On February 13th, 2023, the KM3NeT/ARCA telescope detected a neutrino candidate with an estimated energy in the hundreds of PeV. In this article, the observation of this ultrahigh-energy neutrino is discussed in light of null observations above tens of PeV from the IceCube and Pierre Auger observatories. Performing a joint fit of all experiments under the assumption of an isotropic $E^{-2}$ flux, the best-fit single-flavor flux normalization is $E^2{\mathrm{\Phi }}_{\nu +\overline{\nu }}^{1\mathrm{f}}=7.5\times {10}^{-10}\mathrm{GeV}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$ in the 90% energy range of the KM3NeT event. Furthermore, the ultrahigh-energy data are then fit together with the IceCube measurements at lower energies, either with a single power law or with a broken power law, allowing for the presence of a new component in the spectrum. A slight preference for a break in the PeV regime is found for one of the three investigated IceCube samples and no such preference for the other two. In all cases, the observed tension between KM3NeT and other datasets is mild to moderate ($1.6\sigma –2.9\sigma$), and increased statistics are required to resolve this apparent tension and better characterize the neutrino landscape at ultrahigh energies.

The nitrogen-vacancy (NV) center in diamond is a solid-state spin defect that has been widely adopted for quantum sensing and quantum information processing applications. Typically, experiments are performed either with a single isolated NV center or with an unresolved ensemble of many NV centers, resulting in a trade-off between measurement speed and spatial resolution or control over individual defects. In this work, we introduce an experimental platform that bypasses this trade-off by addressing multiple optically resolved NV centers in parallel. We perform charge- and spin-state manipulations selectively on multiple NV centers from within a larger set, and we manipulate and measure the electronic spin states of over 100 NV centers in parallel. We show that the high signal-to-noise ratio of the measurements enables the detection of shot-to-shot pairwise correlations between the spin states of 108 NV centers, corresponding to the simultaneous measurement of 5778 unique correlation coefficients. We discuss how our platform can be scaled to parallel experiments with thousands of individually resolved NV centers. These results enable parallelized high-throughput sensing experiments that retain the spatial resolution of single defects and will, thereby, help to unlock advances in applications such as single-molecule NMR and characterization of integrated circuits. In addition, our approach to multiplexing provides a natural platform for the application of recently developed correlated sensing techniques.

Single nitrogen vacancy (NV) centers in diamond have been used extensively for high-sensitivity nanoscale sensing, but conventional approaches use confocal microscopy to measure individual centers sequentially, limiting throughput and access to nonlocal physical properties, where simultaneous, high-fidelity measurement of multiple centers is required. Here, we design and implement a multiplexed NV sensing platform that allows us to read out many single NV centers simultaneously using a low-noise camera. Using this platform, we coherently manipulate and read out the spin states of hundreds of individual NV centers in parallel, achieving comparable magnetic field sensitivity to confocal measurements. We also implement a parallelized version of spin-to-charge-conversion readout for low NV center spin state readout noise and use it to demonstrate multiplexed covariance magnetometry, in which we measure ten two-point magnetic field correlators from five NV centers simultaneously. From these measurements, we demonstrate the quantitative reconstruction of spatially varying magnetic correlations arising from a current-carrying wire. The number of correlators we can measure is limited only by the available laser power, opening the door to massively multiplexed covariance magnetometry. In contrast to scanning probes for imaging spatially varying magnetic fields, our approach measures the temporal dynamics of the magnetic field at many precisely defined positions simultaneously, from which the local noise spectrum and nonlocal properties such as correlation functions can be computed. This high-fidelity readout platform will find immediate applications in studying condensed matter phenomena that are characterized by the noise spectrum or correlation functions, including quantum phase transitions, dynamics far from equilibrium, magnetic order, and correlated electron phenomena.

