Positronium is the simplest bound state, built of an electron and a positron. Studies of positronium in vacuum and its decays in medium tell us about quantum electrodynamics (QED) and about the structure of matter and biological processes of living organisms at the nanoscale, respectively. Spectroscopic measurements constrain our understanding of QED bound state theory. Searches for rare decays and measurements of the effect of gravitation on positronium are used to look for new physics phenomena. In biological materials positronium decays are sensitive to the intermolecular and intramolecular structure and to the metabolism of living organisms ranging from single cells to human beings. This leads to new ideas of positronium imaging in medicine using the fact that during positron emission tomography (PET) as much as 40% of positron annihilation occurs through the production of positronium atoms inside the patient’s body. A new generation of the high sensitivity and multiphoton total-body PET systems opens perspectives for clinical applications of positronium as a biomarker of tissue pathology and the degree of tissue oxidation.

The past decade has witnessed dramatic progress related to various aspects of emergent topological polar textures in oxide nanostructures displaying vortices, skyrmions, merons, hopfions, dipolar waves, or labyrinthine domains, among others. For a long time, these nontrivial structures (the electric counterparts of the exotic spin textures) were not expected due to the high energy cost associated with the dipolar anisotropy: the smooth and continuous evolution of the local polarization to produce topologically protected structures would result in a large elastic energy penalty. However, it was discovered that the delicate balance and intricate interplay between the electric, elastic, and gradient energies can be altered in low-dimensional forms of ferroelectric oxide nanostructures. These can be tuned to manipulate order parameters in ways once considered impossible. This review addresses the historical context that provided the fertile background for the dawning of the polar topological era. This has been possible thanks to a fruitful, positive feedback between theory and experiment: advances in materials synthesis and preparation (with a control at the atomic scale) and characterization have come together with great progress in theoretical modeling of ferroelectrics at larger length and timescales. An in-depth scientific description to formalize and generalize the prediction, observation, and probing of exotic, novel, and emergent states of matter is provided. Extensive discussions of the fundamental physics of such polar textures, a primer explaining the basic topological concepts, an explanation of the modern theoretical and computational methodologies that enable the design and study of such structures, what it takes to achieve deterministic, on-demand control of order-parameter topologies through atomically precise synthesis, the range of characterization methods that are key to probing these structures, and their thermodynamic field-driven (temperature-driven, stress-driven, etc.) susceptibilities are included. The new emergent states of matter join together with exotic functional properties (such as chirality, negative capacitance, and coexistence of phases) that, along with their small size and ultrafast dynamical response, make them potential candidates in multifunctional devices. Finally, some open questions and challenges for the future are presented, underlining the interesting future that is anticipated in this field.

For half a century after the discovery of superconductivity, materials exploration for better superconductors proceeded without knowledge of the underlying mechanism. The 1957 BCS theory cleared that up. The superconducting state occurs due to strong correlation in the electronic system: pairing of electrons over the Fermi surface. Over the following half century a higher critical temperature $T_c$ was achieved only serendipitously as new materials were synthesized. Meanwhile, the formal theory of phonon-coupled superconductivity at the material-dependent level became progressively more highly developed: by 2000, given a known compound, its value of $T_c$, the corresponding superconducting gap function, and several other properties of the superconducting state became available independent of further experimental input. In this century, density-functional-theory-based computational materials design has progressed to a predictive level; new materials can be predicted from free energy functionals on the basis of various numerical algorithms. Taken together these capabilities enable theoretical predictions for new superconductors, justified by applications to superconductors ranging from weak to strong coupling. Limitations of the current procedures are discussed; most of them can be handled with additional procedures. Here the process that has resulted in the three new highest temperature superconductors is recounted, with compressed structures predicted computationally and values of $T_c$ obtained numerically that have subsequently been confirmed experimentally: the designed superconductors ${\mathrm{SH}}_3$, ${\mathrm{LaH}}_{10}$, and ${\mathrm{YH}}_9$. These hydrides have $T_c$ in the 200–260 K range at megabar pressures; the experimental results and confirmations are discussed. While the small mass of hydrogen provides the anticipated strong coupling at high frequency, it is shown that it also enables identification of the atom-specific contributions to coupling, in a manner that was previously possible only for elemental superconductors. The following challenge is posed: that progress in understanding of higher $T_c$ is limited by the lack of understanding of screening of H displacements. Ongoing activities are mentioned and current challenges are suggested, together with regularities that are observed in compressed hydrides that may be useful to guide further exploration.

