We perform three-photon photoassociation to obtain high resolution spectra of ${}^{87}\mathrm{Rb}$ trilobite dimers for the principal quantum numbers $n=22$, 24, 25, 26, and 27. The large binding energy of the molecules in combination with a relative spectroscopic resolution of ${10}^{-4}$ provides a rigorous benchmark for existing theoretical models. A recently developed Green’s function framework, which circumvents the convergence issues that afflicted previous studies, is employed to theoretically reproduce the vibrational spectrum of the molecule with high accuracy. The relatively large molecular binding energy is primarily determined by the low-energy $S$-wave electron-atom scattering length, thereby allowing us to extract the ${}^3{S}_1$ scattering phase shift with unprecedented accuracy, at low-energy regimes inaccessible to free electrons.

Chiral and axial materials offer platforms for intriguing phenomena, such as cross-correlated responses and chirality-induced spin selectivity. However, quantifying the properties of such materials has generally been considered challenging. Here, we demonstrate that the spatial distribution of the electron chirality, represented by ${\mathrm{\Psi }}^{†}{\gamma }^5\mathrm{\Psi }$ with the four-component Dirac field $\mathrm{\Psi }$, characterizes the chirality and axiality of materials. Furthermore, we reveal that spin-derived electric polarization can serve as an effective indicator of material polarity. We present quantitative evaluations of electron chirality distribution and spin-derived electric polarization based on first-principles calculations. Additionally, we propose that electron chirality can be directly observed via circular dichroism in photoemission spectroscopy, which measures the difference between right- and left-handed circularly polarized light. Electron chirality and spin-derived electric polarization provide a new framework for quantifying chirality, axiality, and polarity in asymmetric materials, paving the way for the exploration of novel functional materials.

Waves propagating through weakly disordered smooth linear media undergo a universal phenomenon called branched flow. Branched flow has been observed and studied experimentally in various systems by considering coherent waves. Recent experiments have reported the observation of optical branched flow by using an incoherent light source, thus revealing the key role of coherent phase-sensitive effects in the development of incoherent branched flow. By considering the paraxial wave equation as a generic representative model, we elaborate a stochastic theory of both coherent and incoherent branched flow. We derive closed-form equations that determine the evolution of the intensity correlation function, as well as the value and the propagation distance of the maximum of the scintillation index, which characterize the dynamical formation of incoherent branched flow. We report accurate numerical simulations that are found in quantitative agreement with the theory without free parameters. Our theory highlights the important impact of coherence and interference on branched flow, thereby providing a framework for exploring branched flow in nonlinear media, in relation to the formation of freak waves in oceans.

The current experimental and theoretical values of the ionization energy of metastable ${}^4\mathrm{He}$ [$(1s)(2s){{}^{3}S}_1$] differ by $9\sigma$, which prevents the determination of the alpha-particle charge radius from spectroscopic measurements in ${}^4\mathrm{He}$. To help clarify the origin of this discrepancy, we report on a precision measurement of hyperfine-resolved transitions from the $(1s)(2s){{}^{3}S}_1$ metastable state of ${}^3\mathrm{He}$ to high $np$ Rydberg states converging on the $F^{+}=0$, 1 hyperfine levels of the ${}^3{\mathrm{He}}^{+}$ $(1s{)}^2{S}_{1/2}$ ground state. Rydberg-series extrapolation using multichannel quantum-defect theory (MQDT) enabled the determination of the ionization energy of the $(1s)(2s){{}^{3}S}_1$ state of ${}^3\mathrm{He}$ [$E_{\mathrm{I}}({}^3\mathrm{He})/h=1152788844.6154(77{)}_{\mathrm{stat}}(25{)}_{\mathrm{sys}}\mathrm{MHz}$] and of the corresponding isotopic shift [$(E_{\mathrm{I}}({}^4\mathrm{He})-E_{\mathrm{I}}({}^3\mathrm{He}))/h=53898.093(9)\mathrm{MHz}$]. The MQDT analysis also permitted the quantification of singlet-triplet mixing in the $np$ series induced by the hyperfine interaction. From the isotopic shift of the ionization energy of He, the difference $\delta r^2$ between the squared charge radii of the helion and alpha particles is determined to be $1.060(10){\mathrm{fm}}^2$.

We address the challenge of incorporating non-Markovian electronic friction effects in quantum-mechanical approximations of dynamical observables. A generalized Langevin equation is formulated for ring-polymer molecular dynamics rate calculations, which combines electronic friction with a description of nuclear quantum effects for adsorbates on metal surfaces. An efficient propagation algorithm is introduced that captures both the spatial dependence of friction strength and non-Markovian frictional memory. This framework is applied to a model of hydrogen diffusing on Cu(111) derived from ab initio density functional theory calculations, revealing significant alterations in rate constants and tunneling crossover temperatures due to non-Markovian effects. Our findings explain why previous classical molecular dynamics simulations with Markovian friction showed unexpectedly good agreement with experiment, highlighting the critical role of non-Markovian effects in first-principles atomistic simulations.

