Although charge density waves (CDWs) are omnipresent in cuprate high-temperature superconductors, they occur at significantly different wave vectors, confounding efforts to understand their formation mechanism. Here, we use resonant inelastic x-ray scattering to investigate the doping- and temperature-dependent CDW evolution in ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ ($x=0.115–0.155$). We discover that the CDW develops in two stages with decreasing temperature. A precursor CDW with a quasicommensurate wave vector emerges first at high temperature. This doping-independent precursor CDW correlation originates from the CDW phase mode coupled with a phonon and “seeds” the low-temperature CDW with a strongly doping-dependent wave vector. Our observation reveals the precursor CDW and its phase mode as the building blocks of the highly intertwined electronic ground state in the cuprates.

Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and optimizes them using gradient search. The concept emerges from deep learning but is not limited to training neural networks. We present the theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher-order derivatives of the program accurately and efficiently using automatic differentiation. We present essential techniques to differentiate through the tensor networks contraction algorithms, including numerical stable differentiation for tensor decompositions and efficient backpropagation through fixed-point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second-order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient-based variational optimization of infinite projected entangled pair states for the quantum antiferromagnetic Heisenberg model and obtain state-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications.

We present the results from three gravitational-wave searches for coalescing compact binaries with component masses above $1M_{\odot }$ during the first and second observing runs of the advanced gravitational-wave detector network. During the first observing run ($O1$), from September 12, 2015 to January 19, 2016, gravitational waves from three binary black hole mergers were detected. The second observing run ($O2$), which ran from November 30, 2016 to August 25, 2017, saw the first detection of gravitational waves from a binary neutron star inspiral, in addition to the observation of gravitational waves from a total of seven binary black hole mergers, four of which we report here for the first time: GW170729, GW170809, GW170818, and GW170823. For all significant gravitational-wave events, we provide estimates of the source properties. The detected binary black holes have total masses between ${18.6}_{-0.7}^{+3.2}{M}_{\odot }$ and ${84.4}_{-11.1}^{+15.8}{M}_{\odot }$ and range in distance between ${320}_{-110}^{+120}$ and ${2840}_{-1360}^{+1400}\mathrm{Mpc}$. No neutron star–black hole mergers were detected. In addition to highly significant gravitational-wave events, we also provide a list of marginal event candidates with an estimated false-alarm rate less than 1 per 30 days. From these results over the first two observing runs, which include approximately one gravitational-wave detection per 15 days of data searched, we infer merger rates at the 90% confidence intervals of $110-3840{\mathrm{Gpc}}^{-3}{\mathrm{y}}^{-1}$ for binary neutron stars and $9.7-101{\mathrm{Gpc}}^{-3}{\mathrm{y}}^{-1}$ for binary black holes assuming fixed population distributions and determine a neutron star–black hole merger rate 90% upper limit of $610{\mathrm{Gpc}}^{-3}{\mathrm{y}}^{-1}$.

We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric and objective, and the required data processing is parsimonious. The main ingredients include a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise “etalon” used to characterize arbitrary stationary stochastic processes. The method readily distinguishes both the Ornstein-Uhlenbeck process and chaos generated by the logistic map from white noise. Ranking within randomness differs fundamentally from that in deterministic chaos and signals, thus forming the basis for signal detection. To further illustrate the breadth of applications, we apply this ordinate method to the canonical nonlinear parameter estimation problem of two-species radioactive decay, outperforming special-purpose least squares software. We demonstrate that the method excels when extracting trends in heavy-tailed noise and, unlike the Thiele-Sen estimator, is not limited to linear regression. A simple expression is given that yields a close approximation for signal extraction of an underlying, generally nonlinear signal.

On-demand spin orientation with a long polarized lifetime and an easily detectable signal is the ultimate goal for spintronics. However, there still exists a trade-off between controllability and stability of spin polarization, awaiting a significant breakthrough. Here, we demonstrate switchable optomagnet effects in $({\mathrm{Fe}}_{1-x}{\mathrm{Zn}}_x{)}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$, from which we can obtain tunable magnetization (spanning from $-40\%$ to 40% of a saturated magnetization) that is created from zero magnetization in the antiferromagnetic state without magnetic fields. It is accomplishable by utilizing circularly polarized laser pulses to excite spin-flip transitions in polar antiferromagnets that have no spin canting, traditionally hard to control without very strong magnetic fields. The spin controllability in $({\mathrm{Fe}}_{1-x}{\mathrm{Zn}}_x{)}_2{\mathrm{Mo}}_3{\mathrm{O}}_8$ originates from its polar structure that breaks the crystal inversion symmetry, allowing distinct on-site $d\text{−}d$ transitions for selective spin flip. By chemical doping, we exploit the phase competition between antiferromagnetic and ferrimagnetic states to enhance and stabilize the optomagnet effects, which result in long-lived photoinduced Kerr rotations. The present study creating switchable giant optomagnet effects in polar antiferromagnets sketches a new blueprint for the function of antiferromagnetic spintronics.

