A single crystal of isovalently substituted $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x{)}_2{\mathrm{As}}_2$ ($x=0.24$) is sequentially irradiated with 2.5 MeV electrons up to a maximum dose of $2.1\times 10^{19}$ $e^{-}/{\mathrm{cm}}^2$. The electrical resistivity is measured in situ at $T=22\mathrm{K}$ during the irradiation and ex situ as a function of temperature between subsequent irradiation runs. Upon irradiation, the superconducting transition temperature $T_c$ decreases and the residual resistivity ${\rho }_0$ increases. We find that electron irradiation leads to the fastest suppression of $T_c$ compared to other types of artificially introduced disorder, probably due to the strong short-range potential of the pointlike irradiation defects. A more detailed analysis within a multiband scenario with variable scattering potential strength shows that the observed $T_c$ versus ${\rho }_0$ is fully compatible with $s_{\pm }$ pairing, in contrast to earlier claims that this model leads to a too rapid suppression of $T_c$ with scattering.

The phenomenon of ultrastrong light-matter interaction of a two-dimensional electron gas within a lumped element electronic circuit resonator is explored. The gas is coupled through the oscillating electric field of the capacitor, and in the limit of very small capacitor volumes, the total number of electrons of the system can be reduced to only a few. One of the peculiar features of our quantum mechanical system is that its Hamiltonian evolves from the fermionic Rabi model to the bosonic Hopfield model for light-matter coupling as the number of electrons is increased. We show that the Dicke states, introduced to describe the atomic super-radiance, are the natural base to describe the crossover between the two models. Furthermore, we illustrate how the ultrastrong coupling regime in the system and the associated antiresonant terms of the quantum Hamiltonian have a fundamentally different impact in the fermionic and bosonic cases. In the intermediate regime, our system behaves like a multilevel quantum bit with nonharmonic energy spacing, owing to the particle-particle interactions. Such a system can be inserted into a technological semiconductor platform, thus opening interesting perspectives for electronic devices where the readout of quantum electrodynamical properties is obtained via the measure of a DC current.

Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.

To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.

In some many-body systems, certain ground-state entanglement (Rényi) entropies increase even as the correlation length decreases. This entanglement nonmonotonicity is a potential indicator of nonclassicality. In this work, we demonstrate that such a phenomenon, known as lack of local convertibility, is due to the edge-state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions $(A|B)$ and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show lack of local convertibility if either $A$ or $B$ is smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry-breaking) ground state is always locally convertible. The edge-state behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and nonlocal, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.

Magnetic fluctuations and electrons couple in intriguing ways in the vicinity of zero-temperature phase transitions—quantum critical points—in conducting materials. Quantum criticality is implicated in non-Fermi liquid behavior of diverse materials and in the formation of unconventional superconductors. Here, we uncover an entirely new type of quantum critical point describing the onset of antiferromagnetism in a nodal semimetal engendered by the combination of strong spin-orbit coupling and electron correlations, and which is predicted to occur in the iridium oxide pyrochlores. We formulate and solve a field theory for this quantum critical point by renormalization group techniques and show that electrons and antiferromagnetic fluctuations are strongly coupled and that both these excitations are modified in an essential way. This quantum critical point has many novel features, including strong emergent spatial anisotropy, a vital role for Coulomb interactions, and highly unconventional critical exponents. Our theory motivates and informs experiments on pyrochlore iridates and constitutes a singular realistic example of a nontrivial quantum critical point with gapless fermions in three dimensions.

Many real-world networks contain a statistically surprising number of certain subgraphs, called network motifs. In the prevalent approach to motif analysis, network motifs are detected by comparing subgraph frequencies in the original network with a statistical null model. In this paper, we propose an alternative approach to motif analysis where network motifs are defined to be connectivity patterns that occur in a subgraph cover that represents the network using minimal total information. A subgraph cover is defined to be a set of subgraphs such that every edge of the graph is contained in at least one of the subgraphs in the cover. Some recently introduced random graph models that can incorporate significant densities of motifs have natural formulations in terms of subgraph covers, and the presented approach can be used to match networks with such models. To prove the practical value of our approach, we also present a heuristic for the resulting NP hard optimization problem and give results for several real-world networks.

Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most such schemes characterize a dynamical process by probing it with a specially designed quantum state. The success of such a scheme usually relies on the process belonging to a particular one-parameter family. If this assumption is violated, or if the goal is to measure more than one parameter, a different quantum state may perform better. In the most extreme case, we know nothing about the process and wish to learn everything. This requires quantum process tomography, which demands an informationally complete set of probe states. It is very convenient if this set is group covariant—i.e., each element is generated by applying an element of the quantum system’s natural symmetry group to a single fixed fiducial state. In this paper, we consider metrology with 2-photon (“biphoton”) states and report experimental studies of different states’ sensitivity to small, unknown collective $SU(2)$ rotations [“$SU(2)$ jitter”]. Maximally entangled $N00N$ states are the most sensitive detectors of such a rotation, yet they are also among the worst at fully characterizing an a priori unknown process. We identify (and confirm experimentally) the best $SU(2)$-covariant set for process tomography; these states are all less entangled than the $N00N$ state, and are characterized by the fact that they form a 2-design.

