Large communities of biological oscillators show a prevalent tendency to self-organize in time. This cooperative phenomenon inspired Winfree to formulate a mathematical model that originated the theory of macroscopic synchronization. Despite its fundamental importance, a complete mathematical analysis of the model proposed by Winfree—consisting of a large population of all-to-all pulse-coupled oscillators—is still missing. Here, we show that the dynamics of the Winfree model evolves into the so-called Ott-Antonsen manifold. This important property allows for an exact description of this high-dimensional system in terms of a few macroscopic variables, and also allows for the full investigation of its dynamics. We find that brief pulses are capable of synchronizing heterogeneous ensembles that fail to synchronize with broad pulses, especially for certain phase-response curves. Finally, to further illustrate the potential of our results, we investigate the possibility of “chimera” states in populations of identical pulse-coupled oscillators. Chimeras are self-organized states in which the symmetry of a population is broken into a synchronous and an asynchronous part. Here, we derive three ordinary differential equations describing two coupled populations and uncover a variety of chimera states, including a new class with chaotic dynamics.

We study the dynamics of a $2+1$-dimensional relativistic viscous conformal fluid in Minkowski spacetime. Such fluid solutions arise as duals, under the “gravity/fluid correspondence,” to $3+1$-dimensional asymptotically anti–de Sitter (AAdS) black-brane solutions to the Einstein equation. We examine stability properties of shear flows, which correspond to hydrodynamic quasinormal modes of the black brane. We find that, for sufficiently high Reynolds number, the solution undergoes an inverse turbulent cascade to long-wavelength modes. We then map this fluid solution, via the gravity/fluid duality, into a bulk metric. This suggests a new and interesting feature of the behavior of perturbed AAdS black holes and black branes, which is not readily captured by a standard quasinormal mode analysis. Namely, for sufficiently large perturbed black objects (with long-lived quasinormal modes), nonlinear effects transfer energy from short- to long-wavelength modes via a turbulent cascade within the metric perturbation. As long-wavelength modes have slower decay, this transfer of energy lengthens the overall lifetime of the perturbation. We also discuss various implications of this behavior, including expectations for higher dimensions and the possibility of predicting turbulence in more general gravitational scenarios.

We report a comprehensive study of the binary systems of the platinum-group metals with the transition metals, using high-throughput first-principles calculations. These computations predict stability of new compounds in 28 binary systems where no compounds have been reported in the literature experimentally and a few dozen of as-yet unreported compounds in additional systems. Our calculations also identify stable structures at compound compositions that have been previously reported without detailed structural data and indicate that some experimentally reported compounds may actually be unstable at low temperatures. With these results, we construct enhanced structure maps for the binary alloys of platinum-group metals. These maps are much more complete, systematic, and predictive than those based on empirical results alone.

Focal conic domains (FCDs) in smectic-A liquid crystals have drawn much attention, both for their exquisitely structured internal form and for their ability to direct the assembly of micromaterials and nanomaterials in a variety of patterns. A key to directing FCD assembly is control over the eccentricity of the domain. Here, we demonstrate a new paradigm for creating spatially varying FCD eccentricity by confining a hybrid-aligned smectic with curved interfaces. In particular, we manipulate interface behavior with colloidal particles in order to experimentally produce two examples of what has recently been dubbed the flower texture [C. Meyer et al., Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling, Materials 2, 499, 2009], where the focal hyperbolæ diverge radially outward from the center of the texture, rather than inward as in the canonical éventail or fan texture. We explain how this unconventional assembly can arise from appropriately curved interfaces. Finally, we present a model for this system that applies the law of corresponding cones, showing how FCDs may be embedded smoothly within a “background texture” of large FCDs and concentric spherical layers, in a manner consistent with the qualitative features of the smectic flower. Such understanding could potentially lead to disruptive liquid-crystal technologies beyond displays, including patterning, smart surfaces, microlens arrays, sensors, and nanomanufacturing.

