X-ray free-electron lasers (FELs) are powerful photon sources offering a wide wavelength range, subfemtosecond pulse duration, and high brightness. Most x-ray FELs are based on self-amplified spontaneous emission (SASE). SASE-FEL radiation has excellent transverse but only limited longitudinal coherence, with power and spectral profiles consisting of multiple randomly distributed spikes. In this Letter, we present the first experimental demonstration of mode-locked SASE, which generates periodic trains of phase-locked subfemtosecond pulses, thus providing an x-ray analog of the optical frequency comb. Our approach combines the mode-coupled SASE scheme, where magnetic chicanes between the undulator modules of the FEL increase the coherence of the output radiation, and an external optical laser that restricts the FEL amplification to periodic and short regions of the electron bunch. The work relies on evidence in the frequency and time domains for photons and electrons, respectively, and will benefit investigations of ultrafast dynamics as well as coherent spectroscopy, and enable new types of experiments requiring phase-correlated x-ray pulses.

As a quintessential quantum matter, realizing robust Wigner crystals and achieving their angstrom-scale imaging remain formidable challenges. Here, we devise an original charge-transfer-crystallization strategy to realize an intrinsic electron solid made of $4f$ electrons. The highly localized and correlated nature of $4f$ electrons gives rise to a heavy Wigner crystal. This unprecedented heaviness manifests as an electron solid with record-high density ($2.02\times {10}^{13}/{\mathrm{cm}}^{-2}$) and melting temperature ($>60\mathrm{K}$). $Q$-plus atomic force microscopy and Kelvin probe force microscopy are employed to directly image the Wigner crystal, by which the sub-unit-cell localization and electrostatic influence of Wigner electrons are accurately determined. Moreover, the collective tunneling is captured, underlining the quantum nature of a Wigner crystal. Our discovery presents the $4f$ system as a tunable platform with the charge-transfer degree of freedom to study the 2D many-body correlation of heavy electrons.

Quantum error correction (QEC) enables practical quantum computing by encoding logical qubits in many physical qubits, which can exponentially suppress the logical error rate with increasing code size provided that the physical error rate is below a critical threshold. However, the leakage of quantum information from the computational subspace presents a critical challenge to the development of scalable QEC, which creates long-lived, correlated errors that spread across space and time. Here, we demonstrate a quantum memory operating below the threshold by implementing an all-microwave leakage suppression architecture on a distance-7 surface code. We achieve a logical error suppression factor of $\mathrm{\Lambda }=1.40(6)$, definitively reversing the above-threshold scaling ($\mathrm{\Lambda }<1$) caused by unmitigated leakage. This scheme integrates a hardware-efficient leakage reduction unit for data qubits with a fast, unconditional reset for ancilla qubits, suppressing the average leakage population after 40 cycles by a factor of 72 to $6.4(5)\times {10}^{-4}$. Our results demonstrate the viability of all-microwave control architectures for suppressing critical errors at scale, paving the way for more advanced quantum error correction implementations.

The interface between semiconductors and ion-conducting electrolytes is characterized by charge distributions and potential drops that vary substantially with the evolution of surface states. These surface states at the very interface to the liquid can form or be passivated, depending on the applied potential between electrode and electrolyte, and hereby fundamentally impact properties such as charge transfer. Characterization and understanding of such potential-dependent surface states with high spatial and temporal resolution is a significant challenge for the understanding and control of semiconductor-electrolyte interfaces. Here, we show that the optical anisotropy of InP(100) can be used to detect the potential-dependent formation of highly ordered surface states under operating conditions. Upon formation of a surface state in the band gap of the semiconductor, the potential drop and hence the electric field is shifted away from the semiconductor to the Helmholtz layer of the electrolyte. This modifies the instantaneous response of the optical anisotropy to disturbances of the applied potential. We propose an electrochemical variant of the linear electro-optical effect and our findings open a novel route for understanding these interfaces. The results show how surface states from surface reconstructions at this reactive interface can be switched on or off with the applied potential.

Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such as operation precision, circuit depth, and connectivity. With improved hardware efficiency by using superconducting qutrits (three-level systems), we experimentally demonstrate a scalable DTQW in a superconducting circuit, observing the ballistic spreading of quantum walk in a qutrit chain. The usage of qutrits in our implementation allows hardware efficiently encoding of the walker position and the coin degree of freedom. By exploiting the flexibility and intrinsic symmetries of qutrit-based DTQWs, we successfully prepare two topological phases in the chain. For the first time, particle-hole-symmetry-protected edge states, bounded at the interface between these two topological phases, are observed in the superconducting platform. Measured parameter dependencies further validate the properties of edge states. The scalability and gate-control compatibility of the demonstrated DTQWs enable a versatile tool for superconducting quantum computing and quantum simulation.