Network backbones provide useful sparse representations of weighted networks by keeping only their most important links, permitting a range of computational speedups and simplifying network visualizations. A key limitation of existing network backboning methods is that they either require the specification of a free parameter (e.g., significance level) that determines the number of edges to keep in the backbone or impose specific restrictions on the topology of the backbone (e.g., that it is a spanning tree). Here we develop a completely nonparametric framework for inferring the backbone of a weighted network that overcomes these limitations and automatically selects the optimal set of edges to retain using the minimum description length principle. We develop objective functions for global and local network backboning which evaluate the importance of an edge in the context of the whole network and individual node neighborhoods, respectively, and are generalizable to any weight distribution under Bayesian model specifications that fix the average edge weight either exactly or in expectation. We then construct an efficient and provably optimal greedy algorithm to identify the backbone minimizing our objectives, whose run-time complexity is log-linear in the number of edges. We demonstrate our methods by comparing them with existing methods in a range of tasks on real and synthetic networks, finding that both the global and local backboning methods can preserve network connectivity, weight heterogeneity, and spreading dynamics while removing a substantial fraction of edges.

Orbital selectivity is pivotal in dictating the phase diagrams of multiorbital systems, with prominent examples including the orbital-selective Mott phase and superconductivity. The intercalation of anisotropic layers represents an effective method for enhancing orbital selectivity and thereby shaping the low-energy physics of multiorbital systems. Despite its potential, related experimental studies, especially those elucidating the correlation between orbital selectivity and magnetism, remain limited. In this work, we systematically examine the interplay between orbital selectivity and magnetism in the newly discovered anisotropic kagome ${\mathrm{TbTi}}_3{\mathrm{Bi}}_4$ single crystal, and report the coexistence of orbital-selective dual-band modulations ($q_1\sim 1/3a^{*}$, $q_2\sim 0.28b^{*}$) within the antiferromagnetic (AFM) state. By combining soft x-ray and vacuum ultraviolet angle-resolved photoemission spectroscopy measurements, neutron powder diffraction, scanning tunneling microscopy, and density-functional-theory calculations, we identify these dual-band reconstructions as manifestations of the AFM order driven by a (approximately $1/3$, 0.28, 0) nesting instability of the intercalated Tb $5d_{xz}$ orbitals. These orbital-selective modulations induce unusual momentum-dependent band folding and lead to the emergence of Dirac cones only at the ${\overline{M}}_1$ point, signaling a topological phase transition in the AFM state. Importantly, the discovery of orbital-selective (approximately $1/3$, 0.28, 0) AFM order offers crucial insights into the mechanism underlying the fractional magnetization plateau in this kagome AFM metal. Our findings not only underscore the essential role of both conducting and localized electrons in determining the magnetic orders of $\mathrm{Ln}{\mathrm{Ti}}_3{\mathrm{Bi}}_4$ ($\mathrm{Ln}=\mathrm{lanthanide}$) kagome metals but also offer a pathway for manipulating magnetism through selective control of anisotropic electronic structures.

We consider theories of gauged quark flavor and identify noninvertible Peccei-Quinn symmetries arising from fractional instantons when the resulting gauge group has nontrivial global structure. Such symmetries exist solely because the standard model has the same number of generations as colors, $N_g=N_c$, which leads to a massless down-type quark solution to the strong $CP$ problem in an ultraviolet $SU(9)$ theory of quark color-flavor unification. We show how the Cabibbo-Kobayashi-Maskawa flavor structure and weak $CP$ violation can be generated without upsetting our solution.

