Topographical and chemical defects on solid surfaces tend to pin three-phase contact lines of moving liquid drops. Our quantitative understanding of the pinning process is, however, still poor. Here we use an atomic force microscope to slide $\approx 100\mathrm{pL}$ droplets of water-glycerol mixtures over hydrophobic surfaces and measure friction forces. By using picoliter droplets, the sensitivity for detecting processes at the contact line is enhanced. We have found that only a region $<200\mathrm{nm}$ around the contact line contributes to friction. By imaging isolated nanospherical defects, we could quantify the force and energy dissipation when the front and rear of the droplet passes the defect and compare it to theory.

To demonstrate supremacy of quantum computing, increasingly large-scale superconducting quantum computing chips are being designed and fabricated. However, the complexity of simulating quantum systems poses a significant challenge to computer-aided design of quantum chips, especially for large-scale chips. Harnessing the scalability of graph neural networks (GNNs), we here propose a parameter designing algorithm for large-scale superconducting quantum circuits. The algorithm depends on the so-called “three-stair scaling” mechanism, which comprises two neural-network models: an evaluator supervisedly trained on small-scale circuits for applying to medium-scale circuits, and a designer unsupervisedly trained on medium-scale circuits for applying to large-scale ones. We demonstrate our algorithm in mitigating quantum crosstalk errors. Frequencies for both single- and two-qubit gates (corresponding to the parameters of nodes and edges) are considered simultaneously. Numerical results indicate that the well-trained designer achieves notable advantages in efficiency, effectiveness, and scalability. For example, for large-scale superconducting quantum circuits consisting of around 870 qubits, our GNNs-based algorithm achieves 51% of the errors produced by the state-of-the-art algorithm, with a time reduction from 90 min to 27 s. Overall, a better-performing and more scalable algorithm for designing parameters of superconducting quantum chips is proposed, which demonstrates the advantages of applying GNNs in superconducting quantum chips.

We measured the $g$-factor of the excited-state ${}^3{\mathrm{P}}_1$ in ${\mathrm{Ca}}^{14+}$ ion to be $g=1.499032(6)$ with a relative uncertainty of $4\times {10}^{-6}$. The magnetic field magnitude is derived from the Zeeman splitting of a ${\mathrm{Be}}^{+}$ ion, cotrapped in the same linear Paul trap as the highly charged ${\mathrm{Ca}}^{14+}$ ion. Furthermore, we experimentally determined the second-order Zeeman coefficient $C_2$ of the ${}^3{\mathrm{P}}_0\text{−}{}^3{\mathrm{P}}_1$ clock transition. For the $m_J=0\to m_{J^{\prime }}=0$ transition, we obtained $C_2=0.39\pm 0.04\mathrm{Hz}{\mathrm{mT}}^{-2}$, which is to our knowledge the smallest reported for any atomic transition to date. This confirms the predicted low sensitivity of highly charged ions to higher-order Zeeman effects, making them ideal candidates for high-precision optical clocks. Comparison of the experimental results with our state-of-the art electronic structure calculations shows good agreement and demonstrates the significance of the frequency-dependent Breit contribution, negative energy states, and QED effects on magnetic moments.

Rovibrational energies, wave functions, and Raman transition moments are reported for the lowest-energy states of the ${\mathrm{H}}_3^{+}$ molecular ion including the magnetic couplings of the proton spins and molecular rotation in the presence of a weak external magnetic field. The rovibrational-hyperfine-Zeeman Hamiltonian matrix is constructed and diagonalized using the rovibrational eigenstates and the proton spin functions. The developed methodology can be used to compute hyperfine-Zeeman effects also for higher-energy rovibrational excitations of ${\mathrm{H}}_3^{+}$ and other closed-shell polyatomic molecules. These developments will guide future experiments extending quantum logic spectroscopy to polyatomic systems.

