${\mathrm{SmB}}_6$, a well-known Kondo insulator, has been proposed to be an ideal topological insulator with states of topological character located in a clean, bulk electronic gap, namely, the Kondo-hybridization gap. Since the Kondo gap arises from many-body electronic correlations, ${\mathrm{SmB}}_6$ would be placed at the head of a new material class: topological Kondo insulators. Here, for the first time, we show that the $k$-space characteristics of the Kondo-hybridization process is the key to unraveling the origin of the two types of metallic states experimentally observed by angle-resolved photoelectron spectroscopy (ARPES) in the electronic band structure of ${\mathrm{SmB}}_6(001)$. One group of these states is essentially of bulk origin and cuts the Fermi level due to the position of the chemical potential 20 meV above the lowest-lying $5d\mathrm{\text{−}}4f$ hybridization zone. The other metallic state is more enigmatic, being weak in intensity, but represents a good candidate for a topological surface state. However, before this claim can be substantiated by an unequivocal measurement of its massless dispersion relation, our data raise the bar in terms of the ARPES resolution required, as we show there to be a strong renormalization of the hybridization gaps by a factor 2–3 compared to theory, following from the knowledge of the true position of the chemical potential and a careful comparison with the predictions from recent local-density-approximation $(\mathrm{LDA})+\mathrm{\text{Gutzwiller}}$ calculations. All in all, these key pieces of evidence act as triangulation markers, providing a detailed description of the electronic landscape in ${\mathrm{SmB}}_6$ and pointing the way for future, ultrahigh-resolution ARPES experiments to achieve a direct measurement of the Dirac cones in the first topological Kondo insulator.

We propose a mechanism of coherent coupling between distant spin qubits interacting dipolarly with a ferromagnet. We derive an effective two-spin interaction Hamiltonian and find a regime where the dynamics is coherent. Finally, we present a sequence for the implementation of the entangling controlled-not gate and estimate the corresponding operation time to be a few tens of nanoseconds. A particularly promising application of our proposal is to atomistic spin qubits such as silicon-based qubits and nitrogen-vacancy centers in diamond to which existing coupling schemes do not apply.

A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.

Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments.

While the well-established Prandtl-Tomlinson (PT) model of atomic friction predicts that the friction force decreases with temperature and grows with velocity, several recent experiments reported that a nonmonotonic temperature dependence and a decreasing velocity dependence may also occur. We propose a minimal extension of the PT model, incorporating the possibility of thermally activated contact strengthening and providing one common framework to quantitatively explain all those “anomalous” experimental findings, as well as the previously known “normal” (PT-like) behavior.

Magneto-optical effects in ferrimagnetic or ferromagnetic materials are usually too weak for potential applications. The transverse magneto-optical Kerr effect (TMOKE) in ferromagnetic films is typically on the order of 0.1%. Here, we demonstrate experimentally the enhancement of TMOKE due to the interaction of particle plasmons in gold nanowires with a photonic waveguide consisting of magneto-optical material, where hybrid waveguide-plasmon polaritons are excited. We achieve a large TMOKE that modulates the transmitted light intensity by 1.5%, accompanied by high transparency of the system. Our concept may lead to novel devices of miniaturized photonic circuits and switches, which are controllable by an external magnetic field.

We discuss how a lattice Schwinger model can be realized in a linear ion trap, allowing a detailed study of the physics of Abelian lattice gauge theories related to one-dimensional quantum electrodynamics. Relying on the rich quantum-simulation toolbox available in state-of-the-art trapped-ion experiments, we show how one can engineer an effectively gauge-invariant dynamics by imposing energetic constraints, provided by strong Ising-like interactions. Applying exact diagonalization to ground-state and time-dependent properties, we study the underlying microscopic model and discuss undesired interaction terms and other imperfections. As our analysis shows, the proposed scheme allows for the observation in realistic setups of spontaneous parity- and charge-symmetry breaking, as well as false-vacuum decay. Besides an implementation aimed at larger ion chains, we also discuss a minimal setting, consisting of only four ions in a simpler experimental setup, which enables us to probe basic physical phenomena related to the full many-body problem. The proposal opens a new route for analog quantum simulation of high-energy and condensed-matter models where gauge symmetries play a prominent role.

One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their non-Abelian nature allows for processing quantum information by braiding operations that are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum-information processing on a finite time scale, we study domain walls moving at a constant velocity. We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum after the domain wall propagates at luminal or even superluminal velocities. This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system.

