The numerical treatment of quantum systems often requires large amounts of computing power and time. As a result, performing calculations repeatedly for different values of the input parameters is often not feasible. One remedy is using eigenvectors describing the system that are analytic functions that vary smoothly for real values of the input parameters. This allows one to replace computationally expensive calculations with emulators that project onto a reduced-basis set. This Colloquium explores a particular class of reduced-basis methods known as eigenvector continuation and its applications, with emphasis on nuclear physics.

Rayleigh-Bapos{e}nard convection is the flow in a closed box heated from below and cooled from above. The ultimate regime of Rayleigh-Bapos{e}nard turbulence occurs when the dimensionless temperature difference between the bottom and top plates is large. This review gives a comprehensive overview of the theoretical approaches to the ultimate regime and of the experimental and numerical results on the transition to this regime. These are reconciled by realizing that the transition is of non-normal–nonlinear nature, as typical for the laminar to turbulent transition in shear flow. The review also suggests experimental and numerical approaches to further understand the transition to the ultimate regime.

Storage of energy in quantum devices is of practical relevance for applications in quantum technologies. The topic attracts attention also of a more foundational character due to the possibility that the charging power and work extraction can benefit from quantum coherence and collective effects. This Colloquium reviews theoretical concepts and experimental implementations of energy storage in quantum batteries drawing on work in quantum thermodynamics and quantum information science.

A branch of quantum information is concerned with transformations that are possible given certain resources: for example, quantum teleportation moves a quantum state from one place to another, aided by entanglement and classical communication. Certain other tasks are provably impossible. But, as surveyed in this review, a surprising fact is that some tasks become possible if another quantum state is present, even if this state is returned untouched at the end of the task. This “quantum catalysis” enables a large variety of interesting tasks, with applications ranging from cryptography to thermodynamics.

Neutrinos can change flavors due to their nonzero masses and mixings as well as their interactions with matter and other neutrinos. In dense astrophysical environments, such as core-collapse supernovae or neutron star mergers, the problem of neutrino flavor evolution becomes very complex. Connections to other domains such as quantum information theory have been uncovered. Understanding the neutrino flavor evolution in dense environments can shed light on the dynamics of massive star explosions and the origin of heavy elements in the Universe and is important for future observations of supernova neutrinos.

For centuries, human fascination with the living world motivated the development of tools for visualizing life’s events at the spatiotemporal scales beyond our visual range. While all optical microscopes use light to probe the object of interest, fluorescence microscopes can discern between the object and background at the molecular scale. At this scale, the stochastic properties of light are fundamental to interpreting fluorescence microscopy data. Accordingly quantitative methods that enable such interpretation necessitate stochastic perspective and the use of statistical concepts. The physical-optical principles governing the formation of fluorescent images and modeling tools interpreting these images while accounting for the stochasticity of light and measurements are reviewed.

In many solids, the spin-orbit interaction is only a small effect. However, in certain materials it leads to new phenomena. This Colloquium reviews the role of spin-orbit interaction in superconducting hybrid structures, where it can lead to exotic states such as spin-triplet pairing, topological superconductivity, and the superconducting diode effect. These are fundamental interest and importance for applications, including spintronics and quantum computing.

The theory of unconventional superconductors continues to provide profound puzzles. The crossover between the weakly coupled Bardeen-Cooper-Schrieffer (BCS) state and the strong-pairing Bose-Einstein condensate (BEC) provides a useful perspective on how to address these questions. This paper describes a self-consistent framework for thinking about the crossover regime in between these two limits. The review discusses to what extent this BCS-BEC theory applies to a range of classes of superconducting materials including the cuprates, iron pnictides, twisted bilayer graphene, and interfacial superconductivity among others.

Nitrogen-vacancy centers in diamond are sensitive to magnetic fields, and a single center permits detection of electron and nuclear spins and imaging of single molecules in its vicinity. This article reviews the achievements of advanced methods to obtain spectral and spatial resolution and it points to technical problems that remain to be solved for widespread and multidisciplinary adoption of single-molecule magnetic resonance spectroscopy.

Artificially engineered mechanical systems, sometimes called metamaterials, offer many promising applications on length scales ranging from macroscopic systems to the nanoscale. A topic of particular interest is the existence of topologically protected phononic edge states in such systems that are analogous to the electronic edge states that give rise to the quantum Hall effect. This Colloquium gives an introduction to topologically protected transport in metamaterials and its applications for controlling acoustic transport.

