The distribution of quantum states over long distances is limited by photon loss. Straightforward amplification as in classical telecommunications is not an option in quantum communication because of the no-cloning theorem. This problem could be overcome by implementing quantum repeater protocols, which create long-distance entanglement from shorter-distance entanglement via entanglement swapping. Such protocols require the capacity to create entanglement in a heralded fashion, to store it in quantum memories, and to swap it. One attractive general strategy for realizing quantum repeaters is based on the use of atomic ensembles as quantum memories, in combination with linear optical techniques and photon counting to perform all required operations. Here the theoretical and experimental status quo of this very active field are reviewed. The potentials of different approaches are compared quantitatively, with a focus on the most immediate goal of outperforming the direct transmission of photons.

This work tabulates measured and derived values of coefficients for Lorentz and $CPT$ violation in the standard-model extension. Summary tables are extracted listing maximal attained sensitivities in the matter, photon, and gravity sectors. Tables presenting definitions and properties are also compiled.

The stability of pulse arrival times from pulsars and white dwarfs have been reanalyzed using several analysis tools for measuring the noise characteristics of sampled time and frequency data. The best terrestrial artificial clocks are shown to substantially exceed the performance of astronomical sources as timekeepers in terms of accuracy (as defined by cesium primary frequency standards) and stability. This superiority in stability can be directly demonstrated over time periods up to 2 years, where there is high quality data for both. Beyond 2 years there is a deficiency of data for clock-to-clock comparisons, and both terrestrial and astronomical clocks show equal performance being equally limited by the quality of the reference time scales used to make the comparisons. Nonetheless, the detailed accuracy evaluations of modern terrestrial clocks imply that these new clocks are likely to have a stability better than any astronomical source up to comparison times of at least hundreds of years. This article is intended to provide a correct appreciation of the relative merits of natural and artificial clocks. The use of natural clocks as tests of physics under the most extreme conditions is entirely appropriate; however, the contention that these natural clocks, particularly white dwarfs, can compete as timekeepers against devices constructed by mankind is shown to be doubtful.

The Galactic Center is an excellent laboratory for studying phenomena and physical processes that may be occurring in many other galactic nuclei. The center of our Milky Way is by far the closest galactic nucleus, and observations with exquisite resolution and sensitivity cover 18 orders of magnitude in energy of electromagnetic radiation. Theoretical simulations have become increasingly more powerful in explaining these measurements. This review summarizes the recent progress in observational and theoretical work on the central parsec, with a strong emphasis on the current empirical evidence for a central massive black hole and on the processes in the surrounding dense nuclear star cluster. Current evidence is presented, from the analysis of the orbits of more than two dozen stars and from the measurements of the size and motion of the central compact radio source, Sgr $\mathrm{A}*$, that this radio source must be a massive black hole of about $4.4\times {10}^6{M}_{☉}$, beyond any reasonable doubt. What is known about the structure and evolution of the dense nuclear star cluster surrounding this black hole is reported, including the astounding fact that stars have been forming in the vicinity of Sgr $\mathrm{A}*$ recently, apparently with a top-heavy stellar-mass function. A dense concentration of fainter stars centered in the immediate vicinity of the massive black hole are discussed, three of which have orbital peri-bothroi of less than one light day. This “S-star cluster” appears to consist mainly of young early-type stars, in contrast to the predicted properties of an equilibrium “stellar cusp” around a black hole. This constitutes a remarkable and presently not fully understood “paradox of youth.” What is known about the emission properties of the accreting gas onto Sgr $\mathrm{A}*$ is also summarized and how this emission is beginning to delineate the physical properties in the hot accretion zone around the event horizon.