We study the emergence of strong interactions between dissipative coherent structures (pulses) in spatially extended systems. Focusing first on a prototypical model problem from fluid dynamics, that of liquid film flowing down a vertical plane, we show that under certain conditions, a two-pulse system undergoes a transition from a regime of decaying oscillatory dynamics to one with self-sustained oscillations. Intriguingly, such a transition is not governed by the standard Hopf bifurcation. Instead, a novel governing mechanism for transition to oscillatory dynamics is unraveled via a peculiar and atypical Hopf bifurcation in which a complex-conjugate resonance pair crosses the imaginary axis in the complex plane. Prior to crossing the essential spectrum (including at the bifurcation point), this resonance pair does not appear in the standard $L_{\mathbb{C}}^2$-based spectral analysis but reveals itself when appropriate weighted functional spaces are used. We show that such a resonance pair originates from the splitting of a resonance pole of the single-pulse system. While this object is not part of the classical spectrum, it plays a vital role in shaping the system’s dynamics. We further demonstrate that this resonance-pole mechanism extends to a broad range of systems. Specifically, in the generalised Kuramoto-Sivashinsky equation—a model prototype applicable across a wide range of fields from fluid dynamics to geophysics and plasma physics—we observe the same bifurcation and resulting oscillatory pulse interactions. By contrast, in the FitzHugh-Nagumo model—a central model prototype in reaction-diffusion systems—the resonance pole splits into real eigenvalues, and monotonic pulse interactions occur. In addition, we illustrate that the resonance pole may induce oscillatory interactions in three-pulse systems and eventually lead to chaotic dynamics in strongly interacting multipulse systems, which can be quantified in terms of a positive Lyapunov exponent.

Over the past decade, neutrino astronomy has emerged as a new window into the extreme and hidden Universe. Current-generation experiments have detected high-energy neutrinos of astrophysical origin and identified the first sources, opening the field to discovery. Looking ahead, in this Perspective we identify seven major open questions in neutrino astrophysics and particle physics that could lead to transformative discoveries over the next 20 years. These multidisciplinary questions range from understanding the vicinity of a black hole to unveiling the nature of neutrino mass, among other topics. Additionally, we critically review the current experimental capabilities and their limitations and, from there, discuss the interplay between different proposed neutrino telescope technologies and analysis techniques. We firmly believe that achieving the immense discovery potential over the next two decades demands a model of global partnership and specialized, complementary detectors. This collaborative neutrino telescope network will pave the way for a thriving multimessenger era, transforming our understanding of neutrino physics, astrophysics, and the extreme Universe.

Science is founded on the benchmarking of theoretical models against experimental measurements, with the challenge that, for all but the simplest systems, the calculations required for high precision become extremely challenging. ${\mathrm{H}}_2^{+}$ is the simplest stable molecule, and its structure is calculable to high precision. However, studying ${\mathrm{H}}_2^{+}$ experimentally presents significant challenges: Standard control methods such as laser cooling are not applicable due to the long lifetimes of its rotational and vibrational states. Here, we solve this issue by combining buffer gas cooling to quench the ${\mathrm{H}}_2^{+}$ rovibrational excitation with quantum logic operations between ${\mathrm{H}}_2^{+}$ and a cotrapped “helper” ion to control the molecule’s hyperfine structure. This enables us to perform pure quantum state preparation, coherent control, and nondestructive readout, which we use to demonstrate high-resolution microwave spectroscopy in the hyperfine structure of ${\mathrm{H}}_2^{+}$ with a precision of 2 Hz. Our results pave the way for high-precision spectroscopy of ${\mathrm{H}}_2^{+}$ in both the microwave and optical domains. Because of the wide applicability of buffer gas cooling, our method provides a general tool for molecular ion species that are hard to control with quantum logic tools alone.

Many hot, diffuse astrophysical plasmas are collisionless, with collision times that exceed dynamical timescales of interest. Without a standard viscosity, the mechanisms by which mechanical energy dissipates into heat via a turbulent cascade are complex and nonuniversal, with important consequences for the partition of heat between different species and directions. Recent theory has argued that in some parameter regimes a barrier to the turbulent cascade of energy forms at small scales, profoundly altering the nature of the heating of the plasma by changing how fluctuations dissipate. The solar wind is an environment, when in this parameter regime, where such a barrier would be expected to form. Here, using data from NASA’s Parker Solar Probe, we find that the shape of the magnetic energy spectrum around ion scales varies with solar wind parameters in a manner consistent with the presence of the barrier. This allows us to identify critical values of parameters necessary for the barrier to form; we show that the barrier appears fully developed for ion plasma beta of below $\simeq 0.5$ and becomes increasingly prominent with increasing normalized cross helicity (the difference in energy in wave packets propagating parallel and antiparallel to the background magnetic field) for values greater than $\simeq 0.4$. As these conditions are frequently met in the solar wind, particularly close to the Sun, our results suggest that the barrier is likely playing a significant role in turbulent dissipation in the solar wind and so is an important mechanism in explaining its heating and acceleration.