The Helfrich-Hurault (HH) elastic instability is a well-known mechanism behind patterns that form as a result of strain upon liquid crystal systems with periodic ground states. In the HH model, layered structures undulate and buckle in response to local, geometric incompatibilities in order to maintain the preferred layer spacing. Classic HH systems include cholesteric liquid crystals under electromagnetic field distortions and smectic liquid crystals under mechanical strains, where both materials are confined between rigid substrates. However, richer phenomena are observed when undulation instabilities occur in the presence of deformable interfaces and variable boundary conditions. Understanding how the HH instability is affected by deformable surfaces is imperative for applying the instability to a broader range of materials. In this review, the HH mechanism is reexamined and special focus is given to how the boundary conditions influence the response of lamellar systems to geometrical frustration. Lamellar liquid crystals confined within a spherical shell geometry are used as the model system. Made possible by the relatively recent advances in microfluidics within the past 15 years, liquid crystal shells are composed entirely of fluid interfaces and have boundary conditions that can be dynamically controlled at will. Past and recent work that exemplifies how topological constraints, molecular anchoring conditions, and boundary curvature can trigger the HH mechanism in liquid crystals with periodic ground states is examined. The review ends by identifying similar phenomena across a wide variety of materials, both biological and synthetic. The fact that the HH mechanism is a generic and often overlooked response of periodic materials to geometrical frustration is highlighted.

The Dzyaloshinskii-Moriya interaction (DMI), one of the origins of chiral magnetism, is currently attracting considerable attention in the research community focusing on applied magnetism and spintronics. For future applications, an accurate measurement of its strength is indispensable. Here the state of the art of measurement techniques involving the coefficient of the Dzyaloshinskii-Moriya interaction, the DMI constant $D$, is reviewed, with a focus on systems where the interaction arises from the interface between two materials (i.e., the interfacial DMI). An overview of the experimental techniques, as well as their theoretical background and models for the quantification of the DMI constant, is given. The measurement techniques are divided into three categories: (a) domain-wall-based measurements, (b) spin-wave-based measurements, and (c) spin-orbit torque-based measurements. The advantages and disadvantages of each method are analyzed, and $D$ values at different interfaces are compared. The review aims to obtain a better understanding of the applicability of the different techniques to various stacks and of the origin of apparent disagreements among literature values.

This review describes the emerging field of waveguide quantum electrodynamics concerned with the interaction of photons propagating in a waveguide with localized quantum emitters. The collective emitter-photon interactions can lead to both enhanced and suppressed coupling compared to the case of independent emitters. Here the focus is on guided photons and ordered emitter arrays, manifesting superradiant and subradiant states, bound photon states, and quantum correlations with promising quantum information applications. Recent groundbreaking experiments performed with different quantum platforms, including cold atoms, superconducting qubits, semiconductor quantum dots, and quantum solid-state defects, are highlighted. The review also provides a comprehensive introduction to theoretical techniques to study the interactions and dynamics of these emitters and the photons in the waveguide.

Research on actinide materials, both basic and applied, has been greatly advanced by the general techniques available from high-intensity photon beams from x-ray synchrotron sources. The most important single reason is that such x-ray sources can work with minute (e.g., microgram) samples, and at this level the radioactive hazards of actinides are significantly reduced. The form and encapsulation procedures used for different techniques are discussed, followed by the basic theory for interpreting the results. To demonstrate the potential of synchrotron radiation techniques for the study of lattice and electronic structure, hybridization effects, multipolar order, and lattice dynamics in actinide materials, a selection of x-ray diffraction, resonant elastic x-ray scattering, x-ray magnetic circular dichroism, resonant and nonresonant inelastic scattering, dispersive inelastic x-ray scattering, and conventional and resonant photoemission experiments are reviewed.

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

Some measurements in quantum mechanics disturb each other. This has puzzled physicists since the formulation of the theory, but only in recent decades has the incompatibility of measurements been analyzed in depth and detail, using the notion of joint measurability of generalized measurements. In this Colloquium joint measurability and incompatibility are reviewed from the perspective of quantum information science. The Colloquium starts by discussing the basic definitions and concepts. An overview on applications of incompatibility, such as in measurement uncertainty relations, the characterization of quantum correlations, or information processing tasks like quantum state discrimination, is then presented. Finally, emerging directions of research, such as a resource theory of incompatibility as well as other concepts to grasp the nature of measurements in quantum mechanics, are discussed.