Stromatolites can grow under the influence of microbial processes, but it is often unclear whether and how the macroscopic morphology of these rocks records biological processes. Conical stromatolites, which formed in the absence of sedimentation, provide a comparatively simple record of the interplay between microbial growth and lithification. Here, we show that the dynamics shaping conical stromatolites result from diffusive gradients within the overlying microbial mat. These gradients cause minerals to precipitate faster in regions of high curvature, resulting in measurable properties of the shapes of stromatolite laminas. This model allows us to estimate the thickness of ancient stromatolite-forming mats to be approximately $1\mathrm{mm}$, consistent with modern systems. Proceeding from the assumption that the ubiquitous process of diffusion is recorded in the translating form of a stromatolite, we derive the shape of a diffusion-driven stromatolite. The conical morphology—a distinctive feature of stromatolites growing in the absence of sedimentation—arises from these dynamics. This form is quantitatively consistent with the shape of conical stromatolites that grew for more than $2.9\times {10}^9$ yrs of Earth history.

We report an experiment in which an atomic excitation is localized to a spatial width that is a factor of 8 smaller than the wavelength of the incident light. The experiment utilizes the sensitivity of the dark state of electromagnetically induced transparency (EIT) to the intensity of the coupling laser beam. A standing-wave coupling laser with a sinusoidally varying intensity yields tightly confined Raman excitations during the EIT process. The excitations, located near the nodes of the intensity profile, have a width of 100 nm. The experiment is performed using ultracold ${}^{87}\mathrm{Rb}$ atoms trapped in an optical dipole trap, and atomic localization is achieved with EIT pulses that are approximately 100 ns long. To probe subwavelength atom localization, we have developed a technique that can measure the width of the atomic excitations with nanometer spatial resolution.

We create squeezed light by exploiting the quantum nature of the mechanical interaction between laser light and a membrane mechanical resonator embedded in an optical cavity. The radiation-pressure shot noise (fluctuating optical force from quantum laser amplitude noise) induces resonator motion well above that of thermally driven motion. This motion imprints a phase shift on the laser light, hence correlating the amplitude and phase noise, a consequence of which is optical squeezing. We experimentally demonstrate strong and continuous optomechanical squeezing of $1.7\pm 0.2\mathrm{dB}$ below the shot-noise level. The peak level of squeezing measured near the mechanical resonance is well described by a model whose parameters are independently calibrated and that includes thermal motion of the membrane with no other classical noise sources.

Progress in materials science depends on the ability to discover new materials and to obtain and understand their properties. This has recently become particularly apparent for compounds with reduced dimensionality, which often display unexpected physical and chemical properties, making them very attractive for applications in electronics, graphene being so far the most noteworthy example. Here, we report some previously unknown two-dimensional materials and their electronic structure by data mining among crystal structures listed in the International Crystallographic Structural Database, combined with density-functional-theory calculations. As a result, we propose to explore the synthesis of a large group of two-dimensional materials, with properties suggestive of applications in nanoscale devices, and anticipate further studies of electronic and magnetic phenomena in low-dimensional systems.

The origin of superconductivity in bulk ${\mathrm{SrTiO}}_3$ is a mystery since the nonmonotonous variation of the critical transition with carrier concentration defies the expectations of the crudest version of the BCS theory. Here, employing the Nernst effect, an extremely sensitive probe of tiny bulk Fermi surfaces, we show that, down to concentrations as low as $5.5\times {10}^{17}{\mathrm{cm}}^{-3}$, the system has both a sharp Fermi surface and a superconducting ground state. The most dilute superconductor currently known therefore has a metallic normal state with a Fermi energy as little as 1.1 meV on top of a band gap as large as 3 eV. The occurrence of a superconducting instability in an extremely small, single-component, and barely anisotropic Fermi surface implies strong constraints for the identification of the pairing mechanism.

We have measured the electrophoretic mobility of single, optically trapped colloidal particles, while gradually depleting the co-ions and counterions in the liquid around the particle by applying a dc voltage. This is achieved in a nonpolar liquid, where charged reverse micelles act as co-ions and counterions. By increasing the dc voltage, the mobility first increases when the concentrations of co-ions and counterions near the particle start to decrease. At sufficiently high dc voltage (around 2 V), the mobility reaches a saturation value when the co-ions and counterions are fully separated. The increase in mobility is larger when the equilibrium ionic strength is higher. The dependence of the experimental data on the equilibrium ionic strength and on the applied voltage is in good agreement with the standard theory of electrophoretic retardation, assuming that the bare particle charge remains constant. This method is useful for studying the electrophoretic retardation effect and charging mechanisms for nonpolar colloids, and it sheds light on previously unexplained particle acceleration in electronic ink devices.

