Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. The control over all relevant degrees of freedom in these atoms has enabled relative frequency uncertainties at a level of ${10}^{-18}$. This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as a possible variation of fundamental constants, a violation of the local Lorentz invariance, and the existence of forces beyond the standard model of physics. In addition, novel clocks are driving the development of sophisticated technical applications. Crucial for applications of clocks in fundamental physics are a high sensitivity to effects beyond the standard model and a small frequency uncertainty of the clock. Highly charged ions offer both. They possess optical transitions which can be extremely narrow and less sensitive to external perturbations compared to current atomic clock species. The large selection of highly charged ions offers narrow transitions that are among the most sensitive ones for the “new physics” effects. Recent experimental advances in trapping and sympathetic cooling of highly charged ions will in the future enable advanced quantum logic techniques for controlling motional and internal degrees of freedom and thus enable high-accuracy optical spectroscopy. Theoretical progress in calculating the properties of selected highly charged ions has allowed the evaluation of systematic shifts and the prediction of the sensitivity to the physics beyond the standard model. New theoretical challenges and opportunities emerge from relativistic, quantum electrodynamics, and nuclear-size contributions that become comparable with interelectronic correlations. This article reviews the current status of the field, addresses specific electronic configurations and systems which show the most promising properties for research, their potential limitations, and the techniques for their study.

Thermotropic liquid crystals can be formed by various molecular shapes, some discovered over 125 years ago. The simplest and most-studied liquid crystals are made of rod-shaped molecules and led to today’s omnipresent liquid crystal displays. While applied scientists and engineers have been perfecting liquid crystal displays, a large group of liquid crystal scientists have become excited about liquid crystals of bent-shaped (banana-shaped) molecules. These compounds were first reported 20 years ago and since then have taken center stage in current liquid crystal science. The “banana mania” is due to the fact that even a small kink in the molecular shape leads to fundamentally new properties and phases. This review summarizes the large variety of novel structures and physical properties and describes the underlying physics. The dependence of macroscopic properties on both the shape of the molecules and the flexibility of the central core is emphasized. Most rigid bent-core molecules form smectic and sometimes columnar structures; only a minority forms nematic phases. By contrast, most flexible bent-core molecules form nanostructured nematic phases, including the twist-bend nematic phase discovered very recently.

Following the emergence of many novel two-dimensional (2D) materials beyond graphene, interest has grown in exploring implications for fundamental physics and practical applications ranging from electronics, photonics, and phononics to thermal management and energy storage. In this Colloquium, a summary and comparison are given of the phonon properties, such as phonon dispersion and relaxation time, of pristine 2D materials with single-layer graphene to understand the role of crystal structure and dimension on thermal conductivity. A comparison is made of the phonon properties, contrasting idealized 2D crystals, realistic 2D crystals, and 3D crystals, and synthesizing this to develop a physical picture of how the sample size of 2D materials affects their thermal conductivity. The effects of geometry such as the number of layers and the nanoribbon width, together with the presence of defects, mechanical strain, and substrate interactions on the thermal properties of 2D materials are discussed. Intercalation affects both the group velocities and phonon relaxation times of layered crystals and thus tunes the thermal conductivity along both the through-plane and basal-plane directions. This Colloquium concludes with a discussion of the challenges in theoretical and experimental studies of thermal transport in 2D materials. The rich and special phonon physics in 2D materials make them promising candidates for exploring novel phenomena such as topological phonon effects and applications such as phononic quantum devices.

These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when—as in quantum field theory—it is a property of the algebra of observables and not just of the states.

Although dark matter is a central element of modern cosmology, the history of how it became accepted as part of the dominant paradigm is often ignored or condensed into an anecdotal account focused around the work of a few pioneering scientists. The aim of this review is to provide a broader historical perspective on the observational discoveries and the theoretical arguments that led the scientific community to adopt dark matter as an essential part of the standard cosmological model.