The recently introduced “fuzzy-sphere” method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the noncommutative geometry of the lowest Landau level filled by electrons, such that the charge is trivially gapped due to the Pauli exclusion principle at filling factor $\nu =1$, while the electron spins encode the desired CFT. Successful applications of the fuzzy sphere to paradigmatic CFTs, such as the 3D Ising model, raise an important question: How finely tuned does the underlying electron system need to be? Here, we show that the 3D Ising CFT can also be realized at fractional electron fillings. In such cases, the CFT spectrum is intertwined with the charge-neutral spectrum of the underlying fractional quantum Hall state—a feature that is trivially absent in the previously studied $\nu =1$ case. Remarkably, we show that the mixing between the CFT spectrum and the fractional quantum Hall spectrum is strongly suppressed within the numerically accessible system sizes. Moreover, we demonstrate that the CFT critical point is unaffected by the exchange statistics of the particles and by the nature of topological order in the charge sector. Our results set the stage for the fuzzy-sphere exploration of conformal critical points between topologically ordered states.

The traditional view of the anomalous Hall effect (AHE) in ferromagnets is that it arises from the magnetization perpendicular to the measurement plane and that there is a linear dependence on the latter. Underlying such a view is the thinking that the AHE is a time-reversal symmetry breaking phenomenon and can therefore be treated in terms of a power series in the magnetic order. However, this view is squarely challenged by a number of recent experiments, urging for a thorough theoretical investigation on the fundamental level. We find that for strong magnets, it is more appropriate and fruitful to regard the AHE as a spin-group symmetry breaking phenomenon where the critical parameter is the spin-orbit interaction strength, which involves a much smaller energy scale. In collinear ferromagnets, the spin-orbit coupling breaks the $\infty 2^{\prime }$ spin rotation symmetry, and the key to characterizing such symmetry breaking is the identification of spin-orbit vectors which transform regularly under spin-group operations. Born out of our framework is a rich multipolar relationship between the anomalous Hall conductivity and the magnetization direction, with each pole being expanded progressively in powers of the spin-orbit coupling strength. For the leading order contribution, i.e., the dipole, its isotropic part corresponds to the traditional view, and its anisotropic part can lead to the in-plane AHE where the magnetization lies within the measurement plane. Beyond the dipolar structure, the octupolar structure offers the leading order source of nonlinearity and hence introduces unique anisotropy where the dipolar structure cannot. Our theory thus offers a unified explanation for the in-plane AHE recently observed in various ferromagnets, and further extends the candidate material systems. It can also be generalized to study the anomalous Hall effect in crystals with any periodic spin structure and to study the nonlinear Hall effect and the spin Hall effect. Our theory lays the ground for decoding the coupling between various transport and optical phenomena and the magnetic orders.