We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the $Z_2$ lattice gauge theory and the Rokhsar-Kivelson point of the $U(1)$ gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.

We report temperature-dependent measurements of longitudinal spin Seebeck effects (LSSEs) in $\mathrm{Pt}/{\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ $(\mathrm{YIG})/\mathrm{Pt}$ systems in a high temperature range from room temperature to above the Curie temperature of YIG. The experimental results show that the magnitude of the LSSE voltage in the $\mathrm{Pt}/\mathrm{YIG}/\mathrm{Pt}$ systems rapidly decreases with increasing the temperature and disappears above the Curie temperature. The critical exponent of the LSSE voltage in the $\mathrm{Pt}/\mathrm{YIG}/\mathrm{Pt}$ systems at the Curie temperature is estimated to be 3, which is much greater than that for the magnetization curve of YIG. This difference highlights the fact that the mechanism of the LSSE cannot be explained in terms of simple static magnetic properties in YIG.

Topological insulators (TIs) have attracted immense interest because they host helical surface states. Protected by time-reversal symmetry, they are robust to nonmagnetic disorder. When superconductivity is induced in these helical states, they are predicted to emulate $p$-wave pairing symmetry, with Majorana states bound to vortices. Majorana bound states possess non-Abelian exchange statistics that can be probed through interferometry. Here, we take a significant step towards Majorana interferometry by observing pronounced Fabry-Pérot oscillations in a TI sandwiched between a superconducting and a normal lead. For energies below the superconducting gap, we observe a doubling in the frequency of the oscillations, arising from an additional phase from Andreev reflection. When a magnetic field is applied perpendicular to the TI surface, a number of very sharp and gate-tunable conductance peaks appear at or near zero energy, which has consequences for interpreting spectroscopic probes of Majorana fermions. Our results demonstrate that TIs are a promising platform for exploring phase-coherent transport in a solid-state system.

Many-body localization, the persistence against electron-electron interactions of the localization of states with nonzero excitation energy density, poses a challenge to current methods of theoretical and numerical analyses. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed. The limitations of quantum measurement, which preclude the possibility of directly obtaining the entanglement entropy, make it difficult to apply some of the definitions of many-body localization used in the recent literature. We discuss alternative tests of localization that can be implemented on a quantum computer.

The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most common topological characteristic observed in many real networked systems. In this paper, we report an extensive numerical study on the effects of clustering on the structural properties of complex networks. Strong clustering in heterogeneous networks induces the emergence of a core-periphery organization that has a critical effect on the percolation properties of the networks. We observe a novel double phase transition with an intermediate phase in which only the core of the network is percolated and a final phase in which the periphery percolates regardless of the core. This result implies breaking of the same symmetry at two different values of the control parameter, in stark contrast to the modern theory of continuous phase transitions. Inspired by this core-periphery organization, we introduce a simple model that allows us to analytically prove that such an anomalous phase transition is, in fact, possible.

We perform systematic investigations of transport through graphene on hexagonal boron nitride (hBN) substrates, together with confocal Raman measurements and a targeted theoretical analysis, to identify the dominant source of disorder in this system. Low-temperature transport measurements on many devices reveal a clear correlation between the carrier mobility $\mu$ and the width $n^{*}$ of the resistance peak around charge neutrality, demonstrating that charge scattering and density inhomogeneities originate from the same microscopic mechanism. The study of weak localization unambiguously shows that this mechanism is associated with a long-ranged disorder potential and provides clear indications that random pseudomagnetic fields due to strain are the dominant scattering source. Spatially resolved Raman spectroscopy measurements confirm the role of local strain fluctuations, since the linewidth of the Raman 2D peak—containing information of local strain fluctuations present in graphene—correlates with the value of maximum observed mobility. The importance of strain is corroborated by a theoretical analysis of the relation between $\mu$ and $n^{*}$ that shows how local strain fluctuations reproduce the experimental data at a quantitative level, with $n^{*}$ being determined by the scalar deformation potential and $\mu$ by the random pseudomagnetic field (consistently with the conclusion drawn from the analysis of weak localization). Throughout our study, we compare the behavior of devices on hBN substrates to that of devices on ${\mathrm{SiO}}_2$ and ${\mathrm{SrTiO}}_3$, and find that all conclusions drawn for the case of hBN are compatible with the observations made on these other materials. These observations suggest that random strain fluctuations are the dominant source of disorder for high-quality graphene on many different substrates, and not only on hexagonal boron nitride.

