The present status and development of strong-field nano-optics, an emerging field of nonlinear optics, is discussed. A nonperturbative regime of light-matter interactions is reached when the amplitude of the external electromagnetic fields that are driving a material approach or exceed the field strengths that bind the electrons inside the medium. In this strong-field regime, light-matter interactions depend on the amplitude and phase of the field, rather than its intensity, as in more conventional perturbative nonlinear optics. Traditionally such strong-field interactions have been intensely investigated in atomic and molecular systems, and this has resulted in the generation of high-harmonic radiation and laid the foundations for contemporary attosecond science. Over the past decade, however, a new field of research has emerged, the study of strong-field interactions in solid-state nanostructures. By using nanostructures, specifically those made out of metals, external electromagnetic fields can be localized on length scales of just a few nanometers, resulting in signficantly enhanced field amplitudes that can exceed those of the external field by orders of magnitude in the vicinity of the nanostructures. This leads not only to dramatic enhancements of perturbative nonlinear optical effects but also to significantly increased photoelectron yields. It resulted in a wealth of new phenomena in laser-solid interactions that have been discovered in recent years. These include the observation of above-threshold photoemission from single nanostructures, effects of the carrier-envelope phase on the photoelectron emission yield from metallic nanostructures, and strong-field acceleration of electrons in optical near fields on subcycle timescales. The current state of the art of this field is reviewed, and several scientific applications that have already emerged from the fundamental discoveries are discussed. These include, among others, the coherent control of localized electromagnetic fields at the surface of solid-state nanostructures and of free-electron wave packets by such optical near fields, resulting in the creation of attosecond electron bunches, the coherent control of photocurrents on nanometer length and femtosecond timescales by the electric field of a laser pulse, and the development of new types of ultrafast electron microscopes with unprecedented spatial, temporal, and energy resolution. The review concludes by highlighting possible future developments, discussing emerging topics in photoemission and potential strong-field nanophotonic devices, and giving perspectives for coherent ultrafast microscopy techniques. More generally, it is shown that the synergy between ultrafast science, plasmonics, and strong-field physics holds promise for pioneering scientific discoveries in the upcoming years.

After the first unequivocal demonstration of spin transport in graphene [Tombros et al., Nature (London) 448, 571–574 (2007)], surprisingly at room temperature, it was quickly realized that this novel material was relevant for both fundamental spintronics and future applications. In the decade since, exciting results have made the field of graphene spintronics blossom, and a second generation of studies has extended to new two-dimensional (2D) compounds. This Colloquium reviews recent theoretical and experimental advances on electronic spin transport in graphene and related 2D materials, focusing on emergent phenomena in van der Waals heterostructures and the new perspectives provided by them. These phenomena include proximity-enabled spin-orbit effects, the coupling of electronic spin to light, electrical tunability, and 2D magnetism.

In principle, quantum key distribution (QKD) offers information-theoretic security based on the laws of physics. In practice, however, the imperfections of realistic devices might introduce deviations from the idealized models used in security analyses. Can quantum code breakers successfully hack real systems by exploiting the side channels? Can quantum code makers design innovative countermeasures to foil quantum code breakers? Theoretical and experimental progress in the practical security aspects of quantum code making and quantum code breaking is reviewed. After numerous attempts, researchers now thoroughly understand and are able to manage the practical imperfections. Recent advances, such as the measurement-device-independent protocol, have closed critical side channels in the physical implementations, paving the way for secure QKD with realistic devices.

Bell’s theorem rules out many potential reformulations of quantum mechanics, but within a generalized framework it does not exclude all locally mediated models. Such models describe the correlations between entangled particles as mediated by intermediate parameters that track the particle worldlines and respect Lorentz covariance. These locally mediated models require the relaxation of an arrow-of-time assumption that is typically taken for granted. Specifically, some of the mediating parameters in these models must functionally depend on measurement settings in their future, i.e., on input parameters associated with later times. This option, often called retrocausal, has been repeatedly pointed out in the literature, but the exploration of explicit locally mediated toy models capable of describing specific entanglement phenomena has begun only in the past decade. A brief survey of such models is included here. These models provide a continuous and consistent description of events associated with spacetime locations, with aspects that are solved “all at once” rather than unfolding from the past to the future. The tension between quantum mechanics and relativity that is usually associated with Bell’s theorem does not occur here. Unlike in conventional quantum models, the number of parameters needed to specify the state of a system does not grow exponentially with the number of entangled particles. The promise of generalizing such models to account for all quantum phenomena is identified as a grand challenge.