Quadratic quasinormal modes encode fundamental properties of black hole spacetimes. They are also one of the key ingredients of nonlinearities of general relativity in the ringdown stage of binary black hole coalescence. In this Letter, we classify all possible quadratic coupling channels of quasinormal modes for a generic Kerr black hole and use a frequency-domain pseudospectral code with hyperboloidal slicing to calculate these couplings. After accounting for all the channels in systems with reflection symmetry, our results become consistent with those extracted from numerical simulations and time-domain fits. This agreement provides a compelling example demonstrating the success of black hole second-order perturbation theory. We also explore potential applications of our calculations in future ringdown data analysis by carrying out a detectability survey for various quadratic modes. We find that a few of them are observationally relevant for third-generation ground-based detectors like Cosmic Explorer, as well as the spaceborne Laser Interferometer Space Antenna.

Supply networks are essential for modern production, yet their critical properties remain understudied. We present a stochastic model with random production capacities to analyze material flow to a root node, focusing on topology and buffer stocks. The critical demand, where unsatisfied demand diverges, is examined mostly through numerical simulations. Without stocks, minimal production dictates behavior, making topology irrelevant. With stocks, memory effects arise, making topology crucial. Increased local connectivity is beneficial: firms should favor broad, short supply chains over long, narrow ones.

Quantum key distribution (QKD) offers a secure means of communication based on the laws of quantum physics. Despite its remarkable advancements, the current reliance of QKD on attenuated coherent (laser) light sources has imposed a fundamental limit on the secure key rate (SKR) per channel use. This constraint stems from the scarcity of single-photon components within coherent light, inherently bounded by a maximum of $1/e$. Here, we report comprehensive demonstrations of single-photon-source-based high-rate QKD, surpassing the fundamental SKR limit imposed by the weak coherent light. By employing an on-demand, bright single-photon source with an efficiency of 0.71(2), coupled with narrow-bandwidth filtering and random polarization modulation, we demonstrated a field QKD trial over a 14.6(1.1) dB-loss free-space urban channel, achieving a SKR of $1.08\times {10}^{-3}\mathrm{bits}$ per pulse. This SKR surpasses the practical limit of weak coherent-light-based QKD by 79%. These findings unequivocally demonstrate the superior performance of single-photon sources over weak coherent light for QKD applications, marking a pivotal stride towards realizing a global quantum internet.

Valley Hall phases (VHPs) in electronic and classical wave systems have been extensively explored and brought fruitful wave manipulations and associated applications. However, the concept of VHPs is so far restricted to two-dimensional (2D) systems. VHPs in 3D platforms remain an open question, which is not a straightforward extension of theirs 2D counterparts. In this work, we generalize the 2D VHPs into the 3D case in phononic crystals, which are derived from a nodal-line semimetal. The variation of geometric parameters gives rise to band inversion and generates two distinct VHPs possessing a pair of valleys with opposite Berry curvature distributions in the Brillouin zone. Topological surface states protected by the 3-tuple valley Chern numbers emerge at the interface between two different VHPs. Thanks to the configuration of the equal-frequency contour, some intriguing surface wave propagations have been observed experimentally. At the corner surrounded by two VHPs, interestingly, circular propagation of the surface wave exhibits negative refraction to form a closed loop around the corner. Furthermore, 3D partition is demonstrated in a four-channel structure. The 3D VHPs will stimulate other exotic transports, such as 3D collimation and wave guiding, and provide new means for designing 3D acoustic devices.

We singled out the surface and bulk spin dynamics in magnetic hollow nanoparticles by means of nuclear magnetic resonance relaxometry. Experimental ${}^1\mathrm{H}\text{−}\mathrm{NMR}$-dispersion curves (NMR-D), measured across a wide frequency range (${10}^4\mathrm{Hz}<f<3\times {10}^8\mathrm{Hz}$), show the presence of a high-frequency contribution to the longitudinal relaxation rate, evidenced for the first time and ascribed to the surface spin dynamics. The nuclear longitudinal relaxation rates were successfully analyzed by means of a phenomenological model accounting for the two spin populations, i.e., surface and core spins. The fit of the longitudinal NMR-D data by means of this model allowed for the estimation of the hyperfine coupling constant of the surface spins, and of the superparamagnetic $1/{\tau }_N$ and surface-paramagnetic-like $1/{\tau }_C^{\mathrm{surf}}$ spin-spin correlation frequency, the last one being larger by more than 1 order of magnitude. These experimental results provide a substantial contribution to the basic knowledge of spin dynamics in nanoscale systems.