Three-dimensional (3D) topological superconductors (TScs) protected by time-reversal ($\mathcal{T}$) symmetry are characterized by gapless Majorana cones on their surface. Free-fermion phases with this symmetry (class DIII) are indexed by an integer $\nu$, of which $\nu =1$ is realized by the $B$ phase of superfluid ${}^3\mathrm{He}$. Previously, it was believed that the surface must be gapless unless time-reversal symmetry is broken. Here, we argue that a fully symmetric and gapped surface is possible in the presence of strong interactions, if a special type of topological order appears on the surface. The topological order realizes $\mathcal{T}$ symmetry in an anomalous way, one that is impossible to achieve in purely two dimensions. For odd $\nu \mathrm{TScs}$, the surface topological order must be non-Abelian. We propose the simplest non-Abelian topological order that contains electronlike excitations, $\mathrm{SO}(3{)}_6$, with four quasiparticles, as a candidate surface state. Remarkably, this theory has a hidden $\mathcal{T}$ invariance that, however, is broken in any two-dimensional realization. By explicitly constructing an exactly soluble Walker-Wang model, we show that it can be realized at the surface of a short-ranged entangled 3D fermionic phase protected by $\mathcal{T}$ symmetry, with bulk electrons transforming as Kramers pairs, i.e. ${\mathcal{T}}^2=-1$ under time reversal. We also propose an Abelian theory, the semion-fermion topological order, to realize an even $\nu \mathrm{TSc}$ surface, for which an explicit model is derived using a coupled-layer construction. We argue that this is related to the $\nu =2\mathrm{TSc}$, and we use this to build candidate surface topological orders for $\nu =4$ and $\nu =8\mathrm{TScs}$. The latter is equivalent to the three-fermion state, which is the surface topological order of a ${\mathbb{Z}}_2$ bosonic topological phase protected by $\mathcal{T}$ invariance. One particular consequence of this equivalence is that a $\nu =16\mathrm{TSc}$ admits a trivially gapped $\mathcal{T}$-symmetric surface.

We report new results of Bose-Einstein condensation of polaritons in specially designed microcavities with a very high quality factor, on the order of ${10}^6$, giving polariton lifetimes of the order of 100 ps. When the polaritons are created with an incoherent pump, a dissipationless, coherent flow of the polaritons occurs over hundreds of microns, which increases as density increases. At high density, this flow is suddenly stopped, and the gas becomes trapped in a local potential minimum, with strong coherence.

Ratchets are devices that are able to rectify an otherwise oscillatory behavior by exploiting an asymmetry of the system. In rocking ratchets, the asymmetry is induced through a proper choice of external forces and modulations of nonlinear symmetric potentials. The ratchet currents thus obtained in systems as different as semiconductors, Josephson junctions, optical lattices, or ferrofluids show a set of universal features. A satisfactory explanation for them has challenged theorists for decades, and so far, we still lack a general theory of this phenomenon. Here, we provide such a theory by exploring—through functional analysis—the constraints that the simple assumption of time-shift invariance of the ratchet current imposes on its dependence on the external drivings. Because the derivation is based on so general a principle, the resulting expression is valid irrespective of the details and the nature of the physical systems to which it is applied, and of whether they are classical, quantum, or stochastic. The theory also explains deviations observed from universality under special conditions and allows us to make predictions of phenomena not yet observed in any experiment or simulation.

Adiabatic quantum computation (AQC) has been lauded for its inherent robustness to control imperfections and relaxation effects. A considerable body of previous work, however, has shown AQC to be acutely sensitive to noise that causes excitations from the adiabatically evolving ground state. In this paper, we develop techniques to mitigate such noise, and then we point out and analyze some obstacles to further progress. First, we examine two known techniques that leverage quantum error-detecting codes to suppress noise and show that they are intimately related and may be analyzed within the same formalism. Next, we analyze the effectiveness of such error-suppression techniques in AQC, identify critical constraints on their performance, and conclude that large-scale, fault-tolerant AQC will require error correction, not merely suppression. Finally, we study the consequences of encoding AQC in quantum stabilizer codes and discover that generic AQC problem Hamiltonians rapidly convert physical errors into uncorrectable logical errors. We present several techniques to remedy this problem, but all of them require unphysical resources, suggesting that the adiabatic model of quantum computation may be fundamentally incompatible with stabilizer quantum error correction.

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.

Active electromagnetic cloaking uses an array of elementary sources to cancel the scattered fields created by an object. An active interior cloak does this by placing the sources along the boundary of the object. This process can be thought of as introducing a discontinuity in the field to cancel out the scattered field by the object. Here, an experimental version of a thin active cloak at microwave frequencies is demonstrated for an aluminum cylinder with a radius of $0.56\lambda$. The cloak consists of a 12-element magnetic-dipole array. By controlling the weights of the current on each element of the array, the scattering off of the cylinder is reduced in the backward and forward directions. The ability to disguise the aluminum cylinder as another object by varying the weights of the dipole array is also demonstrated. Finally, potential ways of overcoming the constraint of requiring a priori knowledge of the incident field leading to camouflaging-type behavior are discussed.