This Colloquium discusses the recent progress in understanding the properties of spin-split superconductors under nonequilibrium conditions. Recent experiments and theories demonstrate a rich variety of transport phenomena occurring in devices based on such materials that suggest direct applications in thermoelectricity, low-dissipative spintronics, radiation detection, and sensing. This text discusses different experimental situations and presents a theoretical framework based on quantum kinetic equations. This framework provides an accurate description of the nonequilibrium distribution of charge, spin, and energy, which are the relevant nonequilibrium modes, in different hybrid structures. This Colloquium also reviews experiments on spin-split superconductors and shows how transport measurements reveal the properties of the nonequilibrium modes and their mutual coupling. In particular, the emphasis of the text is on spin injection and diffusion and very large thermoelectric effects in spin-split superconductors.

If colloidal solute particles are suspended in a solvent close to its critical point, they act as cavities in a fluctuating medium and thereby restrict and modify the fluctuation spectrum in a way that depends on their relative configuration. As a result, effective, so-called critical Casimir forces (CCFs) emerge between the colloids. The range and the amplitude of CCFs depend sensitively on the temperature and the composition of the solvent as well as on the boundary conditions of the order parameter of the solvent at the particle surfaces. These remarkable, moreover universal features of the CCFs provide the possibility for an active control over the assembly of colloids. This has triggered a recent surge of experimental and theoretical interest in these phenomena. An overview is presented of current research activities in this area. Various experiments demonstrate the occurrence of thermally reversible self-assembly or aggregation or even equilibrium phase transitions of colloids in the mixed phase below the lower consolute points of binary solvents. The status is discussed of the theoretical description of these phenomena, in particular, the validity of a description in terms of effective, one-component colloidal systems and the necessity of a full treatment of a ternary solvent-colloid mixture. Perspectives are suggested on the directions toward which future research in this field might develop.

Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed viewpoint of field theory and holography. A set of basic methods for the computation is developed and illustrated with simple examples such as free theories and conformal field theories. The structures of the ultraviolet divergences and the universal parts are determined and compared with the holographic descriptions of entanglement entropy. The utility of quantum inequalities of entanglement are discussed and shown to derive the $\mathcal{C}$ theorem that constrains renormalization group flows of quantum field theories in diverse dimensions.

Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following alternative mechanisms are reviewed, notably the use of more general quantum correlations such as quantum discord, identical particles, or nontrivial Hamiltonians; the estimation of thermodynamical parameters or parameters characterizing nonequilibrium states; and the use of quantum phase transitions. Both theoretically achievable enhancements and enhanced sensitivities not primarily based on entanglement that have already been demonstrated experimentally and indicate some possible future research directions are described.

Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well-developed techniques for trapping, controlling, and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold, and ultracold gases of neutral atoms. Moreover, atoms can strongly couple to external forces and fields, which makes them ideal for ultraprecise sensing and time keeping. All these factors call for generating nonclassical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.

This review examines the tendency of light nuclei to exhibit clustering, where correlations between nucleons result in the formation of precipitates, typically $\alpha$ particles. The observation of clustering dates to the earliest days of the subject, where $\alpha$ particles were the building blocks of some nuclear models. The description of a nucleus in terms of clusters was attractive in terms of simplifying the computationally challenging problem through the reduction of the degrees of freedom. However, more recently it has been possible to develop ab initio methods which seek to build nuclei not from the clusters, but from the individual nucleons with a full account of the Pauli exclusion principle. This review links the development of the subject from the assumption of preformed $\alpha$ particles, through to the development of models which demonstrate the appearance of clustering from the $A$-nucleon wave function with realistic but effective interactions, to finally first principle approaches using interactions based on chiral effective field theory and the symmetries of quantum chromodynamics. This places the understanding of clustering as a cornerstone of the development of nuclear theory as it attempts to develop a complete understanding of light nuclei from the fundamental strong force.