The energy resolution per bandwidth $E_R$ is a figure of merit that combines the field resolution, bandwidth or duration of the measurement, and size of the sensed region. Several different dc magnetometer technologies approach $E_R=\hslash$, while to date none have surpassed this level. This suggests a technology-spanning quantum limit, a suggestion that is strengthened by model-based calculations for nitrogen-vacancy centers in diamond, for superconducting quantum interference device sensors, and for some optically pumped alkali-vapor magnetometers, all of which predict a quantum limit close to $E_R=\hslash$. This Colloquium reviews what is known about energy resolution limits, with the aim of understanding when and how $E_R$ is limited by quantum effects. A survey of reported sensitivity versus size of the sensed region for more than 20 magnetometer technologies is included, the known model-based quantum limits are reviewed, and possible sources for a technology-spanning limit are critically assessed, including zero-point fluctuations, magnetic self-interaction, and quantum speed limits. Finally, sensing approaches are described that appear to be unconstrained by any of the known limits, thus making them candidates to surpass $E_R=\hslash$.

Many biological functions are executed by molecular machines, which like man-made motors are powered by chemical energy, released by adenosine triphosphate hydrolysis. They have evolved to transport cargo, facilitate folding of proteins and ribonucleic acids, remodel chromatin, and replicate DNA. Biological machines also serve as the most natural systems for illustrating emergent phenomena in nonequilibrium active systems, thus providing a great impetus to illustrate the general principles governing their functions. Despite their architectural diversity, physics-based theories have provided unifying themes of the inner working of nanoscale biological machines. The theories address questions such as how the trade-off between precision, energetic costs, and optimal performances are balanced. However, many complexities associated with biological machines require molecular level descriptions. Simple point mutations in the enzyme could drastically alter functions, result in unexpected diseases, or dramatically restrict the capacity of molecular chaperones to help proteins fold. These examples are reminders that, while the search for principles of generality in biology is intellectually stimulating and necessary, molecular details must be accounted for to develop a deeper understanding of their functions.

Solid-state spin systems including nitrogen-vacancy (NV) centers in diamond constitute an increasingly favored quantum sensing platform. However, present NV ensemble devices exhibit sensitivities orders of magnitude away from theoretical limits. The sensitivity shortfall both handicaps existing implementations and curtails the envisioned application space. This review analyzes present and proposed approaches to enhance the sensitivity of broadband ensemble-NV-diamond magnetometers. Improvements to the spin dephasing time, the readout fidelity, and the host diamond material properties are identified as the most promising avenues and are investigated extensively. This analysis of sensitivity optimization establishes a foundation to stimulate development of new techniques for enhancing solid-state sensor performance.

One of the most promising suggested applications of quantum computing is solving classically intractable chemistry problems. This may help to answer unresolved questions about phenomena such as high temperature superconductivity, solid-state physics, transition metal catalysis, and certain biochemical reactions. In turn, this increased understanding may help us to refine, and perhaps even one day design, new compounds of scientific and industrial importance. However, building a sufficiently large quantum computer will be a difficult scientific challenge. As a result, developments that enable these problems to be tackled with fewer quantum resources should be considered important. Driven by this potential utility, quantum computational chemistry is rapidly emerging as an interdisciplinary field requiring knowledge of both quantum computing and computational chemistry. This review provides a comprehensive introduction to both computational chemistry and quantum computing, bridging the current knowledge gap. Major developments in this area are reviewed, with a particular focus on near-term quantum computation. Illustrations of key methods are provided, explicitly demonstrating how to map chemical problems onto a quantum computer, and how to solve them. The review concludes with an outlook on this nascent field.

The atomic nucleus is a quantum many-body system whose constituent nucleons (protons and neutrons) are subject to complex nucleon-nucleon interactions that include spin- and isospin-dependent components. For stable nuclei, several decades ago, emerging seemingly regular patterns in some observables could already be described successfully within a shell-model picture that results in particularly stable nuclei at certain magic fillings of the shells with protons and/or neutrons: $N$, $Z=8$, 20, 28, 50, 82, 126. However, in short-lived, so-called exotic nuclei or rare isotopes, characterized by a large $N/Z$ asymmetry and located far from the valley of $\beta$ stability on the nuclear chart, these magic numbers, viewed through observables, were shown to change. These changes in the regime of exotic nuclei offer an unprecedented view at the roles of the various components of the nuclear force when theoretical descriptions are confronted with experimental data on exotic nuclei where certain effects are enhanced. This article reviews the driving forces behind shell evolution from a theoretical point of view and connects this to experimental signatures.

