We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Using techniques from stochastic thermodynamics, we derive the speed-accuracy relations for diffusion models, which are inequalities that relate the accuracy of data generation to the entropy production rate. These relations can be interpreted as the relations between accuracy and the speed of the diffusion dynamics in the absence of the nonconservative force. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the geodesic of space of the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy relations for diffusion models with different noise schedules and different data. We numerically discuss our results for optimal and suboptimal learning protocols. We also demonstrate the applicability of our results to data generation from the real-world image datasets.

Polarons are quasiparticles that arise from the interaction of electrons or holes with lattice vibrations. Though polarons are well studied across multiple disciplines, experimental observations of polarons in two-dimensional crystals are sparse. We use scanning tunneling microscopy and spectroscopy to measure inelastic excitations of polaronic bound states emerging from coupling of nonpolar zone-boundary phonons to Bloch electrons in $n$-doped metallic single-layer ${\mathrm{MoS}}_2$. The latter is kept chemically pristine via contactless chemical doping. Tunneling into the vibrationally coupled polaronic states leads to a series of evenly spaced peaks in the differential conductance on either side of the Fermi level. Combining density functional (perturbation) theory with a recently developed ab initio electron-lattice downfolding technique, we show that the energy spacing stems from the longitudinal-acoustic phonon mode that flattens at the Brillouin zone edge and is responsible for the formation of stable multipolarons in metallic ${\mathrm{MoS}}_2$.

The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological phases, especially for interacting systems. In this paper, we systematically construct and classify all the point-group crystalline topological superconductors and insulators in three-dimensional (3D) interacting fermion systems using the novel concept of a topological crystal. The corresponding higher-order topological surface theory can also be systematically studied via higher-order bulk-boundary correspondence. In particular, we discover several intrinsically interacting topological phases that cannot be realized in any free-fermion systems. Moreover, the crystalline equivalence principle for 3D interacting fermionic systems is also verified, with an additional subtle “twist” on the spin of fermions.

Floquet engineering, in which the properties of a quantum system are modified through the application of strong periodic drives, is an indispensable tool in atomic and condensed matter systems. However, it is inevitably limited by intrinsic heating processes. We describe a simple autonomous scheme, which exploits a static coupling between the driven system and a lossy auxiliary, to cool large classes of Floquet systems into desired states. We present experimental and theoretical evidence for the stabilization of a chosen quasienergy state in a strongly modulated transmon qubit coupled to an auxiliary microwave cavity with fixed frequency and photon loss. The scheme naturally extends to Floquet systems with multiple degrees of freedom. As an example, we demonstrate the stabilization of topological photon pumping in a driven cavity-QED system numerically. The coupling to the auxiliary cavity increases the average photon current and the fidelity of nonclassical states, such as high-photon-number Fock states, that can be prepared in the system cavity.

Superconducting transition-edge sensors are renowned for their extraordinary photon sensitivity and energy resolution, finding applications spanning quantum information, astronomy, and nanophotonics. Here, we report the development of bolometric superconducting optical nanoscopy (BOSON), a novel platform that integrates bolometric detection at the superconducting transition edges with near-field optical techniques. BOSON enables the mapping of photoinduced changes in superconductivity with unprecedented spatial resolution and photon sensitivity. By incorporating BOSON with low-dimensional materials, we achieved polariton imaging at nanowatt excitation levels—at least 4 orders of magnitude lower than the power typically required in prior near-field nanoscopy experiments. Our findings highlight the potential for BOSON to advance scanning-probe-based optical platforms to enable the detection of photons, polaritons, and Cooper pair dynamics at the nanoscale. This paves the way for quantum sensing applications using single-polariton detection and can offer deeper insights into quasiparticle dynamics.

Rhombohedral stacked graphene (RSG) contains two key ingredients for the realization of correlated topological phases of matter: flat electronic bands and concentrated Berry curvature. The fractional quantum anomalous Hall effect was recently observed in an RSG-hexagonal boron nitride (hBN) moiré heterostructure when the conduction electrons were pushed away from the moiré interface by an applied electric displacement field. The question then arises about whether such topological states can also develop in RSG-hBN in a strong moiré potential. Here, we explore the physics in the moiré-proximal limit through capacitance measurements that allow us to determine the electronic compressibility and extract energy gaps of incompressible states. We report the observation of integer and fractional Chern insulator states at low magnetic field in this limit at filling factors $\nu =1$, $2/3$, and $1/3$ in addition to numerous trivial and topological charge density waves. We map out a correlated phase diagram that is highly sensitive to both displacement and magnetic fields, establishing the moiré-proximal regime as a tunable platform for studying the interplay between band topology and strong lattice effects.