The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize high-resolution observational and simulation data to investigate the nature of waves and structures emerging in a weakly collisional, turbulent kinetic plasma. Observational results are based on in situ solar wind measurements from the Cluster and Magnetospheric Multiscale (MMS) spacecraft, and the simulation results are obtained from an externally driven, three-dimensional fully kinetic simulation. Using a set of novel diagnostic measures, we show that both the large-amplitude structures and the lower-amplitude background fluctuations preserve linear features of kinetic Alfvén waves to order unity. This quantitative evidence suggests that the kinetic turbulence cannot be described as a mixture of mutually exclusive waves and structures but may instead be pictured as an ensemble of localized, anisotropic wave packets or “eddies” of varying amplitudes, which preserve certain linear wave properties during their nonlinear evolution.

Charge transport of topological semimetals is the focus of intensive investigations because of their nontrivial band topology. Heat transport of these materials, on the other hand, is largely unexplored and remains elusive. Here, we report on an observation of unprecedented, giant magnetic quantum oscillations of thermal conductivity in the prototypical Weyl semimetal TaAs. The oscillations are antiphase with the quantum oscillating electronic density of states of a Weyl pocket, and their amplitudes amount to 2 orders of magnitude of the estimation based on the Wiedemann-Franz law. Our analyses show that all the conventional heat-transport mechanisms through diffusions of propagating electrons, phonons, and electron-hole bipolar excitations are far inadequate to account for these phenomena. Taking further experimental facts that the parallel field configuration favors much-higher magnetothermal conductivity, we propose that the newly proposed chiral zero sound provides a reasonable explanation to these exotic phenomena. More work focusing on other topological semimetals along the same line is badly called for.

We present an effective field theory approach to the fracton phases. The approach is based on the notion of a multipole algebra. It is an extension of space(time) symmetries of a charge-conserving matter that includes global symmetries responsible for the conservation of various components of the multipole moments of the charge density. We explain how to construct field theories invariant under the action of the algebra. These field theories generally break rotational invariance and exhibit anisotropic scaling. We further explain how to partially gauge the multipole algebra. Such gauging makes the symmetries responsible for the conservation of multipole moments local, while keeping rotation and translations symmetries global. It is shown that upon such gauging one finds the symmetric tensor gauge theories, as well as the generalized gauge theories discussed recently in the literature. We refer to all such theories as multipole gauge theories. The outcome of the gauging procedure depends on the choice of the multipole algebra. In particular, we show how to construct an effective theory for the U(1) version of the Haah code based on the principles of symmetry and provide a two-dimensional example with operators supported on a Sierpinski triangle. We show that upon condensation of charged excitations, fracton phases of both types as well as various Symmetry-protected topological phases emerge. Finally, the relation between the present approach and the formalism based on polynomials over finite fields is discussed.

Preceded by the discovery of topological insulators, Dirac and Weyl semimetals have become a pivotal direction of research in contemporary condensed matter physics. While easily accessible from a theoretical viewpoint, these topological semimetals pose a serious challenge in terms of experimental synthesis and analysis to allow for their unambiguous identification. In this work, we report on detailed transport experiments on compressively strained HgTe. Because of the superior sample quality in comparison to other topological semimetallic materials, this enables us to resolve the interplay of topological surface states and semimetallic bulk states to an unprecedented degree of precision and complexity. As our gate design allows us to precisely tune the Fermi level at the Weyl and Dirac points, we identify a magnetotransport regime dominated by Weyl/Dirac bulk state conduction for small carrier densities and by topological surface state conduction for larger carrier densities. As such, similar to topological insulators, HgTe provides the archetypical reference for the experimental investigation of topological semimetals.