The Worthington jets from bursting bubbles at a gas-liquid interface can break up into small droplets, aerosolizing chemical and biological substances into the atmosphere and impacting both global climate and public health. Despite their importance in contaminant transport, the influence of adsorbed contaminants on bubble-bursting jet dynamics remains poorly understood. Here, we document how an immiscible compound contaminant layer impacts the jet radius, which deviates from the expected jetting dynamics produced by clean bubble bursting. We rationalize the deviation of the jet radius by characterizing the propagation of the capillary waves at the air-oil-water interface. We develop a linearized wave damping model based on the oil thickness profile and the wave dispersion, and we propose a revised Ohnesorge number with a scaling relation that captures the experimental results reasonably well. Our work not only advances the fundamental understanding of bubble bursting jets but also offers valuable insights for predicting bubble-mediated aerosol size distributions and transport of airborne contaminants in realistic environmental scenarios.

We investigate electron heating by magnetic-field-aligned electric fields ($E_{\parallel }$) during antiparallel magnetic reconnection in the Earth’s magnetotail. Using a statistical sample of 140 reconnection outflows, we infer the acceleration potential associated with $E_{\parallel }$ from the shape of the electron velocity distribution functions. We show that heating by $E_{\parallel }$ in the reconnection outflow can reach up to 10 times the inflow electron temperature. We demonstrate that the magnitude of the acceleration potential scales with the inflow Alfvén and electron thermal speeds to maintain quasineutrality in the reconnection region. Our results suggest that, as the inflow plasma parameter ${\beta }_{e\infty }$ increases, $E_{\parallel }$ becomes increasingly important to the ion-to-electron energy partition associated with magnetic reconnection.

High-order nonlinear optical processes beyond four-wave mixing (${\chi }^{(3)}$) are crucial for advancing ultraviolet (UV) light sources and quantum technologies, yet their practical implementation remains challenging due to inherently weak high-order nonlinear susceptibilities and stringent broadband phase-matching requirements—limitations that persist even in state-of-the-art high-Q microresonators. A breakthrough transverse multiwave mixing scheme is proposed in a high-Q lithium niobate microresonator, only under a single continuous-wave (cw) laser pump. Our approach leverages self-organized subwavelength photorefractive gratings (SPGs) generated through a bidirectional stimulated Raman scattering (SRS) process in the microresonator, without using two external counterpropagating lasers. Under single-wavelength pumping (1546 nm), bidirectional SRS (1713 nm) spontaneously generates dynamic SPGs that enable dual-function control: (1) broadband momentum compensation ($\mathrm{\Delta }k\approx 2\pi /\mathrm{\Lambda }$, $\mathrm{\Lambda }=\text{grating}$ period) to resolve broadband phase-matching challenges in high-order nonlinear interactions and (2) preservation of ultrahigh-quality factor ($Q>7\times {10}^6$) for enhanced nonlinear conversion. Moreover, unlike conventional longitudinal configurations requiring more rigid multiwavelength resonance alignment, our transverse architecture decouples nonlinear processes from cavity-mode constraints through SPG-mediated momentum engineering, enabling simultaneous support for sum-frequency generation to six-wave mixing processes across 500-nm bandwidth with high conversion efficiencies. Furthermore, the cascaded SRS process is simultaneously activated to generate a light signal for subsequent nonlinear interactions. Consequently, this novel approach enables the first demonstration of single-pump phase-matched transverse SFG with record conversion efficiency ($590\%/\mathrm{W}$), and transverse multiwave mixing processes from ${\chi }^{(3)}$ (four-wave) to ${\chi }^{(5)}$ (six-wave) processes are achieved for the first time using only the single cw pump, leading to efficient visible and UV light generation, representing a notable advance in nonlinear integration.

Twisted graphene based moiré heterostructures host a flat band at the magic angles where the kinetic energy of the charge carriers is quenched and interaction effects dominate. This results in emergent phases such as superconductors and correlated insulators that are electrostatically tunable. We investigate superconductivity in twisted trilayer graphene by integrating it as the weak link in a superconducting quantum interference device. The measured current phase relation yields a large and tunable kinetic inductance, up to 150 nH per square, of the electron and hole-type intrinsic superconductors. We further show that the specific kinetic inductance and the critical current density are universally related via the superconducting coherence length, and extract an upper bound of $\sim 200\mathrm{nm}$ for the coherence length. We discuss the implications of a large coherence length in twisted graphene superconductors.

The equation of state of quantum chromodynamics with $N_f=3$ flavors is determined nonperturbatively in the range of temperatures between 3 and 165 GeV with a precision of about 0.5%–1.0%. The calculation is carried out by numerical simulations of lattice gauge theory discretized à la Wilson with shifted boundary conditions in the compact direction. At each given temperature the entropy density is computed at several lattice spacings in order to extrapolate the results to the continuum limit. Taken at face value, data point straight to the Stefan-Boltzmann value by following a linear behavior in the strong coupling constant squared. They are also compatible with the known perturbative formula supplemented by higher order terms in the coupling constant, a parametrization which describes well our data together with those present in the literature down to 500 MeV.