Collisionless dissipation of turbulence is important for heating plasmas in astrophysical, space physics, and laboratory environments, controlling energy, momentum, and particle transport. We analyze Parker Solar Probe observations to understand the collisionless heating of the sub-Alfvénic solar wind, which is connected to the solar corona. Our results show that linear resonant heating through parallel-propagating cyclotron waves cannot account for turbulent dissipation in the sub-Alfvénic region, which observations suggest may dissipate turbulence at distances further from the Sun. Instead, we find that stochastic heating can account for the observed ion energization; however, because the dominant contributions arise from infrequent, large-amplitude events, turbulent intermittency must be explicitly incorporated. These observations directly connect stochastic heating via breaking of the proton magnetic moment with the intermittent and inhomogeneous heating of turbulence reported in many previous studies. Our identification of stochastic heating as a dynamic mechanism responsible for intermittent heating of the solar wind has significant implications for turbulent dissipation in the lower corona, other astrophysical environments, and laboratory plasmas.

Bragg coherent diffraction imaging struggles to phase data from nanocrystals exhibiting large strain inhomogeneities, which significantly limits its applicability across many scientific scenarios. Here, we demonstrate the experimental realization of Bragg coherent modulation imaging, an approach that incorporates wavefront modulation into the diffracted beam, enabling unambiguous structure recovery and resolving highly strained crystals. This method provides a more robust tool for three-dimensional lattice strain measurements in nanocrystals.

The spectrum of Markov generators encodes physical information beyond simple decay and oscillation, which reflects irreversibility and governs the structure of correlation functions. In this Letter, we prove an ellipse theorem that provides a universal thermodynamic geometric constraint on the spectrum of Markov rate matrices. The theorem states that all eigenvalues lie within a specific ellipse in the complex plane. In particular, the imaginary parts of the spectrum, which indicate oscillatory modes, are bounded by the maximum thermodynamic force associated with individual transitions. This spectral bound further constrains the initial short-time behavior of correlation functions between two arbitrary observables. Finally, we compare our result with a previously proposed conjecture, which remains an open problem and warrants further investigation.

Interferometers are known for precise measurements of the effects inside of them. Here we show that placing a Dove prism in one of the interferometer arms allows for also detecting minute effects happening outside the device. We derive how the additional reflection in one arm can amplify small tilts or displacements of the input beam in the dark output port of the interferometer, in analogy to weak value amplification. The experiment demonstrates a clear improvement of the measurement signal. Moreover, in the bright output port, small disturbances in the input beam get largely filtered, thereby enabling beam stabilization with a fully passive device.

We introduce new classes of gapped topological phases characterized by quantized crystalline-electromagnetic responses, termed multipolar Chern insulators. These systems are characterized by nonsymmorphic momentum-space symmetries and mirror symmetries, leading to quantization of momentum-weighted Berry curvature multipole moments. We construct lattice models for such phases and numerically confirm their quantized responses. These systems exhibit bound charge and momentum densities at lattice and magnetic defects, as well as currents induced by electric or time-varying strain fields. Our Letter extends the classification of topological matter by uncovering novel symmetry-protected topological phases with quantized responses.

Fractional quantum anomalous Hall effects realized in twisted bilayer ${\mathrm{MoTe}}_2$ and multilayer-graphene-based moiré heterostructures have captured a tremendous growth of interest. In this Letter, we propose that rhombohedral multilayer graphene coupled with an artificial kagome superlattice potential is a new platform to realize various fractional topological phases. Taking Bernal bilayer graphene as the simplest example, when it is placed on top of a prepatterned ${\mathrm{SiO}}_2$ substrate with periodic arrays of holes arranged into kagome lattice, the system would be subject to a tunable kagome superlattice potential once an electrostatic voltage drop between the top and bottom gates is applied. Then, we theoretically study the electronic band structures, topological properties, and quantum geometric properties of the Bloch states of Bernal bilayer graphene coupled with a realistic kagome superlattice potential, which is well benchmarked by transport measurements in the weak superlattice-potential regime. We find that the system may exhibit nearly ideal topological flat bands in a substantial region of the parameter space spanned by superlattice constant and electrostatic potential strength. When these topological flat bands are fractionally filled, exact diagonalization calculations suggest that the system would exhibit rich fractional topological phases at $1/3$, $2/3$, $2/5$, $3/5$, and $1/2$ fillings including both fractional Chern insulators and anomalous composite Fermi liquids under zero magnetic field. We also find that Halperin-type FCI states may emerge from the Chern-number-2 flat bands of trilayer graphene coupled with kagome superlattice potential.