We study light scattering of atomic wave packets in free space and discuss the results in terms of atom-photon entanglement and which-way information. Using ultracold atoms released from an optical lattice, we realize a Gedanken experiment which interferes single photons scattering off of Heisenberg uncertainty-limited wave packets. We unify the free-space and trapped-atom pictures by measuring the light scattered before and during wave packet expansion and show the coherence properties of the scattered light are independent of the presence of the trap. Therefore, recoilless scattering in a trap (Mössbauer effect), the different frequency of sidebands, and the excitation of an excited harmonic oscillator state are not essential to the question of which fraction of light scattering is coherent or incoherent. Our experiment demonstrates the potential of using atomic Mott insulators to create single-atom wave packets for fundamental studies.

We carry out first-principles calculations to demonstrate that the complex energy landscape and competing phases of ${\mathrm{HfO}}_2$ can be understood from the four unstable flat phonon bands of an unconventional high-symmetry structure of ${\mathrm{HfO}}_2$ with the space group $Cmma$. We consider structures generated from the $Cmma$ reference structure by all possible combinations of the zone center and zone boundary modes belonging to the unstable flat phonon branches. We find 12 distinct locally stable structures, of which 5 correspond to well-known phases. We also show that 8 of these 12 structures can be described as period-2 superlattices of the ferroelectric $Pca{2}_1(\mathrm{oIII})$, ferroelectric $Pmn{2}_1(\mathrm{oIV})$, monoclinic $P{2}_1/c(m)$, and distorted monoclinic $P{2}_1/c(\mathrm{dm})$ structures. We demonstrate how the unstable flat phonon bands can explain the atomically thin grain boundaries in the various types of superlattices. Finally, we point out that arbitrary-period ${\mathrm{HfO}}_2$ superlattices derived from the 6 different types of period-2 superlattices are expected to form based on the flatness of the unstable phonon branches. The organizing principle provided by this work deepens our understanding of the underlying physics in the phase stability of ${\mathrm{HfO}}_2$ and provides guidance for functional phase stabilization.

Exceptional points (EPs) have been widely studied in various non-Hermitian systems, exhibiting and underlying many unique topological properties. In photonic systems, multiple degrees of freedom of light enable the EPs with rich properties and high dimensional topology. In this Letter, we propose that the external magnetic field can serve as an additional parameter dimension to manipulate EPs with tunable evolutions and hidden topological structures in magneto-optical photonic crystal slabs. Continuous evolution of EPs can be derived by changing the external magnetic field, where paired EPs gradually approach each other as the Fermi arc shrinks, and eventually merge and annihilate. When considering the parameter space including the magnetic field dimension, these EPs form a closed ring, revealing novel topological structures. The discovered EP ring is further associated with more topological polarization properties, including the closed ring in Poincaré sphere and the transferred topological charge between the Fermi arc and the circularly polarized states in momentum space. Our Letter reveals complex topological properties in magneto-optical photonic crystal slabs, providing a framework to explore non-Hermitian topological systems with additional parameter dimensions.

Feynman diagrams are an essential tool for simulating strongly correlated electron systems. However, stochastic quantum Monte Carlo sampling suffers from the sign problem, particularly when solving a multiorbital quantum impurity model. Recently, two approaches have been proposed for efficient numerical treatment of Feynman diagrams: tensor cross interpolation (TCI) to replace stochastic sampling and the quantics tensor train (QTT) representation for compressing space-time dependence. One of the remaining challenges is the nontrivial task of identifying low-rank structures in weak-coupling Feynman diagrams for multiorbital electron-phonon systems. In particular, the traditional TCI algorithm faces an ergodicity problem, which prevents it from fully exploring the multiorbital space. To address this, we incorporate a new algorithm called global search, which resolves this issue. By combining this approach with QTT, we uncover low-rank structures and achieve efficient numerical integration with exponential resolution in time and faster-than-power-law convergence of error relative to computational cost. Additionally, our approach does not require the division of discontinuous regions necessary in nonquantics TCI.