We present the first experimental demonstration of quantum enhanced detection at x-ray wavelengths. We show that x-ray pairs that are generated by spontaneous down-conversion can be used for the generation of heralded x-ray photons and directly measure the sub-Poissonian statistics of the single photons by using photon number resolving detectors. We utilize the properties of the strong time-energy correlations of the down-converted photons to demonstrate the ability to improve the visibility and the signal-to-noise ratio of an image with a small number of photons in an environment with a noise level that is higher than the signal by many orders of magnitude. A long-term goal of this work is to demonstrate x-ray photon entanglement. However, given the technical challenges, which are much greater than in the visible regime, we take a first step in demonstrating nonclassical (sub-Poisson) photon correlations. In our work, we demonstrate a new protocol for the measurement of quantum effects with x rays using advantages such as background-free measurements that the x-ray regime offers for experiments aiming at testing fundamental concepts in quantum optics.

Phase diagrams reflect the possible kinetic routes and guide various applications such as the designed assembly and synthesis of functional materials. Two-dimensional (2D) materials have been a focus of ongoing research due to their wide applications; therefore, researchers are highly motivated to discover the general principles that control the assembly of such materials. In this study, we map the 2D phase diagrams of short- and long-range attractive colloids at single-particle resolution by video microscopy. Phase boundaries, including (meta)critical or triple points and corresponding real-space configurations, are precisely specified. Profiles of 2D phase diagrams with attractive interactions resemble their 3D counterparts. For short-range systems, by measuring the deepest achievable supercooled states on the phase diagram, a “crater” structure surrounding the metastable fluid-fluid critical point indicates an enhanced nucleation rate within the crater and further suggests a local minimum of the free-energy barrier for crystallization in this area. During a dense fluid-mediated two-step crystallization process, we observe that multiple crystallites could form within a single dense fluid cluster, partly due to its highly amorphous shape. This highly amorphous shape is found for all observed well-developed dense fluid clusters. It is a supplement to the multistep nucleation process. For long-range systems, equilibrium vapor-liquid coexistence is observed, which paves the way for the exploration of critical behaviors. Rigidity percolation of crystallites, and bulk fluid-solid coexistence which provide clear evidence of a possible first-order transition for 2D melting, are observed for both systems. Our experiments reveal the general features of phase behaviors shared by 2D attractive systems including graphene, protein membranes, and adsorbed nanocrystals.

Since the early 1960s, alloys are commonly grouped into two classes that feature either bound states in the band gap (I) or additional, nondiscrete band states (II). Consequently, one can observe either excitons bound to isoelectronic impurities or the typical band edge emission of a semiconductor that shifts and broadens with rising isoelectronic doping concentration. Microscopic parameters for class I alloys can directly be extracted from photoluminescence (PL) spectra, whereas any conclusions drawn for class II alloys usually remain limited to macroscopic assertions. Nonetheless, we present a spectroscopic study on exciton localization in a mixed-crystal alloy (class II) that allows us to access microscopic alloy parameters. In order to illustrate our approach, we study bulk ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ epilayers at the onset of alloying ($0\le x\le 2.4\%$) in order to understand their robustness to point and structural defects. Through an in-depth PL analysis it is demonstrated how different excitonic complexes (free, bound, and complex bound excitons) can serve as a probe to monitor the dilute limit of class II alloys. From an $x$-dependent linewidth analysis we extract the length scales at which excitons become increasingly localized, i.e., their conversion from a free to a bound particle upon alloy formation. Already at $x=2.4\%$ the exciton diffusion length is reduced to $5.7\pm 1.3\mathrm{nm}$ at a temperature of 12 K; hence, detrimental exciton transfer mechanisms toward nonradiative defects are suppressed. In addition, the associated low-temperature PL data suggest that a single indium atom cannot permanently capture an exciton. The low density of silicon impurities in our samples even allows studying their local indium-enriched environment at the scale of the exciton Bohr radius based on impurity bound excitons. The associated temperature-dependent PL data reveal an alloying dependence for the exciton-phonon coupling. Thus, the formation of the random alloy can not only be monitored by the emission of various excitonic complexes, but also more indirectly via the associated coupling(s) to the phonon bath. Micro-PL spectra even give access to a probing of silicon bound excitons embedded in a particular environment of indium atoms thanks to the emergence of a series of individual and energetically sharp emission lines (full width at half maximum $\approx 300\mu \mathrm{eV}$). Consequently, the present study allows us to extract microscopic properties formerly mostly only accessible for class I alloys.