As an exemplary Kondo insulator, ${\mathrm{SmB}}_6$ has been studied for several decades. However, direct evidence for the development of the Kondo coherent state and for the evolution of the electronic structure in the material has not been obtained due to the compound’s rather complicated electronic and thermal transport behavior. Recently, these open questions have attracted increasing attention as the emergence of a time-reversal-invariant topological surface state in the Kondo insulator has been suggested. Here, we use point-contact spectroscopy to reveal the temperature dependence of the electronic states in ${\mathrm{SmB}}_6$. We demonstrate that ${\mathrm{SmB}}_6$ is a model Kondo insulator: Below 100 K, the conductance spectra reflect the Kondo hybridization of Sm ions, but, below about $30\mathrm{K}$, signatures of inter-ion correlation effects clearly emerge. Moreover, we find evidence that the low-temperature insulating state of this exemplary Kondo-lattice compound harbors conduction states on the surface, in support of predictions of nontrivial topology in Kondo insulators.

In this work, we present theoretical tools suitable for quantitative modeling of large superconducting circuits that include one-dimensional Josephson-junction arrays. The large number of low-energy degrees of freedom and the peculiar interactions between them induced by flux quantization present a considerable challenge to the detailed modeling of such circuits. For the concrete example of the fluxonium device, we show how to address this challenge. Starting from the complete degrees of freedom of the circuit, we employ the relevant collective modes and circuit symmetries to obtain a systematic approximation scheme. Important circuit symmetries include approximate invariance under the symmetric group and lead to considerable simplifications of the theory. Selection rules restrict the possible coupling among different collective modes and help explain the remarkable accuracy of previous simplified models. Using this strategy, we obtain new predictions for the energy spectrum of the fluxonium device that can be tested with current experimental technology.

We report cooling of a single neutral atom to its three-dimensional vibrational ground state in an optical tweezer. After employing Raman sideband cooling for tens of milliseconds, we measure via sideband spectroscopy a three-dimensional ground-state occupation of about $90\%$. We further observe coherent control of the spin and motional state of the trapped atom. Our demonstration shows that an optical tweezer, formed simply by a tightly focused beam of light, creates sufficient confinement for efficient sideband cooling. This source of ground-state neutral atoms will be instrumental in numerous quantum simulation and logic applications that require a versatile platform for storing and manipulating ultracold single neutral atoms. For example, these results will improve current optical-tweezer experiments studying atom-photon coupling and Rydberg quantum logic gates, and could provide new opportunities such as rapid production of single dipolar molecules or quantum simulation in tweezer arrays.

Quantum key distribution (QKD) uniquely allows the distribution of cryptographic keys with security verified by quantum mechanical limits. Both protocol execution and subsequent applications require the assistance of classical data communication channels. While using separate fibers is one option, it is economically more viable if data and quantum signals are simultaneously transmitted through a single fiber. However, noise-photon contamination arising from the intense data signal has severely restricted both the QKD distances and secure key rates. Here, we exploit a novel temporal-filtering effect for noise-photon rejection. This allows high-bit-rate QKD over fibers up to 90 km in length and populated with error-free bidirectional $\mathrm{Gb}/\mathrm{s}$ data communications. With a high-bit rate and range sufficient for important information infrastructures, such as smart cities and 10-Gbit Ethernet, QKD is a significant step closer toward wide-scale deployment in fiber networks.

Neurons in cerebral cortical circuits interact by sending and receiving electrical impulses called spikes. The ongoing spiking activity of cortical circuits is fundamental to many cognitive functions including sensory processing, working memory, and decision making. London et al. [Sensitivity to Perturbations In Vivo Implies High Noise and Suggests Rate Coding in Cortex, Nature (London) 466, 123 (2010).] recently argued that even a single additional spike can cause a cascade of extra spikes that rapidly decorrelate the microstate of the network. Here, we show theoretically in a minimal model of cortical neuronal circuits that single-spike perturbations trigger only a very weak rate response. Nevertheless, single-spike perturbations are found to rapidly decorrelate the microstate of the network, although the dynamics is stable with respect to small perturbations. The coexistence of stable and unstable dynamics results from a system of exponentially separating dynamic flux tubes around stable trajectories in the network’s phase space. The radius of these flux tubes appears to decrease algebraically with neuron number $N$ and connectivity $K$, which implies that the entropy of the circuit’s repertoire of state sequences scales as $N\ln (KN)$.