Entangled photon sources (EPSs) are essential for quantum science and technology. Despite advancements in integrated optical platforms like thin-film lithium niobate, a scalable, high-performance, chip-scale EPS has remained elusive. We address this by demonstrating an electrically pumped, post-selection-free polarization EPS, achieved through hybrid integration of a distributed feedback laser with a thin-film lithium niobate chip, which integrates periodically poled lithium niobate waveguides, a beam splitter, and a polarization rotator combiner. By injecting current into the chip, we realize a high-performance EPS with a bandwidth of 73 nm and an entanglement pair generation rate of $4.5\times {10}^{10}\mathrm{pairs}/\mathrm{s}/\mathrm{mW}$. The polarization entanglement shows Bell-state fidelities above 96% across frequency-correlated modes. This compact, integrated EPS enables key applications, including high-speed quantum key distribution via wavelength division multiplexing, satellite-based quantum communication, and entanglement-based quantum metrology.

Recent developments in nanotechnology have enabled us to investigate the dynamic properties of van der Waals materials on a piezoelectric substrate. Here, we report on the dynamics of charge density wave in ${\mathrm{NbSe}}_3$ nanowires induced by surface acoustic waves (SAWs). Clear peaks in the differential resistance were observed at the resonant frequency of the SAW device. These peaks, known as “Shapiro steps,” are typically observed by applying an rf current to ${\mathrm{NbSe}}_3$ nanowires. We found that the Shapiro steps induced by SAWs show several features distinct from the ones induced by an rf current. Our detailed study revealed that a strain induced by SAWs plays a significant role in the Shapiro steps. The result clearly demonstrates the importance of the strain in charge density wave materials and paves the way for strain-induced device applications.

Elastic edge states, formed by interfacing different topological phases and appealing for various cutting-edge applications based on surface acoustic waves, often exhibit limits due to the lack of strong topological protection. Here, we overcome this difficulty by engineering a synthetic three-dimensional (3D) Dirac semimetal phase in a 2D elastic metamaterial. By tuning a geometry parameter, we drive topological transitions, which can be mapped into Dirac points in hybrid 3D, i.e., 2D plus a synthetic dimension. Gapless adiabatic spectral flows are found along the synthetic momentum loops when they encircle the Dirac points, emerging as the surface-arc states in hybrid 3D, that restores the bulk-edge correspondence in elastic systems. Experimental measurements confirm the bulk Dirac points, surface-arc states linking oppositely charged Dirac points, and the emergent gapless spectral flows. This Letter brings novel quantum-inspired phenomena to elastic systems and may inspire applications in topological control of mechanical waves and dynamics.

Universal power laws have been scrutinized in physics and beyond, and a long-standing debate exists in econophysics regarding the strict universality of the nonlinear price impact, commonly referred to as the square-root law (SRL). The SRL posits that the average price impact $I$ follows a power law with respect to transaction volume $Q$, such that $I(Q)\propto Q^{\delta }$ with $\delta \approx 1/2$. Some researchers argue that the exponent $\delta$ should be system specific, without universality. Conversely, others contend that $\delta$ should be exactly $1/2$ for all stocks across all countries, implying universality. However, resolving this debate requires high-precision measurements of $\delta$ with errors of around 0.1 across hundreds of stocks, which has been extremely challenging due to the scarcity of large microscopic datasets—those that enable tracking the trading behavior of all individual accounts. Here we conclusively support the universality hypothesis of the SRL by a complete survey of all trading accounts for all liquid stocks on the Tokyo Stock Exchange over eight years. Using this comprehensive microscopic dataset, we show that the exponent $\delta$ is equal to $1/2$ within statistical errors at both the individual stock level and the individual trader level. Additionally, we rejected two prominent models supporting the nonuniversality hypothesis: the Gabaix-Gopikrishnan-Plerou-Stanley and the Farmer-Gerig-Lillo-Waelbroeck models [Gabaix et al., Nature (London) 423, 267 (2003).; Q. J. Econ 121, 461 (2006).; Farmer et al., Quant. Finance 13, 1743 (2013)]. Our Letter provides exceptionally high-precision evidence for the universality hypothesis in social science and could prove useful in evaluating the price impact by large investors—an important topic even among practitioners.

