The field of cavity optomechanics is reviewed. This field explores the interaction between electromagnetic radiation and nanomechanical or micromechanical motion. This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation-pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity-quantum-optomechanics experiments. In addition, the perspectives for fundamental quantum physics and for possible applications of optomechanical devices are described.

This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments. This approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of this review is to integrate several approaches proposed in the literature, from semimicroscopic to phenomenological. In particular, first considered are "dry" systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium. The differences and similarities between two types of orientationally ordered states, the nematic and the polar, are clarified. Next, the active hydrodynamics of suspensions or "wet" systems is discussed and the relation with and difference from the dry case, as well as various large-scale instabilities of these nonequilibrium states of matter, are highlighted. Further highlighted are various large-scale instabilities of these nonequilibrium states of matter. Various semimicroscopic derivations of the continuum theory are discussed and connected, highlighting the unifying and generic nature of the continuum model. Throughout the review, the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material is discussed. Promising extensions toward greater realism in specific contexts from cell biology to animal behavior are suggested, and remarks are given on some exotic active-matter analogs. Last, the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents, is summarized.

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem has been a central theme of research from a variety of perspectives, mainly motivated by quantum information science, where the nonlocality of quantum theory underpins many of the advantages afforded by a quantum processing of information. The focus of this review is to a large extent oriented by these later developments. The main concepts and tools which have been developed to describe and study the nonlocality of quantum theory and which have raised this topic to the status of a full subfield of quantum information science are reviewed.

Photonic nanostructures provide a means of tailoring the interaction between light and matter and the past decade has witnessed tremendous experimental and theoretical progress on this subject. In particular, the combination with semiconductor quantum dots has proven successful. This manuscript reviews quantum optics with excitons in single quantum dots embedded in photonic nanostructures. The ability to engineer the light-matter interaction strength in integrated photonic nanostructures enables a range of fundamental quantum-electrodynamics experiments on, e.g., spontaneous-emission control, modified Lamb shifts, and enhanced dipole-dipole interaction. Furthermore, highly efficient single-photon sources and giant photon nonlinearities may be implemented with immediate applications for photonic quantum-information processing. This review summarizes the general theoretical framework of photon emission including the role of dephasing processes and applies it to photonic nanostructures of current interest, such as photonic-crystal cavities and waveguides, dielectric nanowires, and plasmonic waveguides. The introduced concepts are generally applicable in quantum nanophotonics and apply to a large extent also to other quantum emitters, such as molecules, nitrogen vacancy centers, or atoms. Finally, the progress and future prospects of applications in quantum-information processing are considered.

Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.

This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases. DOI: 10.1103/RevModPhys.85.299

Hybrid quantum circuits combine two or more physical systems, with the goal of harnessing the advantages and strengths of the different systems in order to better explore new phenomena and potentially bring about novel quantum technologies. This article presents a brief overview of the progress achieved so far in the field of hybrid circuits involving atoms, spins, and solid-state devices (dincluding superconducting and nanomechanical systems). Howthese circuits combine elements from atomic physics, quantum optics, condensed matter physics, and nanoscience is discussed, and different possible approaches for integrating various systems into a single circuit are presented. In particular, hybrid quantum circuits can be fabricated on a chip, facilitating their future scalability, which is crucial for building future quantum technologies, including quantum detectors, simulators, and computers. DOI: 10.1103/RevModPhys.85.623

Ion acceleration driven by superintense laser pulses is attracting an impressive and steadily increasing effort. Motivations can be found in the applicative potential and in the perspective to investigate novel regimes as available laser intensities will be increasing. Experiments have demonstrated, over a wide range of laser and target parameters, the generation of multi-MeV proton and ion beams with unique properties such as ultrashort duration, high brilliance, and low emittance. An overview is given of the state of the art of ion acceleration by laser pulses as well as an outlook on its future development and perspectives. The main features observed in the experiments, the observed scaling with laser and plasma parameters, and the main models used both to interpret experimental data and to suggest new research directions are described.