Spin-forbidden ($\mathrm{\Delta }S\ne 0$) multiplet excitations and their coupling to magnetic properties are of increasing importance for magneto-optical studies of correlated materials. Nonetheless, the mechanisms for optically brightening these transitions and their generality remain poorly understood. Here, we report magnetic circular dichroism (MCD) spectroscopy on the van der Waals ferromagnet (FM) ${\mathrm{CrI}}_3$. Previously unreported spin-forbidden ($\mathrm{\Delta }S=1$) ${{}^{4}A}_{2\mathrm{g}}\to {{}^{2}E}_{\mathrm{g}}/{{}^{2}T}_{1\mathrm{g}}$ ${\mathrm{Cr}}^{3+}$ $dd$ excitations are observed near the ligand-to-metal charge-transfer excitation threshold. The assignment of these excitations and their ${\mathrm{Cr}}^{3+}$ multiplet character is established through complementary Cr $L_3$-edge resonant inelastic x-ray scattering measurements along with charge-transfer multiplet calculations and chemical trends in the chromium trihalide series ($\mathrm{Cr}{X}_3$, $X=$ Cl, Br, I). We utilize the high sensitivity of MCD spectroscopy to study the thickness-dependent optical response. The spin-forbidden excitations remain robust down to the monolayer limit, and we observe a significant magnetic-field dependence of the MCD spectrum across the antiferromagnetic-to-FM transition in few-layer samples. We preliminarily attribute this behavior to changes in the metal-ligand covalency with magnetic state. Our results clarify the magneto-optical response of ${\mathrm{CrI}}_3$ and identify covalency as a central mechanism for the brightening and field tunability of spin-forbidden multiplet excitations.

We report charge pickup reaction cross sections for 24 $p$-shell isotopes, including ${}^{8,9}\mathrm{Li}$, ${}^{10-12}\mathrm{Be}$, ${}^{10,13-15}\mathrm{B}$, ${}^{12,14-19}\mathrm{C}$, and ${}^{14,15,17-22}\mathrm{N}$, measured at relativistic energies (approximately $900A\mathrm{MeV}$) on both hydrogen and carbon targets. For the first time, we reveal a universal rapid increase in the charge pickup cross sections of unstable projectiles with isospin asymmetry along several isotopic chains. The cross sections can be decoupled into distinct contributions from the mass number and isospin asymmetry of the projectile, highlighting the critical role of the latter, and can be formulated empirically.

The effect of decoherence on topological order (TO) has been most deeply understood for the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer. We consider both wave-function deformations and quantum channels acting on $D_4$ TO, which has recently been realized on a quantum processor. By identifying the corresponding local statistical mechanical spin or rotor model with $D_4$ symmetry, we find a remarkable stability against proliferating non-Abelian anyons. This is shown by leveraging a reformulation in terms of the tractable O(2) loop model in the pure state case and $n$ coupled O(2) loop models for Rényi-$n$ quantities in the decoherence case—corresponding to worldlines of the proliferating anyon with quantum dimension 2. In particular, we find that the purity ($n=2$) remains deep in the $D_4$ TO for any decoherence strength, while the $n\to \infty$ limit becomes critical upon maximally decohering a particular anyon type, similar to our wave-function deformation result. The information-theoretic threshold ($n\to 1$) appears to be controlled by a disordered version of these statistical mechanical models, akin to the toric code case although significantly more robust. We furthermore use Monte Carlo simulations to explore the phase diagrams when multiple anyon types proliferate at the same time, leading to a continued stability of the $D_4$ TO in addition to critical phases with emergent U(1) symmetry. Instead of loop models, these are now described by net models corresponding to different anyon types coupled together according to fusion rules. This opens up the exploration of statistical mechanical models for decohered non-Abelian TO, which can inform optimal decoders and which in an ungauged formulation provides examples of non-Abelian strong-to-weak symmetry breaking.

Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest. Recently, a strong notion of quantum ergodicity has been proposed, namely, that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity. Here, we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment. For a closed system, where the environment is a complementary subsystem, we predict and observe a smooth quantum-to-classical transition in that observables progress from large, quantum fluctuations to small, Gaussian fluctuations as the bath size grows. This transition exhibits universal properties on a quantitative level among a wide range of systems, including those at finite temperature, those with itinerant particles, and random circuits. For an open system, where the environment is uncontrolled, we predict the statistics of observables under largely arbitrary noise channels including those with correlated errors, allowing us to discriminate between candidate error models both for continuous Hamiltonian time evolution and for digital random circuits. This allows for computationally efficient experimental noise learning and, more broadly, is a new avenue for quantitatively classifying the behavior of noisy quantum systems. Ultimately, our results clarify the role of ergodicity in quantum dynamics, with fundamental and practical consequences.