The intricate competition between coexisting charge density waves (CDWs) can lead to rich phenomena, offering unique opportunities for phase manipulation through electromagnetic stimuli. Leveraging time-resolved x-ray diffraction, we demonstrate ultrafast control of a CDW in ${\mathrm{EuTe}}_4$ upon optical excitation. At low excitation intensities, the amplitude of one of the coexisting CDW orders increases at the expense of the competing CDW, whereas at high intensities, it exhibits a nonmonotonic temporal evolution characterized by both enhancement and reduction. This transient bidirectional controllability, tunable by adjusting photoexcitation intensity, arises from the interplay between optical quenching and phase-competition-induced enhancement. Our findings, supported by phenomenological time-dependent Ginzburg-Landau theory simulations, not only clarify the relationship between the two CDWs in ${\mathrm{EuTe}}_4$, but also highlight the versatility of optical control over order parameters enabled by phase competition.

The acoustic spin Hall effect (ASHE) enables the generation of spin current via lattice vibrations driven by surface acoustic waves (SAWs) in heavy metals. Here, we report its reciprocal counterpart—the inverse ASHE—in which an alternating (ac) spin current induces coherent lattice vibrations that propagate SAWs. By injecting ac spin currents into a heavy metal via interfacial spin backflow in a heavy metal-ferromagnet bilayer, we successfully detect such spin-current-induced nonlocal SAWs over distances up to $400\mathrm{\mu m}$ in an ${\mathrm{LiNbO}}_3$ substrate. As the previously unobserved reciprocal element in spin-lattice interactions, the inverse ASHE completes the framework of spin-phonon interconversion and uncovers a phonon-mediated pathway for long-range spin transport, even through nonmagnetic insulators.

Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater computational demands than their pairwise counterparts. Here, we present an information-theoretic framework for determining the extent to which a hypergraph representation of a networked system is structurally redundant and for identifying its most critical higher orders of interaction that allow us to remove these redundancies while preserving essential higher-order structure.

Communication in quantum networks suffers notoriously from photon loss. Resulting errors can be mitigated with a suitable measurement herald at the receiving node. However, waiting for a herald and communicating the measurement result back to the sender in a repeat-until-success strategy makes the protocol slow and prone to errors from false heralds such as detector dark counts. Here, we implement an entanglement herald at the sending node by employing a cascaded two-photon emission of a single atom into two optical fiber cavities: the polarization of one photon is entangled with the spin of the atom, and the second photon heralds entanglement generation. We show that heralding improves the atom-photon entanglement in-fiber efficiency and fidelity to 68(3)% and 87(2)%, respectively. We highlight the potential of our source for noise-limited long-distance quantum communication by extending the range for constant fidelity or, alternatively, increasing the fidelity for a given distance.

The $\mathrm{SNO}+$ Collaboration reports the first evidence of ${}^8\mathrm{B}$ solar neutrinos interacting on ${}^{13}\mathrm{C}$ nuclei. The charged current interaction proceeds through ${}^{13}\mathrm{C}+{\nu }_e{\to }^{13}\mathrm{N}+e^{-}$ which is followed, with a 10 minute half life, by ${}^{13}\mathrm{N}{\to }^{13}\mathrm{C}+e^{+}+{\nu }_e$. The detection strategy is based on the delayed coincidence between the electron and the positron. Evidence for the charged current signal is presented with a significance of $4.2\sigma$. Using the natural abundance of ${}^{13}\mathrm{C}$ present in the scintillator, 5.7 metric tons of ${}^{13}\mathrm{C}$ over 231 days of data were used in this analysis. The ${5.6}_{-2.3}^{+3.0}$ observed events in the data set are consistent with the expectation of ${4.7}_{-1.3}^{+0.6}$ events. This result is the second real-time measurement of CC interactions of ${}^8\mathrm{B}$ neutrinos with nuclei and constitutes the lowest energy observation of neutrino interactions on ${}^{13}\mathrm{C}$ generally. This enables the first direct measurement of the CC ${\nu }_e$ reaction to the ground state of ${}^{13}\mathrm{N}$, yielding an average cross section of $({16.1}_{-6.7}^{+8.5}(\mathrm{stat}\mathrm{.}{)}_{-2.7}^{+1.6}(\mathrm{syst}\mathrm{.}))\times {10}^{-43}{\mathrm{cm}}^2$ over the relevant ${}^8\mathrm{B}$ solar neutrino energies.