Dictionaries link a given word to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that definitions loop back upon themselves. We demonstrate that such definitional loops are created in order to introduce new concepts into a language. In contrast to the expectations for a random lexical network, in graphs of the dictionary, meaningful loops are quite short, although they are often linked to form larger, strongly connected components. These components are found to represent distinct semantic ideas. This observation can be quantified by a singular value decomposition, which uncovers a set of conceptual relationships arising in the global structure of the dictionary. Finally, we use etymological data to show that elements of loops tend to be added to the English lexicon simultaneously and incorporate our results into a simple model for language evolution that falls within the “rich-get-richer” class of network growth.

Although iron-based superconductors are multiorbital systems with complicated band structures, we demonstrate that the low-energy physics which is responsible for their high-$T_c$ superconductivity is essentially governed by an effective two-orbital Hamiltonian near half filling. This underlying electronic structure is protected by the $S_4$ symmetry. With repulsive or strong next-nearest-neighbor antiferromagnetic exchange interactions, the model results in a robust $A_{1g}$ $s$-wave pairing which can be mapped exactly to the $d$-wave pairing observed in cuprates. The classification of the superconducting (SC) states according to the $S_4$ symmetry leads to a natural prediction of the existence of two different phases, named the $A$ and $B$ phases. In the $B$ phase, the superconducting order has an overall sign change along the $c$ axis between the top and bottom As (or Se) planes in a single Fe-As (or Fe-Se) trilayer structure, the common building block of iron-based superconductors. The sign change is analogous to the sign change in the $d$-wave superconducting state of cuprates upon 90° rotation. Our derivation provides a unified understanding of iron pnictides and iron chalcogenides, and suggests that cuprates and iron-based superconductors share an identical high-$T_c$ superconducting mechanism.

The inevitable presence of decoherence effects in systems suitable for quantum computation necessitates effective error-correction schemes to protect information from noise. We compute the stability of the toric code to depolarization by mapping the quantum problem onto a classical disordered eight-vertex Ising model. By studying the stability of the related ferromagnetic phase via both large-scale Monte Carlo simulations and the duality method, we are able to demonstrate an increased error threshold of 18.9(3)% when noise correlations are taken into account. Remarkably, this result agrees within error bars with the result for a different class of codes—topological color codes—where the mapping yields interesting new types of interacting eight-vertex models.

The electron spin is a natural two-level system that allows a qubit to be encoded. When localized in a gate-defined quantum dot, the electron spin provides a promising platform for a future functional quantum computer. The essential ingredient of any quantum computer is entanglement—for the case of electron-spin qubits considered here—commonly achieved via the exchange interaction. Nevertheless, there is an immense challenge as to how to scale the system up to include many qubits. In this paper, we propose a novel architecture of a large-scale quantum computer based on a realization of long-distance quantum gates between electron spins localized in quantum dots. The crucial ingredients of such a long-distance coupling are floating metallic gates that mediate electrostatic coupling over large distances. We show, both analytically and numerically, that distant electron spins in an array of quantum dots can be coupled selectively, with coupling strengths that are larger than the electron-spin decay and with switching times on the order of nanoseconds.

Ultrashort pulses of extreme ultraviolet light from high-harmonic generation are a new tool for probing coupled charge, spin, and phonon dynamics with element specificity, attosecond pump-probe synchronization, and time resolution of a few femtoseconds in a tabletop apparatus. In this paper, we address an important question in magneto-optics that has implications for understanding magnetism on the fastest time scales: Is the signal from the transverse magneto-optical Kerr effect at the ${\mathrm{M}}_{2,3}$ edges of a magnetic material purely magnetic or is it perturbed by nonmagnetic artifacts? Our measurements demonstrate conclusively that transverse magneto-optical Kerr measurements at the ${\mathrm{M}}_{2,3}$ edges sensitively probe the magnetic state, with almost negligible contributions from the transient variation of the refractive index by the nonequilibrium hot-electron distribution. In addition, we compare pump-probe demagnetization dynamics measured by both high harmonics and conventional visible-wavelength magneto-optics and find that the measured demagnetization times are in agreement.