The emergence of hydrodynamic behavior in electronic flow within clean, particle-hole-symmetric systems at half filling is a nontrivial problem. Navier-Stokes (NS) equations describe the momentum flow, while experimental measurements typically capture the current flow profiles. However, in particle-hole-symmetric systems, electric current and momentum flow are entirely decoupled, because electrons and holes move in opposite directions with equal distribution functions. This makes it challenging to link NS equations to observed flow patterns. In this Letter, we demonstrate that the hydrodynamic behavior of the charge current at half filling can emerge despite the absence of momentum flow. By combining Boltzmann transport theory with numerically exact quantum Monte Carlo simulations of clean graphene samples, we show that NS-type equations can be derived directly for the charge current, eliminating the need for any additional mechanism coupling the velocity field and charge current in explaining the experimentally observed hydrodynamic flow profiles in graphene at half filling. We show that a new transport quantity—the current diffusion coefficient—replaces viscosity and expect this description to be valid for any particle-hole-symmetric system. Our results provide new insights into the interpretation of experimental data and demonstrate how quantum Monte Carlo calculations can serve as an alternative to experiments in transport measurements to verify the kinetic theory results.

Non-Fermi liquid (non-FL) phase is a pivotal enigma in understanding intriguing quantum phases in strongly correlated systems, such as high-temperature superconductivity. Tomonaga-Luttinger liquid (TLL) theory, designed for one-dimensional (1D) systems, serves as one of the microscopic frameworks that elucidates non-FL behavior. Despite its theoretical concreteness, comprehensive experimental verification has remained incomplete. In particular, addressing the persistence of the TLL nature within ordered phases, such as charge density wave (CDW), has posed a significant challenge. We report the observation of TLL characteristics across the CDW transitions in a quasi-1D material ${\mathrm{NbSe}}_3$ using angle-resolved photoemission spectroscopy. Spin-charge separation, a disentanglement of spin and charge degrees of freedom of electrons, is clearly observed within the band, accompanied by the suppression of spectral weight following a power-law behavior with anticipated temperature scaling. Surprisingly, the spin-charge separation persists even below the CDW transition temperatures, indicating the validity of the TLL nature in the CDW phase. Our findings offer a unique opportunity to explore the interplay between the TLL and ordered phases, which could be connected to the interplay between non-FL and ordered phases in strongly correlated systems.

The nonlinear response of yield stress fluids remains difficult to predict and control. Here, we show that the height of the overshoot in the loss modulus $G^{\prime \prime }$, a key characteristic of yielding, depends only on linear viscoelastic properties. Furthermore, the position of this overshoot depends on linear viscoelastic and flow properties, demonstrating the important and enduring role of elasticity in yielding. The physics governing linear viscoelasticity is therefore not only preserved during yielding but also controls two commonly reported yielding metrics.

We report on the first measurement of $J/\psi$ photoproduction from nuclei in the photon energy range of 7 to 10.8 GeV, extending above and below the photoproduction threshold in the free proton of $\sim 8.2\mathrm{GeV}$. The experiment used a tagged photon beam incident on deuterium, helium, and carbon, and the GlueX detector at Jefferson Lab to measure the semi-inclusive $A(\gamma ,e^{+}{e}^{-}p)$ reaction with a dilepton invariant mass $M(e^{+}{e}^{-})\sim m_{J/\psi }=3.1\mathrm{GeV}$. The incoherent $J/\psi$ photoproduction cross sections in the measured nuclei are extracted as a function of the incident photon energy, momentum transfer, and proton-reconstructed missing light-cone momentum fraction. Comparisons with theoretical predictions assuming a dipole form factor allow for extracting a gluonic radius for bound protons of $\sqrt{⟨r^2⟩}=0.85\pm 0.14\mathrm{fm}$. The data also suggest an excess of the measured cross section for subthreshold production and for interactions with high missing light-cone momentum fraction protons. The measured enhancement can be explained by modified gluon structure for high-virtuality bound protons.

We propose and experimentally demonstrate a method for laser cooling an oscillator, using a two-level ancillary spin, based on sequences of spin-state-dependent displacements, followed by spin repumping. For a thermal state with mean occupation $\overline{n}\gg 1$, the method attains a reduction to 0.632 of the initial thermal oscillator occupation for two repumps of the spin state. This is within a factor of 2.53 of the optimum that is expected due to the reduction of the oscillator entropy by 2ln(2). We show that the method, which is based on encoding the value of the modular variable of the oscillator into the spin, has a simple semiclassical description in terms of a Bayesian update. We demonstrate the method experimentally using the internal and motional states of a single trapped ion.