We experimentally demonstrate a novel scheme for efficiently generating intense terahertz surface plasmon polaritons (SPPs) on a subwavelength-diameter meter-long metal wire. Driven by a subrelativistic femtosecond laser ($a_0=0.3$, 3 mJ) focused at the wire’s midpoint, single-cycle 10-MW terahertz SPPs are excited and propagate bidirectionally along it over 25 cm. The measured laser-to-SPPs energy conversion efficiency is reaching up to approximately 2.4%, which is the highest value at present. It is proved that the terahertz SPPs are excited by coherent transition radiation of the subrelativistic-laser-produced escaping electrons. Particle-in-cell together with CST simulations confirm the experimental observations. Our scheme of using readily available subrelativistic laser should thus be useful to applications requiring terawatt level single-cycle terahertz SPPs.

Disordered materials under an imposed forcing can display creep and aging effects, accompanied by intermittent, spatially heterogeneous dynamics. We propose a testable microscopic description of these phenomena, based on the notion that as the system ages, the density of local barriers that enable relaxation displays a slowly evolving gap. As a result, the relaxation dynamics is dominated by the activation of the lowest, extremal tail of the distribution. This framework predicts logarithmic creep, as well as correlated bursts of slow activated rearrangements, or “thermal avalanches,” whose size grows logarithmically with their duration. The time interval between events within avalanches obeys a universal power-law distribution, with a cutoff that is simply proportional to the age of the system. We show that these predictions hold both in numerical models of amorphous solids, as well as in experiments with thin crumpled sheets. This analysis suggests that the heterogeneous dynamics occurring during logarithmic creep is related to other phenomena, including dynamical heterogeneities characterizing the glass transition.

A two-dimensional electron system exposed to a strong magnetic field produces a plethora of strongly interacting fractional quantum Hall (FQH) states, the complex topological orders of which are revealed through exotic emergent particles, such as composite fermions, and fractionally charged Abelian and non-Abelian anyons. Much insight has been gained by the study of multicomponent FQH states, where spin and pseudospin indices of the electron contribute additional correlation. Traditional multicomponent FQH states develop in situations where the components share the same orbital states and the resulting interactions are pseudospin independent; this homo-orbital nature is also crucial to their theoretical understanding. Here, we study “hetero-orbital” two-component FQH states, in which the orbital index is part of the pseudospin, rendering the multicomponent interactions strongly SU(2) anisotropic in the pseudospin space. Such states, obtained in bilayer graphene at the isospin transition between $\mathit{N}=0$ and $\mathit{N}=1$ electron Landau levels, are markedly different from previous homo-orbital two-component FQH states. In particular, we observe strikingly different behaviors for the parallel-vortex and reverse-vortex attachment composite fermion states, and an anomalously strong two-component $2/5$ state over a wide range of magnetic field before it abruptly disappears at a high field. Our findings, combined with detailed theoretical calculations, reveal the surprising robustness of the hetero-orbital FQH effects, significantly enriching our understanding of FQH physics in this novel regime.

Despite their importance for exotic quantum effects, the surface electronic structure of magnetic topological insulators ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ and ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ remains poorly understood. Using high-efficiency spin- and angle-resolved photoemission spectroscopy, we directly image the spin-polarization and orbital character of the surface states in both compounds and map our observations onto a model wave function to describe the complex spin-orbital texture, which solidifies our understanding of the surface band structure by establishing the single-band nature of the most prominent states. Most importantly, our analysis reveals a new mechanism for reducing the magnetic gap of the topological surface states based on the orbital composition of the wave function.

Quantum fluctuations can disrupt long-range order in one-dimensional systems and replace it with the universal paradigm of the Tomonaga-Luttinger liquid (TLL), a critical phase of matter characterized by power-law decaying correlations and linearly dispersing excitations. Using a Rydberg quantum simulator, we study how TLL physics manifests in the low-energy properties of a spin chain, interacting under either the ferromagnetic or the antiferromagnetic dipolar XY Hamiltonian. Following quasiadiabatic preparation, we directly observe the power-law decay of spin-spin correlations in real space, allowing us to extract the Luttinger parameter. In the presence of an impurity, the chain exhibits tunable Friedel oscillations of the local magnetization. Moreover, by utilizing a quantum quench, we directly probe the propagation of correlations, which exhibit a light-cone structure related to the linear sound mode of the underlying TLL. Our measurements demonstrate the influence of the long-range dipolar interactions, renormalizing the parameters of TLL with respect to the case of nearest-neighbor interactions. Finally, comparison to numerical simulations exposes the high sensitivity of TLLs to doping and finite-size effects.