Natural organisms such as photosynthetic bacteria, algae, and plants employ complex molecular machinery to convert solar energy into biochemical fuel. An important common feature shared by most of these photosynthetic organisms is that they capture photons in the form of excitons typically delocalized over a few to tens of pigment molecules embedded in protein environments of light-harvesting complexes (LHCs). Delocalized excitons created in such LHCs remain well protected despite being swayed by environmental fluctuations and are delivered successfully to their destinations over 100 nanometer distances in about 100 ps times. Decades of experimental and theoretical investigation have produced a large body of information offering insight into major structural, energetic, and dynamical features contributing to LHCs’ extraordinary capability to harness photons using delocalized excitons. The objective of this review is (i) to provide a comprehensive account of major theoretical, computational, and spectroscopic advances that have contributed to this body of knowledge, and (ii) to clarify the issues concerning the role of delocalized excitons in achieving efficient energy transport mechanisms. The focus of this review is on three representative systems: the Fenna-Matthews-Olson complex of green sulfur bacteria, the light-harvesting 2 complex of purple bacteria, and phycobiliproteins of cryptophyte algae. Although we offer a more in-depth and detailed description of theoretical and computational aspects, major experimental results and their implications are also assessed in the context of achieving excellent light-harvesting functionality. Future theoretical and experimental challenges to be addressed in gaining a better understanding and utilization of delocalized excitons are also discussed.

The ability to effectively control brain dynamics holds great promise for the enhancement of cognitive function in humans and the betterment of their quality of life. Yet, successfully controlling dynamics in neural systems is challenging, in part due to the immense complexity of the brain and the large set of interactions that can drive any single change. While some understanding has been gained of the control of single neurons, the control of large-scale neural systems—networks of multiply interacting components—remains poorly understood. Efforts to address this gap include the construction of tools for the control of brain networks, mostly adapted from control and dynamical systems theory. Informed by current opportunities for practical intervention, these theoretical contributions provide models that draw from a wide array of mathematical approaches. Recent developments are presented for effective strategies of control in dynamic brain networks, and potential mechanisms are also described that underlie such processes. Efforts are reviewed on the control of general neurophysiological processes with implications for brain development and cognitive function, as well as the control of altered neurophysiological processes in medical contexts such as anesthesia administration, seizure suppression, and deep-brain stimulation for Parkinson’s disease. This Colloquium is concluded with a forward-looking discussion regarding how emerging results from network control, especially approaches that deal with nonlinear dynamics or more realistic trajectories for control transitions, could be used to directly address pressing questions in neuroscience.

Plasma-based accelerators that impart energy gain as high as several GeV to electrons or positrons within a few centimeters have engendered a new class of diagnostic techniques very different from those used in connection with conventional radio-frequency (rf) accelerators. The need for new diagnostics stems from the micrometer scale and transient, dynamic structure of plasma accelerators, which contrasts with the meter scale and static structure of conventional accelerators. Because of this micrometer source size, plasma-accelerated electron bunches can emerge with smaller normalized transverse emittance (${\epsilon }_n<0.1\mathrm{mm}\mathrm{mrad}$) and shorter duration (${\tau }_b\sim 1\mathrm{fs}$) than bunches from rf linacs. Single-shot diagnostics are reviewed that determine such small ${\epsilon }_n$ and ${\tau }_b$ noninvasively and with high resolution from wide-bandwidth spectral measurement of electromagnetic radiation the electrons emit: ${\epsilon }_n$ from x rays emitted as electrons interact with transverse internal fields of the plasma accelerator or with external optical fields or undulators; ${\tau }_b$ from THz to optical coherent transition radiation emitted upon traversing interfaces. The duration of $\sim 1\mathrm{fs}$ bunches can also be measured by sampling individual cycles of a copropagating optical pulse or by measuring the associated magnetic field using a transverse probe pulse. Because of their luminal velocity and micrometer size, the evolving structure of plasma accelerators, the key determinant of accelerator performance, is exceptionally challenging to visualize in the laboratory. Here a new generation of laboratory diagnostics is reviewed that yield snapshots, or even movies, of laser- and particle-beam-generated plasma accelerator structures based on their phase modulation or deflection of femtosecond electromagnetic or electron probe pulses. Spatiotemporal resolution limits of these imaging techniques are discussed, along with insight into plasma-based acceleration physics that has emerged from analyzing the images and comparing them to simulated plasma structures.