We present a powerful and versatile technique that enables exquisite spatial and temporal control over local solution chemistry in microfluidic devices. Using a microscope and a UV lamp, we use projection lithography to photopolymerize thin ($10–25\mu \mathrm{m}$) hydrogel membrane “microwindows” (HMMs) into standard microfluidic devices. These microwindows are permeable to solute and solvent diffusion and to electric fields, yet act as rigid walls from the standpoint of fluid flow. Reservoirs of solution may thus be rapidly imposed, switched, and maintained on one side of a HMM using standard microfluidic techniques, provoking changes in solution conditions on the other side without active mixing, stirring, or diluting. We highlight three paradigmatic experimental capabilities enabled by HMMs: (1) rapid dialysis and swapping of solute and/or solvent, (2) stable and convection-free localized concentration gradients, and (3) local electric permeability. The functional versatility of hydrogel microwindow membranes, coupled with the ease and speed of their fabrication and integration into simple microchannels or multilayer devices, will open a variety of novel applications and studies in a broad range of fields.

We investigate lasing action in aligned nitrogen molecular ions ($\mathrm{N}_2{}^{+}$) produced in an intense laser field. We find that, besides the population inversion between the ${\mathrm{B}}^2\Sigma _u{}^{+}-{\mathrm{X}}^2\Sigma _g{}^{+}$ states, which is responsible for the observed simulated amplification of a seed pulse, a rotational wave packet in the ground vibrational state ($v=0$) of the excited electronic ${\mathrm{B}}^2\Sigma _u{}^{+}$ state has been created in $\mathrm{N}_2{}^{+}$. The rotational coherence can faithfully encode its characteristics into the amplified seed pulses, enabling reconstruction of rotational wave packets of molecules in a single-shot detection manner from the frequency-resolved laser spectrum. Our results suggest that the air laser can potentially provide a promising tool for remote characterization of coherent molecular rotational wave packets.

The ability to transport energy is a fundamental property of the two-dimensional Dirac fermions in graphene. Electronic thermal transport in this system is relatively unexplored and is expected to show unique fundamental properties and to play an important role in future applications of graphene, including optoelectronics, plasmonics, and ultrasensitive bolometry. Here, we present measurements of bipolar thermal conductances due to electron diffusion and electron-phonon coupling and infer the electronic specific heat, with a minimum value of $10k_B$ (${10}^{-22}\mathrm{J}/\mathrm{K}$) per square micron. We test the validity of the Wiedemann-Franz law and find that the Lorenz number equals $1.32\times ({\pi }^2/3)(k_B/e{)}^2$. The electron-phonon thermal conductance has a temperature power law $T^2$ at high doping levels, and the coupling parameter is consistent with recent theory, indicating its enhancement by impurity scattering. We demonstrate control of the thermal conductance by electrical gating and by suppressing the diffusion channel using NbTiN superconducting electrodes, which sets the stage for future graphene-based single-microwave photon detection.

In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long-time probability distribution for the location of a unitary quantum walker to that of a corresponding classical walker. The distribution of the classical walker is proportional to the distribution of degrees, which measures the connectivity of the network nodes and underlies many methods for analyzing classical networks, including website ranking. The quantum distribution becomes exactly equal to the classical distribution when the walk has zero energy, and at higher energies, the difference, the so-called quantumness, is bounded by the energy of the initial state. We give an example for which the quantumness equals a Rényi entropy of the normalized weighted degrees, guiding us to regimes for which the classical degree-dependent result is recovered and others for which quantum effects dominate.

Single quantum dots are solid-state emitters that mimic two-level atoms but with a highly enhanced spontaneous emission rate. A single quantum dot is the basis for a potentially excellent single-photon source. One outstanding problem is that there is considerable noise in the emission frequency, making it very difficult to couple the quantum dot to another quantum system. We solve this problem here with a dynamic feedback technique that locks the quantum-dot emission frequency to a reference. The incoherent scattering (resonance fluorescence) represents the single-photon output, whereas the coherent scattering (Rayleigh scattering) is used for the feedback control. The fluctuations in emission frequency are reduced to 20 MHz, just approximately $5\%$ of the quantum-dot optical linewidth, even over several hours. By eliminating the $1/f$-like noise, the relative fluctuations in quantum-dot noise power are reduced to approximately ${10}^{-5}$ at low frequency. Under these conditions, the antibunching dip in the resonance fluorescence is described extremely well by the two-level atom result. The technique represents a way of removing charge noise from a quantum device.

We discuss the global scattering response of invisibility cloaks over the entire electromagnetic spectrum, from static to very high frequencies. Based on linearity, causality, and energy conservation, we show that the total extinction and scattering, integrated over all wavelengths, of any linear, passive, causal, and nondiamagnetic cloak, necessarily increase compared to the uncloaked case. In light of this general principle, we provide a quantitative measure to compare the global performance of different cloaking techniques and we discuss solutions to minimize the global scattering signature of an object using thin, superconducting shells. Our results provide important physical insights on how invisibility cloaks operate and affect the global scattering of an object, suggesting ways to defeat countermeasures aimed at detecting cloaked objects using short impinging pulses.