This review compiles results of experimental and theoretical studies on thin films and quantum structures of semiconductors with randomly distributed Mn ions, which exhibit spintronic functionalities associated with collective ferromagnetic spin ordering. Properties of p-type Mn-containing III-V as well as II-VI, IV-VI, V-2 -VI3, I-II-V, and elemental group IV semiconductors are described, paying particular attention to the most thoroughly investigated system (Ga, Mn)As that supports the hole-mediated ferromagnetic order up to 190 K for the net concentration of Mn spins below 10%. Multilayer structures showing efficient spin injection and spin-related magnetotransport properties as well as enabling magnetization manipulation by strain, light, electric fields, and spin currents are presented together with their impact on metal spintronics. The challenging interplay between magnetic and electronic properties in topologically trivial and nontrivial systems is described, emphasizing the entangled roles of disorder and correlation at the carrier localization boundary. Finally, the case of dilute magnetic insulators is considered, such as (Ga, Mn)N, where low-temperature spin ordering is driven by short-ranged superexchange that is ferromagnetic for certain charge states of magnetic impurities.

This review describes recent groundbreaking results in Si, Si/SiGe, and dopant-based quantum dots, and it highlights the remarkable advances in Si-based quantum physics that have occurred in the past few years. This progress has been possible thanks to materials development of Si quantum devices, and the physical understanding of quantum effects in silicon. Recent critical steps include the isolation of single electrons, the observation of spin blockade, and single-shot readout of individual electron spins in both dopants and gated quantum dots in Si. Each of these results has come with physics that was not anticipated from previous work in other material systems. These advances underline the significant progress toward the realization of spin quantum bits in a material with a long spin coherence time, crucial for quantum computation and spintronics.

Spinor Bose gases form a family of quantum fluids manifesting both magnetic order and superfluidity. This article reviews experimental and theoretical progress in understanding the static and dynamic properties of these fluids. The connection between system properties and the rotational symmetry properties of the atomic states and their interactions are investigated. Following a review of the experimental techniques used for characterizing spinor gases, their mean-field and many-body ground states, both in isolation and under the application of symmetry-breaking external fields, are discussed. These states serve as the starting point for understanding low-energy dynamics, spin textures, and topological defects, effects of magnetic-dipole interactions, and various nonequilibrium collective spin-mixing phenomena. The paper aims to form connections and establish coherence among the vast range of works on spinor Bose gases, so as to point to open questions and future research opportunities.

This is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the backaction of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is nonconservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to subwavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides the correlated motion of distant particles, one finds critical behavior and nonequilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum-degenerate gases inside optical resonators can be used to emulate optomechanics as well as novel quantum phases such as supersolids and spin glasses. Nonequilibrium quantum phase transitions as predicted by, e. g., the Dicke Hamiltonian can be controlled and explored in real time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for nondestructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems. DOI: 10.1103/RevModPhys.85.553

Quantum mechanics is an extremely successful theory that agrees with every experimental test. However, the principle of linear superposition, a central tenet of the theory, apparently contradicts a commonplace observation: macroscopic objects are never found in a linear superposition of position states. Moreover, the theory does not explain why during a quantum measurement, deterministic evolution is replaced by probabilistic evolution, whose random outcomes obey the Born probability rule. In this article a review is given of an experimentally falsifiable phenomenological proposal, known as continuous spontaneous collapse: a stochastic nonlinear modification of the Schrodinger equation, which resolves these problems, while giving the same experimental results as quantum theory in the microscopic regime. Two underlying theories for this phenomenology are reviewed: trace dynamics and gravity-induced collapse. As the macroscopic scale is approached, predictions of this proposal begin to differ appreciably from those of quantum theory and are being confronted by ongoing laboratory experiments that include molecular interferometry and optomechanics. These experiments, which test the validity of linear superposition for large systems, are reviewed here, and their technical challenges, current results, and future prospects summarized. It is likely that over the next two decades or so, these experiments can verify or rule out the proposed stochastic modification of quantum theory. DOI: 10.1103/RevModPhys.85.471

White organic light-emitting diodes (OLEDs) are ultrathin, large-area light sources made from organic semiconductor materials. Over the past decades, much research has been spent on finding suitable materials to realize highly efficient monochrome and white OLEDs. With their high efficiency, color tunability, and color quality, white OLEDs are emerging as one of the next-generation light sources. In this review, the physics of a variety of device concepts that have been introduced to realize white OLEDs based on both polymer and small-molecule organic materials are discussed. Owing to the fact that about 80% of the internally generated photons are trapped within the thin-film layer structure, a second focus is put on reviewing promising concepts for improved light outcoupling.