For over 40 years, physicists have considered possible uses for neutrino detectors in nuclear nonproliferation, arms control, and fissile materials security. Neutrinos are an attractive fission signature because they readily pass through matter. The same property makes neutrinos challenging to detect in systems that would be practical for nuclear security applications. This Colloquium presents a broad overview of several potential neutrino applications, including the near-field monitoring of known reactors, far-field monitoring of known or discovery of undeclared reactors, detection of reactor waste streams, and detection of nuclear explosions. Recent detector advances have made near-field monitoring feasible, whereas farther-field reactor detection and waste stream detection monitoring may be possible in some cases with further research and development. Very long-range reactor monitoring and nuclear explosion detection do not appear feasible for the foreseeable future due to considerable physical and/or practical constraints.

Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favor of the incompleteness of quantum mechanics. Schrödinger noted that an essential point is the fact that one party can influence the wave function of the other party by performing suitable measurements. He called this phenomenon quantum steering and studied its properties, but only in recent years has this kind of quantum correlation attracted significant interest in quantum information theory. In this paper, the theory of quantum steering is reviewed. First, the basic concepts of steering and local hidden state models are presented and their relation to entanglement and Bell nonlocality is explained. Then various criteria for characterizing steerability and structural results on the phenomenon are described. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, applications of steering in quantum information processing and further related topics are reviewed.

Angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM) have become indispensable tools in the study of correlated quantum materials. Both probe complementary aspects of the single-particle excitation spectrum. Taken together, ARPES and STM have the potential to explore properties of the electronic Green’s function, a central object of many-body theory. This review explicates this potential with a focus on heavy-electron quantum criticality, especially the role of Kondo destruction. A discussion on how to probe the Kondo destruction effect across the quantum-critical point using ARPES and STM measurements is presented. Particular emphasis is placed on the question of how to distinguish between the signatures of the initial onset of hybridization-gap formation, which is the “high-energy” physics to be expected in all heavy-electron systems, and those of Kondo destruction, which characterizes the low-energy physics and, hence, the nature of quantum criticality. Recent progress and possible challenges in the experimental investigations are surveyed, the STM and ARPES spectra for several quantum-critical heavy-electron compounds are compared, and the prospects for further advances are outlined.

In this Colloquium, the wave-function-based multiconfigurational time-dependent Hartree approaches to the dynamics of indistinguishable particles (MCTDH-F for fermions and MCTDH-B for bosons) are reviewed. MCTDH-B and MCTDH-F or, together, MCTDH-X are methods for describing correlated quantum systems of identical particles by solving the time-dependent Schrödinger equation from first principles. MCTDH-X is used to accurately model the dynamics of real-world quantum many-body systems in atomic, molecular, and optical physics. The key feature of these approaches is the time dependence and optimization of the single-particle states employed for the construction of a many-body basis set, which yields nonlinear working equations. The historical developments that have led to the formulation of the MCTDH-X method and motivate the necessity for wave-function-based approaches are briefly described. The derivation of the unified MCTDH-F and MCTDH-B equations of motion for complete and also specific restricted configuration spaces are sketched. The strengths and limitations of the MCTDH-X approach are assessed via benchmarks against an exactly solvable model and via convergence checks. Applications to some instructive and experimentally realized quantum many-body systems are highlighted: the dynamics of atoms in Bose-Einstein condensates in magneto-optical and optical traps and of electrons in atoms and molecules. The current development and frontiers in the field of MCTDH-X are discussed: theories and numerical methods for indistinguishable particles, for mixtures of multiple species of indistinguishable particles, the inclusion of nuclear motion for the nonadiabatic dynamics of atomic and molecular systems, as well as the multilayer and second-quantized-representation approaches, and the orbital-adaptive time-dependent coupled-cluster theory.

Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial constraints. The second, in its more general sense, represents a prescription for the minimization of the topological charges in a constrained system. Both can lead to manifolds of high susceptibility and nontrivial, constrained disorder where exotic behaviors can appear and even be designed deliberately. This Colloquium describes the emergence of geometric frustration and the ice rule in soft condensed matter. It excludes the extensive developments of mathematical physics within the field of geometric frustration, but rather focuses on systems of confined microscopic or mesoscopic particles that emerge as a novel paradigm exhibiting spin degrees of freedom. In such systems, geometric frustration can be engineered artificially by controlling the spatial topology and geometry of the lattice, the position of the individual particle units, or their relative filling fraction. These capabilities enable the creation of novel and exotic phases of matter and also potentially lead toward technological applications related to memory and logic devices that are based on the motion of topological defects. The rapid progress in theory and experiments is reviewed and the intimate physical connections with other frustrated systems at different length scales are discussed.