We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the notion of entropy production in thermodynamics is extended to the quantum regime. Our result shows that the fluctuation theorems, which are normally considered for thermodynamic processes, can be a powerful tool to study the detailed statistics of quantum systems as well as the effect of coherence transfer in an arbitrary nonequilibrium quantum process. We introduce a complex-valued entropy production to fully understand the relation between the forward and backward processes through the quantum channel. We find the physical meaning of the imaginary part of entropy production to witness the broken symmetry of the quantum channel. We also show that the imaginary part plays a crucial role in deriving the second law from the quantum fluctuation theorem. The dissipation and fluctuation of various quantum resources including quantum free energy, asymmetry, and entanglement can be coherently understood in our unified framework. Our fluctuation theorem can be applied to a wide range of physical systems and dynamics to query the reversibility of a quantum state for the given quantum processing channel involving coherence and entanglement.

The joint detection of the gravitational wave (GW) GW170817 and its electromagnetic (EM) counterparts GRB170817A and kilonova AT 2017gfo has triggered extensive study of the EM emission of binary neutron star mergers. A parameter which is common to and plays a key role in both the GW and the EM analyses is the viewing angle of the binary’s orbit. If a binary is viewed from different angles, the amount of GW energy changes (implying that orientation and distance are correlated) and the EM signatures can vary, depending on the structure of the emission. Information about the viewing angle of the binary orbital plane is therefore crucial to the interpretation of both the GW and the EM data and can potentially be extracted from either side. In the first part of this study, we present a systematic analysis of how well the viewing angle of binary neutron stars can be measured from the GW data. We show that if the sky position and the redshift of the binary can be identified via the EM counterpart and an associated host galaxy, then for 50% of the systems the viewing angle can be constrained to $\le 7°$ uncertainty from the GW data, independent of electromagnetic emission models. On the other hand, if no redshift measurement is available, the measurement of the viewing angle with GWs alone is not informative, unless the true viewing angle is close to 90°. This holds true even if the sky position is measured independently. Then, we consider the case where some constraints on the viewing angle can be placed from the EM data themselves. We show that the EM measurements can then be used in the analysis of GW data to improve the precision of the luminosity distance, and hence of the Hubble constant, by a factor of 2–3.

Hysteresis is a major feature of the solid-liquid transition in granular materials. This property, by allowing metastable states, can potentially yield catastrophic phenomena such as earthquakes or aerial landslides. The origin of hysteresis in granular flows is still debated. However, most mechanisms put forward so far rely on the presence of inertia at the particle level. In this paper, we study the avalanche dynamics of non-Brownian suspensions in slowly rotating drums and reveal large hysteresis of the avalanche angle even in the absence of inertia. By using microsilica particles whose interparticle friction coefficient can be turned off, we show that microscopic friction, conversely to inertia, is key to triggering hysteresis in granular suspensions. To understand this link between friction and hysteresis, we use the rotating drum as a rheometer to extract the suspension rheology close to the flow onset for both frictional and frictionless suspensions. This analysis shows that the flow rule for frictionless particles is monotonous and follows a power law of exponent $\alpha =0.37\pm 0.05$, in close agreement with the previous theoretical prediction, $\alpha =0.35$. By contrast, the flow rule for frictional particles suggests a velocity-weakening behavior, thereby explaining the flow instability and the emergence of hysteresis. These findings show that hysteresis can also occur in particulate media without inertia, questioning the intimate nature of this phenomenon. By highlighting the role of microscopic friction, our results may be of interest in the geophysical context to understand the failure mechanism at the origin of undersea landslides.

Understanding the nature of the excitation spectrum in quantum spin liquids is of fundamental importance, in particular for the experimental detection of candidate materials. However, current theoretical and numerical techniques have limited capabilities, especially in obtaining the dynamical structure factor, which gives a crucial characterization of the ultimate nature of the quantum state and may be directly assessed by inelastic neutron scattering. In this work, we investigate the low-energy properties of the $S=1/2$ Heisenberg model on the triangular lattice, including both nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ superexchanges, by a dynamical variational Monte Carlo approach that allows accurate results on spin models. For $J_2=0$, our calculations are compatible with the existence of a well-defined magnon in the whole Brillouin zone, with gapless excitations at $K$ points (i.e., at the corners of the Brillouin zone). The strong renormalization of the magnon branch (also including rotonlike minima around the $M$ points, i.e., midpoints of the border zone) is described by our Gutzwiller-projected state, where Abrikosov fermions are subject to a nontrivial magnetic $\pi$ flux threading half of the triangular plaquettes. When increasing the frustrating ratio $J_2/J_1$, we detect a progressive softening of the magnon branch at $M$, which eventually becomes gapless within the spin-liquid phase. This feature is captured by the band structure of the unprojected wave function (with two Dirac points for each spin component). In addition, we observe an intense signal at low energies around the $K$ points, which cannot be understood within the unprojected picture and emerges only when the Gutzwiller projection is considered, suggesting the relevance of gauge fields for the low-energy physics of spin liquids.