Computing the equilibrium properties of complex systems, such as free energy differences, is often hampered by rare events in the dynamics. Enhanced sampling methods may be used in order to speed up sampling by, for example, using high temperatures, as in parallel tempering, or simulating with a biasing potential such as in the case of umbrella sampling. The equilibrium properties of the thermodynamic state of interest (e.g., lowest temperature or unbiased potential) can be computed using reweighting estimators such as the weighted histogram analysis method or the multistate Bennett acceptance ratio (MBAR). weighted histogram analysis method and MBAR produce unbiased estimates, the simulation samples from the global equilibria at their respective thermodynamic states—a requirement that can be prohibitively expensive for some simulations such as a large parallel tempering ensemble of an explicitly solvated biomolecule. Here, we introduce the transition-based reweighting analysis method (TRAM)—a class of estimators that exploit ideas from Markov modeling and only require the simulation data to be in local equilibrium within subsets of the configuration space. We formulate the expanded TRAM (xTRAM) estimator that is shown to be asymptotically unbiased and a generalization of MBAR. Using four exemplary systems of varying complexity, we demonstrate the improved convergence (ranging from a twofold improvement to several orders of magnitude) of xTRAM in comparison to a direct counting estimator and MBAR, with respect to the invested simulation effort. Lastly, we introduce a random-swapping simulation protocol that can be used with xTRAM, gaining orders-of-magnitude advantages over simulation protocols that require the constraint of sampling from a global equilibrium.

Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show that this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov optimal noise filter. Using concepts from umbral calculus, we generalize the linear Wiener-Kolmogorov theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function—such as ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways and the manipulation of pathways through experimental probes such as oscillatory input.

The nature of ordering in dilute dipolar interacting systems dates back to the work of Debye and is one of the most basic, oldest and as-of-yet unsettled problems in magnetism. While spin-glass order is readily observed in several RKKY-interacting systems, dipolar spin glasses are the subject of controversy and ongoing scrutiny, e.g., in ${\mathrm{LiHo}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$, a rare-earth randomly diluted uniaxial (Ising) dipolar system. In particular, it is unclear if the spin-glass phase in these paradigmatic materials persists in the limit of zero concentration or not. We study an effective model of ${\mathrm{LiHo}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$ using large-scale Monte Carlo simulations that combine parallel tempering with a special cluster algorithm tailored to overcome the numerical difficulties that occur at extreme dilutions. We find a paramagnetic to spin-glass phase transition for all ${\mathrm{Ho}}^{+}$ ion concentrations down to the smallest concentration numerically accessible, 0.1%, and including ${\mathrm{Ho}}^{+}$ ion concentrations that coincide with those studied experimentally up to 16.7%. Our results suggest that randomly diluted dipolar Ising systems have a spin-glass phase in the limit of vanishing dipole concentration, with a critical temperature vanishing linearly with concentration. The agreement of our results with mean-field theory testifies to the irrelevance of fluctuations in interactions strengths, albeit being strong at small concentrations, to the nature of the low-temperature phase and the functional form of the critical temperature of dilute anisotropic dipolar systems. Deviations from linearity in experimental results at the lowest concentrations are discussed.

The olfactory system of male moths is exquisitely sensitive to pheromones emitted by females and transported in the environment by atmospheric turbulence. Moths respond to minute amounts of pheromones, and their behavior is sensitive to the fine-scale structure of turbulent plumes where pheromone concentration is detectible. The signal of pheromone whiffs is qualitatively known to be intermittent, yet quantitative characterization of its statistical properties is lacking. This challenging fluid dynamics problem is also relevant for entomology, neurobiology, and the technological design of olfactory stimulators aimed at reproducing physiological odor signals in well-controlled laboratory conditions. Here, we develop a Lagrangian approach to the transport of pheromones by turbulent flows and exploit it to predict the statistics of odor detection during olfactory searches. The theory yields explicit probability distributions for the intensity and the duration of pheromone detections, as well as their spacing in time. Predictions are favorably tested by using numerical simulations, laboratory experiments, and field data for the atmospheric surface layer. The resulting signal of odor detections lends itself to implementation with state-of-the-art technologies and quantifies the amount and the type of information that male moths can exploit during olfactory searches.

We introduce a new “universality class” of artificial optical media—photonic hypercrystals. These hyperbolic metamaterials, with periodic spatial variation of dielectric permittivity on subwavelength scale, combine the features of optical metamaterials and photonic crystals. In particular, surface waves supported by a hypercrystal possess the properties of both the optical Tamm states in photonic crystals and surface-plasmon polaritons at the metal-dielectric interface.