This article reviews odd-frequency (odd-$\omega$) pairing with a focus on superconducting systems. Since Berezinskii introduced the concept of odd-frequency order in 1974 it has been viewed as exotic and rarely occurring in nature. A view is presented in which the Berezinskii state is in fact a ubiquitous superconducting order that is both nonlocal and odd in time. This state appears under quite general circumstances in many physical settings including bulk materials, heterostructures, and dynamically driven superconducting states, and it is therefore important to understand the nature of odd-$\omega$ pairing. Presented are the properties of odd-$\omega$ pairing in bulk materials, including possible microscopic mechanisms, and definitions of the odd-$\omega$ superconducting order parameter and the unusual Meissner response of odd-frequency superconductors are discussed. Also presented is how odd-$\omega$ pairing is generated in hybrid structures of nearly any sort and its relation to Andreev bound states, spin-polarized Cooper pairs, and Majorana states is focused on. How odd-$\omega$ pairing can be applied to nonsuperconducting systems such as ultracold Fermi gases, Bose-Einstein condensates, and chiral spin nematics is overviewed. Because of the growing importance of dynamic orders in quantum systems also discussed is the emergent view that the odd-$\omega$ state is an example of phase coherent dynamic order. The recent progress made in understanding the emergence of odd-$\omega$ states in driven superconducting systems is summarized. A more general view of odd-$\omega$ superconductivity suggests an interesting approach to this state as a realization of the hidden order with inherently dynamic correlations that have no counterpart in conventional orders discussed earlier. The progress made in this rapidly evolving field is reviewed and an illustration of the ubiquity of the odd-$\omega$ states and the potential for future discoveries of these states in a variety of settings are given. The general rules or design principles, to induce odd-$\omega$ components in various settings, using the $S{P}^{*}O{T}^{*}$ rule, are summed up. Since the pioneering prediction of odd-$\omega$ superconductivity by Berezinskii, this state has become a part of every-day conversations on superconductivity. To acknowledge this, the odd-$\omega$ state is called a Berezinskii pairing as well in this article.

Life is characterized by a myriad of complex dynamic processes allowing organisms to grow, reproduce, and evolve. Physical approaches for describing systems out of thermodynamic equilibrium have been increasingly applied to living systems, which often exhibit phenomena not found in those traditionally studied in physics. Spectacular advances in experimentation during the last decade or two, for example, in microscopy, single-cell dynamics, in the reconstruction of subcellular and multicellular systems outside of living organisms, and in high throughput data acquisition, have yielded an unprecedented wealth of data on cell dynamics, genetic regulation, and organismal development. These data have motivated the development and refinement of concepts and tools to dissect the physical mechanisms underlying biological processes. Notably, landscape and flux theory as well as active hydrodynamic gel theory have proven useful in this endeavor. Together with concepts and tools developed in other areas of nonequilibrium physics, significant progress has been made in unraveling the principles underlying efficient energy transport in photosynthesis, cellular regulatory networks, cellular movements and organization, embryonic development and cancer, neural network dynamics, population dynamics and ecology, as well as aging, immune responses, and evolution. Here recent advances in nonequilibrium physics are reviewd and their application to biological systems is surveyed. Many of these results are expected to be important cornerstones as the field continues to build our understanding of life.

Jet substructure has emerged to play a central role at the Large Hadron Collider, where it has provided numerous innovative ways to search for new physics and to probe the standard model, particularly in extreme regions of phase space. This review focuses on the development and use of state-of-the-art jet substructure techniques by the ATLAS and CMS experiments.

Machine learning (ML) encompasses a broad range of algorithms and modeling tools used for a vast array of data processing tasks, which has entered most scientific disciplines in recent years. This article reviews in a selective way the recent research on the interface between machine learning and the physical sciences. This includes conceptual developments in ML motivated by physical insights, applications of machine learning techniques to several domains in physics, and cross fertilization between the two fields. After giving a basic notion of machine learning methods and principles, examples are described of how statistical physics is used to understand methods in ML. This review then describes applications of ML methods in particle physics and cosmology, quantum many-body physics, quantum computing, and chemical and material physics. Research and development into novel computing architectures aimed at accelerating ML are also highlighted. Each of the sections describe recent successes as well as domain-specific methodology and challenges.