Understanding the predictions of general relativity for the dynamical interactions of two black holes has been a long-standing unsolved problem in theoretical physics. Black-hole mergers are monumental astrophysical events, releasing tremendous amounts of energy in the form of gravitational radiation, and are key sources for both ground- and space-based gravitational-wave detectors. The black-hole merger dynamics and the resulting gravitational wave forms can only be calculated through numerical simulations of Einstein’s equations of general relativity. For many years, numerical relativists attempting to model these mergers encountered a host of problems, causing their codes to crash after just a fraction of a binary orbit could be simulated. Recently, however, a series of dramatic advances in numerical relativity has allowed stable, robust black-hole merger simulations. This remarkable progress in the rapidly maturing field of numerical relativity and the new understanding of black-hole binary dynamics that is emerging is chronicled. Important applications of these fundamental physics results to astrophysics, to gravitational-wave astronomy, and in other areas are also discussed.

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional (2D) topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional (3D) topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on $\mathrm{Hg}\mathrm{Te}∕\mathrm{Cd}\mathrm{Te}$ quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$, ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, and ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.

An experimental and theoretical perspective is provided on the behavior of unpolarized distribution functions for the nucleon and pion on the valence-quark domain, namely, Bjorken $x\gtrsim 0.4$. This domain is a key to much of hadron physics; e.g., a hadron is defined by its flavor content and that is a valence-quark property. Furthermore, its accurate parametrization is crucial to the provision of reliable input for large collider experiments. The focus is on experimental extractions of distribution functions via electron and muon inelastic scattering, and from Drell-Yan interactions; and on theoretical treatments that emphasize an explanation of the distribution functions, providing an overview of major contemporary approaches and issues. Valence-quark physics is a compelling subject, which probes at the heart of our understanding of the standard model. There are numerous outstanding and unresolved challenges, which experiment and theory must confront. In connection with experiment, an explanation that an upgraded Jefferson Laboratory facility is well suited to provide new data on the nucleon is provided, while a future electron-ion collider could provide essential new data for the mesons. There is also great potential in using Drell-Yan interactions, at FNAL, CERN, J-PARC, and GSI, to push into the large-$x$ domain for both mesons and nucleons. Furthermore, it is argued that explanation, in contrast to modeling and parametrization, requires a widespread acceptance of the need to adapt theory: to the lessons learnt already from the methods of nonperturbative quantum-field theory and a fuller exploitation of those methods.

The QCD vacuum shows the dynamical breaking of chiral symmetry. In the hot and/or dense QCD medium, the chiral order parameter such as $⟨\overline{q}q⟩$ is expected to change as a function of temperature $T$ and density $\rho$ of the medium, and its experimental detection is one of the main challenges in modern hadron physics. In this paper, the theoretical expectations for the in-medium hadron spectra associated with partial restoration of chiral symmetry are discussed as well as the current status of experiments with an emphasis on the measurements of properties of mesons produced in near-ground-state nuclei.

Picking up at the conclusion of Viovy’s review of the physics of gel electrophoresis [J.-L. Viovy, Rev. Mod. Phys. 72, 813 (2000)], this review synthesizes the experimental data, theoretical models, and simulation results for DNA electrophoresis in microfabricated and nanofabricated devices appearing since the seminal paper by Volkmuth and Austin [Nature (London) 358, 600 (1992)]. Prototype versions of these devices separate DNA by molecular weight at a rate far superior to gel electrophoresis. After providing an overview of the requisite background material in polymer physics, electrophoresis, and microfluidic device fabrication, the focus is on the following three generic problems: (i) collision with an isolated post, (ii) transport in an array of posts, and (iii) entropic trapping and filtration in the slit-well motif. The transport phenomena are examined here in the context of the length and time scales characterizing the DNA, the device, and the applied electric field.

The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average $S$ matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoretical methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin and parity) and time-reversal invariance.