Realizing odd-parity, time-reversal-preserving, nonrelativistic spin splitting is a central goal for spintronics applications. We propose a group-theory-based microscopic framework to induce odd-parity spin splitting from coplanar antiferromagnetic (AFM) states without spin-orbit coupling (SOC). We develop phenomenological models for 421 conventional period-doubling AFM systems in nonsymmorphic space groups and construct minimal microscopic models for 119 of these. We find that these AFM states can attain three possible competing ground states. These ground states all break symmetries in addition to those broken by the usual AFM order. Specifically, they give rise to either odd-parity spin-splitting, nematic order, or scalar odd-parity order related to multiferroicity. Our microscopic theories reveal that the odd-parity spin-splitting energy scale is generically large and further reveal that the scalar odd-parity order gives a nonzero Berry curvature dipole without SOC. We identify 67 materials in the Magndata database for which our theory applies. We provide density-functional theory (DFT) calculations on Fe-based materials that reveal an $h$-wave spin splitting consistent with our symmetry arguments and apply our microscopic model to determine the nonrelativistic Edelstein response for CeNiAsO.

Magnetic imaging with ultrahigh spatial resolution is crucial to exploring the magnetic textures of emerging quantum materials. We propose a novel magnetic imaging protocol that achieves angstrom-scale resolution by combining spin defects in van der Waals materials and terahertz (THz) scattering scanning near-field optical microscopy. Spin defects in the atomic monolayer enable the probe-to-sample distance diving into angstrom range where the exchange interactions between the probe and sample spins become predominant. This exchange interaction leads to energy splitting of the probe spin in the order of meV, corresponding to THz frequencies. With THz optics and the spin-dependent fluorescence of the probe spin, the interaction energy can be resolved entirely through optical methods. Our proposed all-optical magnetic imaging protocol holds significant promise for investigating magnetic textures in condensed matter physics due to its excellent compatibility and high spatial resolution.

We discuss the universal behavior linked to the Goldstone mode associated with the spontaneous breaking of time-translation symmetry in many-body systems, in which the order parameter traces out a limit cycle. We show that this universal behavior is closely tied to Kardar-Parisi-Zhang physics, which can strongly affect the scaling properties in all dimensions. Our Letter predicts and rationalizes the emergence of Kardar-Parisi-Zhang in numerous systems such as nonreciprocal phases in active matter, active magnets, driven-dissipative quantum systems, and synchronization of oscillators.

We analyze the dynamics of a first order confinement-deconfinement phase transition in an expanding medium using an effective boundary description fitted to the holographic Witten model. We observe and analyze hot plasma remnants, which do not cool down or nucleate bubbles despite the expansion of the system. The appearance of the hot remnants, the dynamics of their shrinking, and subsequent dissolution and further heating up is very robust and persists in such diverse scenarios as boost-invariant expansion with a flat Minkowski metric and cosmological expansion in a Friedmann-Robertson-Walker spacetime.

Using data samples of 102 million $\mathrm{\Upsilon }(1S)$ events and 158 million $\mathrm{\Upsilon }(2S)$ events collected by the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider, we search for $[udsc\overline{c}]$ pentaquark states decaying to $J/\psi \mathrm{\Lambda }$. Using the first observations of $\mathrm{\Upsilon }(1S,2S)$ inclusive decays to $J/\psi \mathrm{\Lambda }$, we find evidence of the $P_{c\overline{c}s}(4459{)}^0$ state with a local significance of 3.3 standard deviations, including statistical and systematic uncertainties. We measure the mass and width of the $P_{c\overline{c}s}(4459{)}^0$ to be $(4471.7\pm 4.8\pm 0.6)\mathrm{MeV}/c^2$ and $(22\pm 13\pm 3)\mathrm{MeV}$, respectively. The branching fractions for $P_{c\overline{c}s}(4459{)}^0$ production are measured to be $\mathcal{B}[\mathrm{\Upsilon }(1S)\to P_{c\overline{c}s}(4459{)}^0/{\overline{P}}_{c\overline{c}s}(4459{)}^0+\mathrm{anything}]=(3.5\pm 2.0\pm 0.2)\times {10}^{-6}$ and $\mathcal{B}[\mathrm{\Upsilon }(2S)\to P_{c\overline{c}s}(4459{)}^0/{\overline{P}}_{c\overline{c}s}(4459{)}^0+\mathrm{anything}]=(2.9\pm 1.7\pm 0.4)\times {10}^{-6}$. The inclusive branching fractions of $\mathrm{\Upsilon }(1S,2S)\to J/\psi \mathrm{\Lambda }/\overline{\mathrm{\Lambda }}$ are measured to be $\mathcal{B}[\mathrm{\Upsilon }(1S)\to J/\psi \mathrm{\Lambda }/\overline{\mathrm{\Lambda }}+\mathrm{anything}]=(36.9\pm 5.3\pm 2.4)\times {10}^{-6}$ and $\mathcal{B}[\mathrm{\Upsilon }(2S)\to J/\psi \mathrm{\Lambda }/\overline{\mathrm{\Lambda }}+\mathrm{anything}]=(22.3\pm 5.7\pm 3.1)\times {10}^{-6}$. We measure the visible cross section $\sigma (e^{+}{e}^{-}\to J/\psi \mathrm{\Lambda }/\overline{\mathrm{\Lambda }}+\mathrm{anything})=(90\pm 14\pm 6)\mathrm{fb}$ for the continuum production at $\sqrt{s}=10.52\mathrm{GeV}$. In all cases, the first uncertainties are statistical and the second are systematic.