Fractional excitations hold immense promise for both fundamental physics and quantum technologies. However, constructing lattice models for their dynamics under gauge fields remains a formidable challenge due to inherent obstructions. Here, we introduce a novel and systematic framework for deriving low-energy lattice models of fractional orbitals coupled to tight-binding gauge fields. Departing from conventional geometric approaches, our method systematically eliminates the high-energy states via virtual hopping, thereby deriving the gauge potential and quantum metric through a superexchange mechanism. We demonstrate the framework by constructing Wannier orbitals for Majorana states and a tight-binding $Z_2$ gauge field across various flux-crystalline phases in the Kitaev spin model on a honeycomb lattice. Our study reveals a striking phase transition between two nontrivial topological phases characterized by gapless flat band with extensive degeneracy. Furthermore, we develop a gauge-invariant mean-field theory for interacting Majorana orbitals, leading to a fractional Chern state. Our work establishes a general framework for gauge-mediated tight-binding models and a gauge-invariant mean-field theory for interacting fractional orbitals that can be readily extended to U(1), SU(N) lattice gauge theories.

Landau levels (LLs) are cornerstones of the fractional quantum Hall effect, which is a paradigm of topologically ordered phases of matter. Predicting and understanding the emergence of fractional Chern insulators in a Chern band, to a large extent, relies on judging the similarity between the Chern band and LLs. In this work, we generalize the notion of LLs to Chern bands to allow for nonuniform quantum geometries while preserving certain geometric invariants. Mathematically, generalized LLs can be understood in terms of holomorphic curves and associated moving frames in the sense of Cartan. This formalism enables a thorough analytical discussion of their associated quantum geometries. In practical terms, generalized LLs allow for a systematic discussion of the geometric stability of fractional Chern insulators and provide useful guidance in material design. Approximating Chern bands as superpositions of a few generalized LLs and employing exact diagonalization, we numerically identify a universal geometric criterion for the non-Abelian Moore-Read state to be stabilized in Chern bands, providing useful guidance for searching for such phase in moiré materials. Moreover, a double-twisted bilayer graphene model at the second magic angle is used to suggest a possible experimental realization of generalized LLs and zero-field non-Abelian phases. More broadly, our results point to generalized LLs being an interdisciplinary research direction connecting Kähler geometry, topologically ordered phases, and moiré materials, which we expect will benefit the study of the geometric aspect of correlated phases in a more general sense.

Programmable optical tweezer arrays of molecules are an emerging platform for quantum simulation and quantum information science. For these applications, the reduction and mitigation of errors remain major challenges. In this work, we leverage the rich internal structure of molecules to mitigate two types of errors—internal state preparation and qubit leakage errors. First, we demonstrate robust measurement-enhanced tweezer preparation at a record fidelity using site-resolved error detection followed by tweezer movement. Second, using a new hyperfine qubit encoding well suited for use as a quantum memory, we demonstrate site-resolved detection of qubit leakage errors (erasures) induced by blackbody radiation. This approach constitutes the first demonstration of erasure conversion in molecules, a capability that has found recent interest in quantum error correction. Our work opens the door to new possibilities with molecular tweezer arrays: Measurement-enhanced preparation opens access to mesoscopic defect-free molecular arrays that are important for quantum simulation of interacting many-body systems; erasure conversion in molecular arrays lays the technical groundwork for midcircuit detection, an important capability for explorations in quantum information processing.

A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion, or an epidemic state, that are modeled as compartments. Because of interactions and intrinsic dynamics, the system units are allowed to change category, leading to concentrations varying over time with complex behavior, typical of reaction-diffusion systems. While compartmental modeling provides a powerful framework for studying the dynamics of such populations and describe the spatiotemporal evolution of a system, it mostly relies on deterministic mean-field descriptions to deal with systems with many degrees of freedom. Here, we propose a method to alleviate some of the limitations of compartmental models by capitalizing on tools originating from quantum physics to systematically reduce multidimensional systems to an effective one-dimensional representation. Using this reduced system, we are able not only to investigate the mean-field dynamics and their critical behavior, but we can additionally study stochastic representations that capture fundamental features of the system. We demonstrate the validity of our formalism by studying the critical behavior of models widely adopted to study epidemic, ecological, and economic systems.

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.