This paper presents an elementary introduction to consistent quantum theory, as developed by Griffiths and others over the past $25\text{years}$. The theory is a version of orthodox (Copenhagen) quantum mechanics based on the notion that the unique and mysterious feature of quantum, as opposed to classical systems, is the simultaneous existence of multiple incompatible representations of reality, referred to as “frameworks.” A framework is a maximal set of properties of a system for which probabilities can be consistently defined. This notion is expressed by stating that a framework provides an exhaustive set of exclusive alternatives, but no single framework suffices to fully characterize a quantum system. Any prediction of the theory must be confined to a single framework and combining elements from different frameworks leads to quantum mechanically meaningless statements. This “single-framework rule” is the precise mathematical statement of Bohr’s complementarity. It is shown that if the microscopic description is assumed to incorporate these elements in a local setting, then distant entanglements, macroscopic measurements, wave-function collapse, and other features of quantum behavior follow in a logical manner. The essential elements of the theory are first explained using the simplest quantum system, a single spin-$\frac{1}{2}$ degree of freedom at one time.

The main theme of this review is the many-body physics of vortices in quantum droplets of bosons or fermions in the limit of small particle numbers. Systems of interest include cold atoms in traps as well as electrons confined in quantum dots. When set to rotate, these in principle different quantum systems show remarkable analogies. The topics reviewed include the structure of the finite rotating many-body state, universality of vortex formation and localization of vortices in both bosonic and fermionic systems, and the emergence of particle-vortex composites in the quantum Hall regime. An overview of the computational many-body techniques sets focus on the configuration-interaction and density-functional methods. Studies of quantum droplets with one or several particle components, where vortices as well as coreless vortices may occur, are reviewed, and theoretical as well as experimental challenges are discussed.

The interaction of subpicosecond laser pulses with magnetically ordered materials has developed into a fascinating research topic in modern magnetism. From the discovery of subpicosecond demagnetization over a decade ago to the recent demonstration of magnetization reversal by a single $40\mathrm{fs}$ laser pulse, the manipulation of magnetic order by ultrashort laser pulses has become a fundamentally challenging topic with a potentially high impact for future spintronics, data storage and manipulation, and quantum computation. Understanding the underlying mechanisms implies understanding the interaction of photons with charges, spins, and lattice, and the angular momentum transfer between them. This paper will review the progress in this field of laser manipulation of magnetic order in a systematic way. Starting with a historical introduction, the interaction of light with magnetically ordered matter is discussed. By investigating metals, semiconductors, and dielectrics, the roles of (nearly) free electrons, charge redistributions, and spin-orbit and spin-lattice interactions can partly be separated, and effects due to heating can be distinguished from those that are not. It will be shown that there is a fundamental distinction between processes that involve the actual absorption of photons and those that do not. It turns out that for the latter, the polarization of light plays an essential role in the manipulation of the magnetic moments at the femtosecond time scale. Thus, circularly and linearly polarized pulses are shown to act as strong transient magnetic field pulses originating from the nonabsorptive inverse Faraday and inverse Cotton-Mouton effects, respectively. The recent progress in the understanding of magneto-optical effects on the femtosecond time scale together with the mentioned inverse, optomagnetic effects promises a bright future for this field of ultrafast optical manipulation of magnetic order or femtomagnetism.

Application of non-Abelian finite groups to the theory of neutrino masses and mixing is reviewed, which is strongly suggested by the agreement of the tribimaximal (TB) mixing pattern with experiment. After summarizing the motivation and the formalism, concrete models based on $A_4$, $S_4$, and other finite groups, and their phenomenological implications are discussed, including lepton flavor violating processes, leptogenesis, and the extension to quarks. As an alternative to TB mixing application of discrete flavor symmetries to quark-lepton complementarity and bimaximal mixing is also considered.

An introduction to the transport properties of graphene combining experimental results and theoretical analysis is presented. In the theoretical description simple intuitive models are used to illustrate important points on the transport properties of graphene. The concept of chirality, stemming from the massless Dirac nature of the low-energy physics of the material, is shown to be instrumental in understanding its transport properties: the conductivity minimum, the electronic mobility, the effect of strain, the weak (anti)localization, and the optical conductivity.