We report an ultrasensitive atomic spin sensor employing double spin resonance, achieving a spin signal enhancement of 2600 and a sensitivity of $0.57\mathrm{fT}/\sqrt{\mathrm{Hz}}$ under nonzero magnetic field measurements. Furthermore, we establish an in situ alkali-noble-gas spin sensor by tracing the measured spin precession frequency to the nuclear spins gyromagnetic ratio constant with high accuracy. The dominant systematic uncertainty induced by Fermi-contact interactions during the trace process has been suppressed by more than 2 orders of magnitude via pulsed train sequences. This Letter paves the way for achieving both ultrahigh sensitivity and traceability, offering promising opportunities for exploring new physics beyond the standard model and advancing quantum metrology in complex environments.

Multilayer rhombohedral graphene (RG) has recently emerged as a new, structurally simple flat-band system, which facilitates the exploration of interaction-driven correlation states with highly ordered electron arrangements. Despite a variety of many-body order behaviors observed in RG by transport measurements, the direct microscopic visualization of such correlated phases in real space is still lacking. Here, we show the discovery of a robust intervalley coherent order—a long-predicted ground state in RG—at 77 K in tetralayer RG placed on ${\mathrm{MoS}}_2$ via imaging atomic-scale spatial reconstruction of wave functions for correlated states. This state is visualized in $\sim 60\%$ and $\sim 70\%$ filled flat bands, where clear spectroscopic signatures of electronic correlations are observed, manifesting as a $\sqrt{3}\times \sqrt{3}$ reconstructed supercell on the graphene lattice. Surprisingly, such a $\sqrt{3}\times \sqrt{3}$ pattern is absent in hexagonal-boron-nitride-supported RG under the same experimental conditions. These findings, together with our Hartree-Fock mean-field calculations, suggest a spin-orbit proximity-induced robust intervalley coherent phase of interacting electrons in tetralayer RG. Our results provide microscopic insights into the correlated phases in RG multilayers and highlight the significant potential for realizing highly accessible collective phenomena through van der Waals proximity.

The role of the polarization degree of freedom in lattice dynamics in solids has been underlined recently. We theoretically discover a relaxation mechanism for both linear and circular polarizations of acoustic phonons. In the absence of scattering, the polarization exhibits oscillatory behavior. This behavior leads to a counterintuitive result: unlike linear momentum, more frequent scattering events cause slower polarization relaxation due to motional narrowing. We validate this mechanism using the quantum kinetic equation. We derive the relaxation rates of polarizations analytically for isotropic elastic bodies and numerically for a cubic crystal. Remarkably, we reveal that linear polarizations relax more slowly than circular ones. Our findings provide a pathway to prolong the lifetime of phonon angular momentum by designing disorder. This improvement has the potential to advance thermal management in disordered materials, facilitate phononic information transport, and strengthen spin-phonon coupling in spintronic devices.