The quantum Hall (QH) effect, quantized Hall resistance combined with zero longitudinal resistance, is the characteristic experimental fingerprint of Chern insulators—topologically nontrivial states of two-dimensional matter with broken time-reversal symmetry. In Chern insulators, nontrivial bulk band topology is expressed by chiral states that carry current along sample edges without dissipation. The quantum anomalous Hall (QAH) effect refers to QH effects that occur in the absence of external magnetic fields due to spontaneously broken time-reversal symmetry. The QAH effect has now been realized in four different classes of two-dimensional materials: (i) thin films of magnetically (Cr- and/or V-) doped topological insulators in the $(\mathrm{Bi},\mathrm{Sb}{)}_2{\mathrm{Te}}_3$ family, (ii) thin films of the intrinsic magnetic topological insulator ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, (iii) moiré materials formed from graphene, and (iv) moiré materials formed from transition-metal dichalcogenides. In this Colloquium, the physical mechanisms responsible for each class of QAH insulator are reviewed, with both differences and commonalities highlighted, and potential applications of the QAH effect are commented upon.

The Colloquium reviews recent progress in the effective description of strongly correlated phases of matter with spontaneously broken translations, such as charge density waves or Wigner crystals. In real materials, disorder is inevitable and pins the Goldstones of broken translations. The Colloquium describes how pinning can be incorporated into the effective field theory at low energies without making any assumptions on the presence of boost symmetry. The essential role played by gauge-gravity duality models in establishing these effective field theories with only approximate symmetries is reviewed. The Colloquium closes with a discussion on the relevance of these models to the phenomenology of dc and ac transport in strongly correlated strange and bad metals, such as high-temperature superconductors.

Surfaces are at the frontier of every known solid. They provide versatile supports for functional nanostructures and mediate essential physicochemical processes. Intimately related to two-dimensional materials, interfaces and atomically thin films often feature distinct electronic states with respect to the bulk, which is key to many relevant properties, such as catalytic activity, interfacial charge-transfer, and crystal growth mechanisms. To induce novel quantum properties via lateral scattering and confinement, reducing the surface electrons’ dimensionality and spread with atomic precision is of particular interest. Both atomic manipulation and supramolecular principles provide access to custom-designed molecular assemblies and superlattices, which tailor the surface electronic landscape and influence fundamental chemical and physical properties at the nanoscale. Here the confinement of surface-state electrons is reviewed, with a focus on their interaction with molecular scaffolds created by molecular manipulation and self-assembly protocols under ultrahigh vacuum conditions. Starting with the quasifree two-dimensional electron gas present at the $(111)$-oriented surface planes of noble metals, the intriguing molecule-based structural complexity and versatility is illustrated. Surveyed are low-dimensional confining structures in the form of artificial lattices, molecular nanogratings, or quantum dot arrays, which are constructed upon an appropriate choice of their building constituents. Whenever the realized (metal-)organic networks exhibit long-range order, modified surface band structures with characteristic features emerge, inducing noteworthy physical phenomena such as discretization, quantum coupling or energy, and effective mass renormalization. Such collective electronic states can be additionally modified by positioning guest species at the voids of open nanoarchitectures. The designed scattering potential landscapes can be described with semiempirical models, bringing thus the prospect of total control over surface electron confinement and novel quantum states within reach.

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained, and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.

A future quantum network will consist of quantum processors that are connected by quantum channels, just like conventional computers are wired up to form the Internet. In contrast to classical devices, however, the entanglement and nonlocal correlations available in a quantum-controlled system facilitate novel fundamental tests of quantum theory. In addition, they enable numerous applications in distributed quantum information processing, quantum communication, and precision measurement. While pioneering experiments have demonstrated the entanglement of two quantum nodes separated by up to 1.3 km, and three nodes in the same laboratory, accessing the full potential of quantum networks requires scaling of these prototypes to many more nodes and global distances. This is an outstanding challenge, posing high demands on qubit control fidelity, qubit coherence time, and coupling efficiency between stationary and flying qubits. This Colloquium describes how optical resonators facilitate quantum network nodes that achieve the aforementioned prerequisites in different physical systems (trapped atoms, defect centers in wide-band-gap semiconductors, and rare-earth dopants) by enabling high-fidelity qubit initialization and readout, efficient generation of qubit-photon and remote qubit-qubit entanglement, and quantum gates between stationary and flying qubits. These advances open a realistic perspective toward the implementation of global-scale quantum networks in the near future.

Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling to different baths at their edges. This was possible because of concurrent advances in the models used to represent these systems, the methods employed, and the analysis of the emerging phenomenology. A comprehensive review of these three integrated research directions is given. First provided is an overarching view of the models of boundary-driven open quantum systems, in both the weak- and strong-coupling regimes. This is followed by a review of state-of-the-art analytical and numerical methods that are exact, perturbative, and approximate. Finally, the transport properties of some paradigmatic one-dimensional chains are discussed, with an emphasis on disordered and quasiperiodic systems, the emergence of rectification and negative differential conductance, and the role of phase transitions, and an outlook on further research options is given.

Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations already become nonlinear for comparatively small amplitudes, and new mechanisms of dissipation come into play. At the same time, the exquisite control of these systems makes them a platform for studying many problems of classical and quantum physics far from thermal equilibrium in a well-characterized setting. This review describes, at a conceptual level, basic theoretical ideas and explicative experiments pertaining to mesoscopic physics of nanomechanical systems. Major applications of nanomechanics in science and technology are also outlined. A broad range of phenomena related to the conservative as well as dissipative nonlinearity and fluctuations are discussed within a unifying framework. They include the linear response of single and coupled vibrational modes as well as nonlinear effects of periodic driving. Such driving breaks the continuous time-translation symmetry and the detailed balance, with conspicuous consequences for fluctuations, particularly in the presence of the driving-induced bistability and multistability. Mathematical techniques are described in the appendixes to provide an introduction to the theory. The goal of the review is to show the richness of the physics at work. The continuous experimental and theoretical advances make nanomechanical systems a vibrant area of research with many new phenomena to discover.

Since the discovery of electron-wave duality, electron scattering instrumentation has developed into a powerful array of techniques for revealing the atomic structure of matter. Beyond detecting local lattice variations in equilibrium structures with the highest possible spatial resolution, recent research efforts have been directed toward the long-sought-after dream of visualizing the dynamic evolution of matter in real time. The atomic behavior at ultrafast timescales carries critical information on phase transition and chemical reaction dynamics, the coupling of electronic and nuclear degrees of freedom in materials and molecules, and the correlation among structure, function, and previously hidden metastable or nonequilibrium states of matter. Ultrafast electron pulses play an essential role in this scientific endeavor, and their generation has been facilitated by rapid technical advances in both ultrafast laser and particle accelerator technologies. This review presents a summary of the noteworthy developments in this field in the last few decades. The physics and technology of ultrafast electron beams is presented with an emphasis on the figures of merit most relevant for ultrafast electron diffraction experiments. Recent developments in the generation, manipulation, and characterization of ultrashort electron beams aimed at improving the combined spatiotemporal resolution of these measurements are discussed. The fundamentals of electron scattering from atomic matter and the theoretical frameworks for retrieving dynamic structural information from solid-state and gas-phase samples is described. Essential experimental techniques and several landmark works that have applied these approaches are also highlighted to demonstrate the widening applicability of these methods. Ultrafast electron probes with ever-improving capabilities, combined with other complementary photon-based or spectroscopic approaches, hold tremendous potential for revolutionizing our ability to observe and understand energy and matter at atomic scales.

The appearance of the Planckian time ${\tau }_{\mathrm{Pl}}=\hslash /k_{B}T$ is reviewed in both conventional and unconventional metals. A pedagogical discussion of the various different timescales (quasiparticle, transport, many-body) that characterize metals is given, with an emphasis on conditions under which these times are the same or different. The possibility of a Planckian bound on dissipation is discussed from both a quasiparticle and a many-body perspective. Planckian quasiparticles can arise naturally from a combination of inelastic scattering and mass renormalization. Many-body dynamics, on the other hand, is constrained by the basic timescales and length scales of local thermalization.

Atomtronics is an emerging field that aims to manipulate ultracold atom moving in matter-wave circuits for fundamental studies in both quantum science and technological applications. In this Colloquium, recent progress in matter-wave circuitry and atomtronics-based quantum technology is reviewed. After an introduction to the basic physical principles and the key experimental techniques needed to realize atomtronic systems, the physics of matter waves in simple circuits such as ring traps and two-terminal systems is described. The main experimental observations and outstanding questions are discussed. Also presented are possible applications to a broad range of quantum technologies, from quantum sensing with atom interferometry to future quantum simulation and quantum computation architectures.