The topological understanding of nematic liquid crystals has traditionally centered on defects and their classification via homotopy invariants. Here, we draw upon several aspects of Morse theory to describe a finer approach to topology that characterizes the isotopy invariants within a given homotopy class. This approach unifies various disparate ideas in liquid crystal physics, including the homotopy and Volterra classifications of defects, the winding and self-linking of disclinations, and the Pontryagin-Thom construction. Specifically, we use singularity theory and dividing curves to characterize nematic textures via tomography, as well as to provide a full topological classification of the rewiring and crossing of disclination lines. This process reveals the central role that nonsingular but nontrivial topological solitons—so-called merons—play in mediating interactions between disclination lines. We also clarify the notion of the charge of a disclination line, give a simple method for computing it, and apply this to examples drawn from experiment. In particular, this method shows that restricting a disclination line’s charge modulo 2 is incorrect; we construct examples of disclinations with point defect charges 0 and $-2$, which have the same local structure but very different global structures, underscoring the need for a more nuanced topological understanding of nematic systems.

The quantum mechanics of three interacting particles gives rise to fundamental and universal phenomena, such as the staircase of Efimov trimers predicted in the context of nuclear physics and observed in ultracold gases. Here, we observe a novel type of halo trimer using radio-frequency spectroscopy in an ultracold mixture of ${}^{23}\mathrm{Na}$ and ${}^{40}\mathrm{K}$ atoms. The trimers consist of two light bosons and one heavy fermion, and they have the structure of a Feshbach dimer weakly bound to one additional boson. We find that the trimer peak closely follows the dimer resonance over the entire range of explored interaction strengths and across an order-of-magnitude variation of the dimer energy, as reproduced by our theoretical analysis. The presence of this halo trimer is of direct relevance for many-body physics in ultracold mixtures and the association of ultracold molecules.

Allostery, the phenomenon by which the perturbation of a molecule at one site alters its behavior at a remote functional site, enables control over biomolecular function. Allosteric modulation is a promising avenue for drug discovery and is employed in the design of mechanical metamaterials. However, a general principle of allostery, i.e., a set of quantitative and transferable “ground rules,” remains elusive. It is neither a set of structural motifs nor intrinsic motions. Focusing on elastic network models, we here show that an allosteric lever—a mode-coupling pattern induced by the perturbation—governs the directional, source-to-target, allosteric communication: A structural perturbation of an allosteric site couples the excitation of localized hard elastic modes with concerted long-range soft-mode relaxation. Perturbations of nonallosteric sites instead couple hard and soft modes uniformly. The allosteric response is shown to be generally nonlinear and nonreciprocal, and allows for minimal structural distortions to be efficiently transmitted to specific changes at distant sites. Allosteric levers exist in proteins and “pseudoproteins”—networks designed to display an allosteric response. Interestingly, protein sequences that constitute allosteric transmission channels are shown to be evolutionarily conserved. To illustrate how the results may be applied in drug design, we use them to successfully predict known allosteric sites in proteins.

Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems [1]. However, existing control and measurement schemes for qudit systems scale unfavorably with qudit dimension since they decompose $SU(d)$ operations into series of qubitlike rotations and perform measurements on a small number of states [2–6]. Here, we address these challenges by employing simultaneous multifrequency drives to generate rotations and projections in an effective spin-$7/2$ system mapped onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the eight states using a multitone dispersive readout ($F_{\text{assignment}}=88.3\%$) and exploit the strong nonlinearity in a high-$E_J/E_C$ transmon to simultaneously address each transition and realize a spin displacement operator. Combining this displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in $\mathcal{O}(d)$ physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size $j=1$ to $j=7/2$. We demonstrate the potential of our control scheme in three ways: the direct measurement of the spin qudit Wigner function, randomized benchmarking of a logical qubit encoded into the qudit state, and randomized benchmarking of the full qudit Clifford group. In the latter experiment, we implement the $d$-dimensional quantum Fourier transform with an average gate fidelity of 0.91(6) in $d=8$. Our multifrequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multilevel system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.