This Colloquium describes a new paradigm for creating strong quantum interactions of light and matter by way of single atoms and photons in nanoscopic lattices. Beyond the possibilities for quantitative improvements for familiar phenomena in atomic physics and quantum optics, there is a growing research community that is exploring novel quantum phases and phenomena that arise from atom-photon interactions in one- and two-dimensional nanophotonic lattices. Nanophotonic structures offer the intriguing possibility to control atom-photon interactions by engineering the medium properties through which they interact. An important aspect of these new research lines is that they have become possible only by pushing the state-of-the-art capabilities in nanophotonic device fabrication and by the integration of these capabilities into the realm of ultracold atoms. This Colloquium attempts to inform a broad physics community of the emerging opportunities in this new field on both theoretical and experimental fronts. The research is inherently multidisciplinary, spanning the fields of nanophotonics, atomic physics, quantum optics, and condensed matter physics.

This paper provides a review of the experimental studies of processes with a single top quark at the Tevatron proton-antiproton collider and the LHC proton-proton collider. Single top-quark production in the $t$-channel process has been measured at both colliders. The $s$-channel process has been observed at the Tevatron, and its rate has also been measured at the center-of-mass energy of 8 TeV at the LHC in spite of the comparatively harsher background contamination. LHC data also brought the observation of the associated production of a single top quark with a $W$ boson as well as with a $Z$ boson. The Cabibbo-Kobayashi-Maskawa matrix element $|V_{tb}|$ is extracted from the single top-quark production cross sections, and $t$-channel events are used to measure several properties of the top quark and set constraints on models of physics beyond the standard model. Rare final states with a single top quark are searched for, as enhancements in their production rates, if observed, would be clear signs of new physics.

A celebrated and controversial hypothesis suggests that some biological systems—parts, aspects, or groups of them—may extract important functional benefits from operating at the edge of instability, halfway between order and disorder, i.e., in the vicinity of the critical point of a phase transition. Criticality has been argued to provide biological systems with an optimal balance between robustness against perturbations and flexibility to adapt to changing conditions as well as to confer on them optimal computational capabilities, large dynamical repertoires, unparalleled sensitivity to stimuli, etc. Criticality, with its concomitant scale invariance, can be conjectured to emerge in living systems as the result of adaptive and evolutionary processes that, for reasons to be fully elucidated, select for it as a template upon which further layers of complexity can rest. This hypothesis is suggestive as it proposes that criticality could constitute a general and common organizing strategy in biology stemming from the physics of phase transitions. However, despite its implications, this is still in its infancy state as a well-founded theory and, as such, it has elicited some skepticism. From the experimental side, the advent of high-throughput technologies has created new prospects in the exploration of biological systems, and empirical evidence in favor of criticality has proliferated, with examples ranging from endogenous brain activity and gene-expression patterns to flocks of birds and insect-colony foraging, to name but a few. Some pieces of evidence are quite remarkable, while in some other cases empirical data are limited, incomplete, or not fully convincing. More stringent experimental setups and theoretical analyses are certainly needed to fully clarify the picture. In any case, the time seems ripe for bridging the gap between this theoretical conjecture and its empirical validation. Given the profound implications of shedding light on this issue, it is both pertinent and timely to review the state of the art and to discuss future strategies and perspectives.

This article reviews recent developments in tests of fundamental physics using atoms and molecules, including the subjects of parity violation, searches for permanent electric dipole moments, tests of the $CPT$ theorem and Lorentz symmetry, searches for spatiotemporal variation of fundamental constants, tests of quantum electrodynamics, tests of general relativity and the equivalence principle, searches for dark matter, dark energy, and extra forces, and tests of the spin-statistics theorem. Key results are presented in the context of potential new physics and in the broader context of similar investigations in other fields. Ongoing and future experiments of the next decade are discussed.