Magnetotactic bacteria have a built-in compass, in the form of a magnetosome chain made up of magnetic biominerals, that allows them to passively align along terrestrial magnetic field lines. They also sense oxygen gradients and swim using at least one flagellum. Hence, these bacteria are self-propelled active matter capable of displaying flocking behavior. This Colloquium explains the physics behind these various capabilities, as well as their interactions and biological significance.

The standard model is successful at describing most of the data at the electroweak scale, but there are indications that new physics should exist at a higher energy scale. To identify, quantify, and elucidate the new physics, one can use the framework of the standard model effective field theory. This article reviews the construction and theoretical tools provided by the effective field theory for analyzing the present and future experimental data, as well as theoretical ideas for new physics.

Electronic devices that incorporate magnetism, called spintronic devices, can increase the functionality of electronic circuits and lead to increases in efficiency. Such devices are useful if the magnetization can be manipulated electrically rather than by magnetic fields. This review covers the materials, underlying physics, and applications involved in such manipulation, focusing on two control mechanisms. The first is control by manipulating the magnetization through its coupling to ferroelectric order and the second is control by spin-polarized currents manipulating the magnetization through the angular momentum flowing into it.

Recent observations of compact astrophysical objects have opened the possibility to probe the nature of gravity in its strong-field regime. Such observations could reveal deviations from general relativity or the standard model. Spontaneous scalarization, which is controlled by scalar-field couplings to gravity, leads to a behavior that resembles a phase transition: the scalar induces measurable effects in the strong-field regime while remaining undetectable in weak-field gravitational experiments. This review presents the spontaneous scalarization mechanism, several scalarization models considered in the literature, and their astrophysical implications for neutron stars and black holes. It also discusses the generalization of such models to other types of fields and instabilities.

Time-resolved angle-resolved photoemission spectroscopy provides access to light-induced changes in the electronic band structure and interactions of solids, and to the out-of-equilibrium electron dynamics. This article reviews the history and future prospects for the development of the technique, and offers an overview of recent achievements in studying unoccupied and light-driven states, photoinduced phase transitions, electron-phonon scattering, and electron dynamics in quantum materials, including topological insulators, unconventional superconductors, traditional and novel semiconductors, excitonic insulators, and spin-textured systems.

Metamaterials are artificially patterned structures designed to behave as artificial materials with novel properties. A popular application is controlling electromagnetic waves with subwavelength patterning, leading to properties like negative indices of refraction. Metamaterials can also control diffusion processes, which are different from wave propagation. This review describes metamaterials in diffusive systems in terms of their underlying physics, the theory used to describe them, and their potential applications in areas such as heat management, drug transport, and particle separation.

Friction at highly lubric interfaces of two-dimensional materials is important yet incompletely characterized. This Colloquium discusses sliding and pinning between two-dimensional layers, using simulations of twisted graphene interfaces as a prototypical system. The resulting insights are of potential relevance for a larger category of bilayer and multilayer systems as well.

This article reviews recent literature and presents new calculations of the Lamb shift in light muonic atoms. Point-nucleus QED and nuclear structure effects are treated consistently among all muonic and electronic atoms to allow for improved determination of nuclear charge radii and fundamental constants.

Fractons are exotic excitations originally conceived as platforms for reliable quantum memories. They are characterized by highly restricted mobilities. In the continuum, they are described by tensor fields with higher gauge symmetries. In this Colloquium, the focus is on a class of duality mappings between fracton models and elasticity theory, building the reader’s intuition and understanding in a more familiar setting.

Probing of electromagnetic fields in high-energy-density experiments is key to understanding questions in fusion processes such as how the fields are compressed, diffuse through the plasma, and can seed instabilities. Many kinetic processes studied, including collisionless shocks, filamentary instabilities, jets, magnetic reconnection, and turbulence, all depend on the field structure. In this review, an overview of experimental techniques and the underpinning theoretical principles and modeling of proton-based imaging is presented, followed by a review of experiments and an outlook for future frontiers in the technique.

The gravitational form factors encode fundamental particle properties including mass, spin, and $D$-term. Their physical interpretation promises, for composed particles, insights on spatial distributions of energy, angular momentum, and internal forces. This Colloquium reviews the theoretical and recent experimental advances in this field with focus on the quark-gluon structure of the proton in QCD.

Quantum technology is now at a point where practical work can begin on creating the quantum internet. However, numerous challenges must be overcome before this vision becomes a reality. A global-scale quantum internet requires the development of the quantum repeater, a device that stores and manipulates qubits while interacting with or emitting entangled photons. This review examines different approaches to quantum repeaters and networks, covering their conceptual frameworks, architectures, and current progress in experimental implementation.