The enormous experimental progress in atomic, molecular and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even many-body ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthinkable some years ago. This versatile set of tools has enabled the development of the well-established concept of engineering of many-body Hamiltonians in various physical platforms. These available tools, however, can also be harnessed to extend the scenario of Hamiltonian engineering to a more general Liouvillian setting, which in addition to coherent dynamics also includes controlled dissipation in many-body quantum systems. Here, we review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems of atoms and ions. This comprises digital quantum simulations in a general open system setting, as well as engineering and understanding new classes of systems far away from thermodynamic equilibrium.
The enormous experimental progress in atomic, molecular and optical (AMO) physics during the last decades allows us nowadays to isolate single, a few or even many-body ensembles of microscopic particles, and to manipulate their quantum properties at a level of precision, which still seemed unthinkable some years ago. This versatile set of tools has enabled the development of the well-established concept of engineering of many-body Hamiltonians in various physical platforms. These available tools, however, can also be harnessed to extend the scenario of Hamiltonian engineering to a more general Liouvillian setting, which in addition to coherent dynamics also includes controlled dissipation in many-body quantum systems. Here, we review recent theoretical and experimental progress in different directions along these lines, with a particular focus on physical realizations with systems of atoms and ions. This comprises digital quantum simulations in a general open system setting, as well as engineering and understanding new classes of systems far away from thermodynamic equilibrium.
The study of open quantum systems – microscopic systems exhibiting quantum coherence that are coupled to their environment – has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This method was developed in quantum optics as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. In this article, we review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods in these systems. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.
Recent advances in coherent manipulation and control have led to new opportunities to study non-equilibrium dynamics in quantum many-body systems. Using a variety of experimental platforms ranging from cold atoms and ions to solid-state spin defects, small building blocks of fully controllable quantum systems can be assembled into a strongly interacting many-body system. With this approach, one can gain new insights into fundamental questions in basic science such as the mechanism of quantum thermalization or the existence of exotic phases of matter out of equilibrium. At the same time, a fully controllable large-scale quantum device has promising applications for high precision sensing, secure communication, and quantum information processing.\nThis thesis describes recent progress in engineering quantum dynamics that is robust against various imperfections such as environmental noise, disorder, or imprecise controls. We find that non-equilibrium quantum states of strongly interacting systems can be protected from imperfections upon appropriate external manipulations such as time-dependent periodic controls, engineered coherent or dissipative interactions, or an introduction of strong quenched disorder. Furthermore, under certain conditions, these imperfections can be utilized to stabilize non-trivial quantum states. Our results challenge conventional wisdom of statistical mechanics, shedding light on the microscopic mechanisms of thermalization.\nWe also discuss how engineered dynamics can be harnessed for applications such as quantum metrology, simulations, or information processing.
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.
Rydberg atoms, characterized by their strong and long-range dipole-dipole interactions, provide a versatile platform for exploring intriguing collective and many-body effects. Recently, the experimental realization of these effects in dense ensembles and reconfigurable atomic arrays has attracted significant interest, particularly for applications in quantum simulations and non-equilibrium physics. This review focuses on such recent development, discussing the theoretical foundations of the interactions between Rydberg atoms and the ensuing many-body physics, while providing a critical survey of experimental techniques for their precise manipulation and observation. We further discuss recent breakthroughs in leveraging Rydberg collective effects to probe novel many-body phases and non-equilibrium dynamics of these systems. By synthesizing theoretical insights with experimental milestones, we provide a comprehensive perspective on this rapidly evolving field and its transformative potential for future quantum technologies.
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.
All real-world quantum systems interact with their surrounding environment to some extent. No matter how weak the coupling that prevents the system from being isolated, the evolution of an open quantum system is eventually plagued by non-unitary features, such as decoherence and dissipation. Decoherence is a quantum effect where the system loses its ability to exhibit coherent behavior. Nowadays, decoherence stands as a serious obstacle in quantum information processing. As the manipulation of quantum coherence in experiments has progressed, the need to better understand, control, and utilize dissipative non-equilibrium dynamics of quantum systems has grown in importance. This has ranged from fundamental questions associated with the quantum-to-classical transition and quantum thermodynamics innovation in quantum optics and cavity/circuit quantum electrodynamics. Current studies of many-body dynamics, ultracold atoms in optical lattices, trapped ions, superconducting systems, nanoelectro-mechanical systems, and quantum fields under the influence of external conditions offer new challenges to address questions regarding quantum systems far from equilibrium. On the theoretical side, quantum trajectory-based methods could be the key to both quantum nanodevice design and exploration of new regimes of quantum mechanics and quantum measurement, as well as applications to various quantum technologies.