The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

Relativistic interaction of short-pulse lasers with underdense plasmas has recently led to the emergence of a novel generation of femtosecond x-ray sources. Based on radiation from electrons accelerated in plasma, these sources have the common properties to be compact and to deliver collimated, incoherent, and femtosecond radiation. In this article, within a unified formalism, the betatron radiation of trapped and accelerated electrons in the so-called bubble regime, the synchrotron radiation of laser-accelerated electrons in usual meter-scale undulators, the nonlinear Thomson scattering from relativistic electrons oscillating in an intense laser field, and the Thomson backscattered radiation of a laser beam by laser-accelerated electrons are reviewed. The underlying physics is presented using ideal models, the relevant parameters are defined, and analytical expressions providing the features of the sources are given. Numerical simulations and a summary of recent experimental results on the different mechanisms are also presented. Each section ends with the foreseen development of each scheme. Finally, one of the most promising applications of laser-plasma accelerators is discussed: the realization of a compact free-electron laser in the x-ray range of the spectrum. In the conclusion, the relevant parameters characterizing each sources are summarized. Considering typical laser-plasma interaction parameters obtained with currently available lasers, examples of the source features are given. The sources are then compared to each other in order to define their field of applications. DOI: 10.1103/RevModPhys.85.1

Since its introduction 25 years ago, the quantum weak value has gradually transitioned from a theoretical curiosity to a practical laboratory tool. While its utility is apparent in the recent explosion of weak value experiments, its interpretation has historically been a subject of confusion. Here a pragmatic introduction to the weak value in terms of measurable quantities is presented, along with an explanation for how it can be determined in the laboratory. Further, its application to three distinct experimental techniques is reviewed. First, as a large interaction parameter it can amplify small signals above technical background noise. Second, as a measurable complex value it enables novel techniques for direct quantum state and geometric phase determination. Third, as a conditioned average of generalized observable eigenvalues it provides a measurable window into nonclassical features of quantum mechanics. In this selective review, a single experimental configuration to discuss and clarify each of these applications is used.

Positron annihilation spectroscopy is particularly suitable for studying vacancy-type defects in semiconductors. Combining state-of-the-art experimental and theoretical methods allows for detailed identification of the defects and their chemical surroundings. Also charge states and defect levels in the band gap are accessible. In this review the main experimental and theoretical analysis techniques are described. The usage of these methods is illustrated through examples in technologically important elemental and compound semiconductors. Future challenges include the analysis of noncrystalline materials and of transient defect-related phenomena.

Complex phenomena in photonics, in particular, dynamical properties of semiconductor lasers due to delayed coupling, are reviewed. Although considered a nuisance for a long time, these phenomena now open interesting perspectives. Semiconductor laser systems represent excellent test beds for the study of nonlinear delay-coupled systems, which are of fundamental relevance in various areas. At the same time delay-coupled lasers provide opportunities for photonic applications. In this review an introduction into the properties of single and two delay-coupled lasers is followed by an extension to network motifs and small networks. A particular emphasis is put on emerging complex behavior, deterministic chaos, synchronization phenomena, and application of these properties that range from encrypted communication and fast random bit sequence generators to bioinspired information processing. DOI: 10.1103/RevModPhys.85.421

Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review the formalism of qubit stabilizer and subsystem stabilizer codes and their possible use in protecting quantum information in a quantum memory are considered. The theory of fault tolerance and quantum error correction is reviewed, and examples of various codes and code constructions, the general quantum error-correction conditions, the noise threshold, the special role played by Clifford gates, and the route toward fault-tolerant universal quantum computation are discussed. The second part of the review is focused on providing an overview of quantum error correction using two-dimensional (topological) codes, in particular, the surface code architecture. The complexity of decoding and the notion of passive or self-correcting quantum memories are discussed. The review does not focus on a particular technology but discusses topics that will be relevant for various quantum technologies.