Understanding the characteristics of jammed particle packings provides basic insights into the structure and bulk properties of crystals, glasses, and granular media and into selected aspects of biological systems. This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature of that diversity is the necessity to classify individual jammed configurations according to whether they are locally, collectively, or strictly jammed. Each of these categories contains a multitude of jammed configurations spanning a wide and (in the large system limit) continuous range of intensive properties, including packing fraction $\varphi$, mean contact number $Z$, and several scalar order metrics. Application of these analytical tools to spheres in three dimensions (an analog to the venerable Ising model) covers a myriad of jammed states, including maximally dense packings (as Kepler conjectured), low-density strictly jammed tunneled crystals, and a substantial family of amorphous packings. With respect to the last of these, the current approach displaces the historically prominent but ambiguous idea of “random close packing” with the precise concept of “maximally random jamming.” Both laboratory procedures and numerical simulation protocols can and, frequently, have been used for creation of ensembles of jammed states. But while the resulting distributions of intensive properties may individually approach narrow distributions in the large system limit, the distinguishing varieties of possible operational details in these procedures and protocols lead to substantial variability among the resulting distributions, some examples of which are presented here. This review also covers recent advances in understanding jammed packings of polydisperse sphere mixtures, as well as convex nonspherical particles, e.g., ellipsoids, “superballs,” and polyhedra. Because of their relevance to error-correcting codes and information theory, sphere packings in high-dimensional Euclidean spaces have been included as well. Some remarks are also made about packings in (curved) non-Euclidean spaces. In closing this review, several basic open questions for future research to consider have been identified.

Trapped laser-cooled atoms and ions are quantum systems which can be experimentally controlled with an as yet unmatched degree of precision. Due to the control of the motion and the internal degrees of freedom, these quantum systems can be adequately described by a well-known Hamiltonian. In this colloquium, powerful numerical tools for the optimization of the external control of the motional and internal states of trapped neutral atoms, explicitly applied to the case of trapped laser-cooled ions in a segmented ion-trap are presented. Inverse problems when optimizing trapping potentials for ions, are solved. The presentation is complemented by a quantum-mechanical treatment of the wave-packet dynamics of a trapped ion. Efficient numerical solvers for both time-independent and time-dependent problems are provided. Shaping the motional wave functions and optimizing a quantum gate is realized by the application of quantum optimal control techniques. The numerical methods presented can also be used to gain an intuitive understanding of quantum experiments with trapped ions by performing virtual simulated experiments on a personal computer. Code and executables are supplied as supplementary online material.

This article presents an overview of current understanding of the interaction of low-energy positrons with molecules with emphasis on resonances, positron attachment, and annihilation. Measurements of annihilation rates resolved as a function of positron energy reveal the presence of vibrational Feshbach resonances (VFRs) for many polyatomic molecules. These resonances lead to strong enhancement of the annihilation rates. They also provide evidence that positrons bind to many molecular species. A quantitative theory of VFR-mediated attachment to small molecules is presented. It is tested successfully for selected molecules (e.g., methyl halides and methanol) where all modes couple to the positron continuum. Combination and overtone resonances are observed and their role is elucidated. Molecules that do not bind positrons and hence do not exhibit such resonances are discussed. In larger molecules, annihilation rates from VFR far exceed those explicable on the basis of single-mode resonances. These enhancements increase rapidly with the number of vibrational degrees of freedom, approximately as the fourth power of the number of atoms in the molecule. While the details are as yet unclear, intramolecular vibrational energy redistribution (IVR) to states that do not couple directly to the positron continuum appears to be responsible for these enhanced annihilation rates. In connection with IVR, experimental evidence indicates that inelastic positron escape channels are relatively rare. Downshifts of the VFR from the vibrational mode energies, obtained by measuring annihilate rates as a function of incident positron energy, have provided binding energies for 30 species. Their dependence upon molecular parameters and their relationship to positron-atom and positron-molecule binding-energy calculations are discussed. Feshbach resonances and positron binding to molecules are compared with the analogous electron-molecule (negative-ion) cases. The relationship of VFR-mediated annihilation to other phenomena such as Doppler broadening of the gamma-ray annihilation spectra, annihilation of thermalized positrons in gases, and annihilation-induced fragmentation of molecules is discussed. Possible areas for future theoretical and experimental investigation are also discussed.