We study a tight-binding model on the honeycomb lattice of chiral $d$-wave superconductivity that breaks time-reversal symmetry. Because of its nontrivial sublattice structure, we show that it is possible to construct a gauge-invariant time-reversal-odd bilinear of the pairing potential. The existence of this bilinear reflects the sublattice polarization of the pairing state. We show that it generates persistent loop current correlations around each lattice site and opens a topological mass gap at the Dirac points, resembling Haldane’s model of the anomalous quantum Hall effect. In addition to the usual chiral $d$-wave edge states, there also exist electronlike edge resonances due to the topological mass gap. We show that the presence of loop-current correlations directly leads to a nonzero intrinsic ac Hall conductivity, which produces the polar Kerr effect without an external magnetic field. Similar results also hold for the nearest-neighbor chiral $p$-wave pairing. We briefly discuss the relevance of our results to superconductivity in twisted bilayer graphene.

Mutualistic interactions, those that are naturally beneficial for both interacting species, are recurrently found in ecosystems. Observations of natural systems show that if we draw mutualistic relationships as links between species, the resulting mutualistic network of interactions displays a widespread particular ordering called nestedness. In such an ordering, the mutualistic partners of a given species conform a subset of the partners of all species with larger degree, that is, of those species having more interactions. On the other hand, theoretical works show that a nested structure has a positive impact on a number of relevant features of mutualistic communities ranging from species coexistence to structural stability and biodiversity. However, how nestedness emerges and what are its determinants, are still open challenges that have led to multiple debates to date. Here we show, by applying a theoretical approach to the analysis of 167 real mutualistic networks, that nestedness is not an irreducibly macroscopic feature but an entropic consequence of the degree sequences (number of mutualistic interactions of each species). Remarkably, we find that an outstanding majority of the analyzed networks does not show statistically significant nestedness. These findings point to the need of revising previous claims about the role of nestedness and might contribute to expand our understanding of how evolution shapes mutualistic interactions and communities by placing the focus on the node-dependent properties rather than on global quantities.

Kerr microresonators generate interesting and useful fundamental states of electromagnetic radiation through nonlinear interactions of continuous-wave (CW) laser light. With photonic-integration techniques, functional devices with low noise, small size, low-power consumption, scalable fabrication, and heterogeneous combinations of photonics and electronics can be realized. Kerr solitons, which stably circulate in a Kerr microresonator, have emerged as a source of coherent, ultrafast pulse trains and ultra-broadband optical-frequency combs. Using the $f\text{−}2f$ technique, Kerr combs can support carrier-envelope-offset phase stabilization to enable optical synthesis and metrology. Here, we introduce a Kerr-microresonator optical clockwork, which is a foundational device that distributes optical-clock signals to the mode-difference frequency of a comb. Our clockwork is based on a silicon-nitride (${\mathrm{Si}}_3{\mathrm{N}}_4$) microresonator that generates a Kerr-soliton frequency comb with a repetition frequency of 1 THz. We measure our terahertz clockwork by electro-optic modulation with a microwave signal, enabling optical-based timing experiments in this wideband and high-speed frequency range. Moreover, by EO phase modulation of our entire Kerr-soliton comb, we arbitrarily generate additional CW modes between the 1-THz modes to reduce the repetition frequency and increase the resolution of the comb. Our experiments characterize the absolute frequency noise of this Kerr-microresonator clockwork to one part in $10^{17}$, which is the highest accuracy and precision ever reported with this technology and opens the possibility of measuring high-performance optical clocks with Kerr combs.

Photon-mediated coupling between distant matter qubits may enable secure communication over long distances, the implementation of distributed quantum computing schemes, and the exploration of new regimes of many-body quantum dynamics. Solid-state quantum emitters coupled to nanophotonic devices represent a promising approach towards these goals, as they combine strong light-matter interaction and high photon collection efficiencies. However, nanostructured environments introduce mismatch and diffusion in optical transition frequencies of emitters, making reliable photon-mediated entanglement generation infeasible. Here we address this long-standing challenge by employing silicon-vacancy color centers embedded in electromechanically deflectable nanophotonic waveguides. This electromechanical strain control enables control and stabilization of optical resonance between two silicon-vacancy centers on the hour timescale. Using this platform, we observe the signature of an entangled, superradiant state arising from quantum interference between two spatially separated emitters in a waveguide. This demonstration and the developed platform constitute a crucial step towards a scalable quantum network with solid-state quantum emitters.