies based on this requires a high degree of coherent control of quantum systems. While early efforts in systematizing methods for high fidelity quantum control focused on isolated or closed quantum systems, recent advances in experimental design, measurement and monitoring, have stimulated both need and interest in the control of complex or large scale quantum systems that may also be coupled to an interactive environment or reservoir. This focus issue brings together new theoretical and experimental work addressing the formulation and implementation of quantum control for a broad range of applications in quantum science and technology today.
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.
Abstract These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.
Quantum control of light and matter is the quest to steer a physical process to a desirable outcome, employing constructive and destructive interference. Three basic questions address feasibility of quantum control: (1) The problem of controllability, does a control field exist for a preset initial and target state; (2) Synthesis, constructively finding the field that leads to the target; and (3) Optimal Control Theory - optimizing the field that carries out this task. These continue to be the fundamental theoretical questions to be addressed in the conference. How to realize control fields in the laboratory is an ongoing challenge. This task is very diverse viewing the emergence of control scenarios ranging from attoseconds to microseconds. How do the experimental observations reflect on the theoretical framework? The typical arena of quantum control is an open environment where much of the control is indirect. How are control scenarios realized in dissipative open systems? Can new control opportunities emerge? Can one null decoherence effects? An ideal setting for control is ultracold matter. The initial and final state can be defined more precisely. Coherent control unifies many fields of physical science. A lesson learned in one field can reflect on another. Currently quantum information processing has emerged as a primary target of control where the key issue is controlling quantum gate operation. Modern nonlinear spectroscopy has emerged as another primary field. The challenge is to unravel the dynamics of molecular systems undergoing strong interactions with the environment. Quantum optics where non-classical fields are to be generated and employed. Finally, coherent control is the basis for quantum engineering. These issues will be under the limelight of the Gordon conference on Quantum Control of Light and Matter.