High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in tabletop. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled state. We also demonstrate its practical application in entanglement-based quantum key distribution (QKD). One pair of polarization spatial-mode hyperentanglement was distributed over 11 km multicore fiber (noisy channel). After purification, the fidelity of polarization entanglement arises from 0.771 to 0.887 and the effective key rate in entanglement-based QKD increases from 0 to 0.332. The values of Clauser-Horne-Shimony-Holt inequality of polarization entanglement arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement and deterministic controlled-NOT gates, the total purification efficiency can be estimated as $6.6\times {10}^3$ times than the experiment using two pairs of entangled states with spontaneous parametric down-conversion sources. Our results offer the potential to be implemented as part of a full quantum repeater and large-scale quantum network.

Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field.

Ice nucleation is a phenomenon that, despite the relevant implications for life, atmospheric sciences, and technological applications, is far from being completely understood, especially under extreme thermodynamic conditions. In this work we present a computational investigation of the homogeneous ice nucleation at negative pressures. By means of the seeding technique we estimate the size of the ice critical nucleus $N_c$ for the TIP4P/Ice water model. This is done along the isotherms 230, 240, and 250 K, from positive to negative pressures until reaching the liquid-gas kinetic stability limit (where cavitation cannot be avoided). We find that $N_c$ is nonmonotonic upon depressurization, reaching a minimum at negative pressures in the doubly metastable region of water. According to classical nucleation theory we establish the nucleation rate $J$ and the surface tension $\gamma$, revealing a retracing behavior of both when the liquid-gas kinetic stability limit is approached. We also predict a reentrant behavior of the homogeneous nucleation line. The reentrance of these properties is related to the reentrance of the coexistence line at negative pressure, revealing new anomalies of water. The results of this work suggest the possibility of having metastable samples of liquid water for long times at negative pressure provided that heterogeneous nucleation is suppressed.

We report measurements of the thermal Hall effect in single crystals of both pristine and isotopically substituted strontium titanate. We discovered a 2 orders of magnitude difference in the thermal Hall conductivity between ${\mathrm{SrTi}}^{16}{\mathrm{O}}_3$ and ${}^{18}\mathrm{O}$-enriched ${\mathrm{SrTi}}^{18}{\mathrm{O}}_3$ samples. In most temperature ranges, the magnitude of thermal Hall conductivity (${\kappa }_{xy}$) in ${\mathrm{SrTi}}^{18}{\mathrm{O}}_3$ is proportional to the magnitude of the longitudinal thermal conductivity (${\kappa }_{xx}$), which suggests a phonon-mediated thermal Hall effect. However, they deviate in the temperature of their maxima, and the thermal Hall angle ratio ($|{\kappa }_{xy}/{\kappa }_{xx}|$) shows anomalously decreasing behavior below the ferroelectric Curie temperature $T_c\sim 25\mathrm{K}$. This observation suggests a new underlying mechanism, as the conventional scenario cannot explain such differences within the slight change in phonon spectrum. Notably, the difference in magnitude of thermal Hall conductivity and rapidly decreasing thermal Hall angle ratio in ${\mathrm{SrTi}}^{18}{\mathrm{O}}_3$ is correlated with the strength of quantum critical fluctuations in this displacive ferroelectric. This relation points to a link between the quantum critical physics of strontium titanate and its thermal Hall effect, a possible clue to explain this example of an exotic phenomenon in nonmagnetic insulating systems.

Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated.

A magnetic impurity on a superconductor induces Yu-Shiba-Rusinov (YSR) bound states, detected by tunneling spectroscopy as long-lived quasiparticle excitations inside the superconducting gap. Coupled YSR states constitute basic elements to engineer artificial superconducting states, but their substrate-mediated interactions are generally weak. In this Letter, we report that intramolecular (Hund’s-like) exchange interactions produce coupled YSR states across a molecular platform. We measured YSR spectra along a magnetic iron-porphyrin on Pb(111) and found evidence of two distinct interaction channels, which invert their particle-hole asymmetry across the molecule. Numerical calculations show that the identical YSR asymmetry pattern of the two channels is caused by two spin-hosting orbitals with opposite potential scattering and coupled strongly. Both channels can be similarly excited by tunneling electrons into each orbital, depicting a new scenario for entangled superconducting bound states using molecular platforms.

Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that knots tied by the eigenenergy strings provide a complete topological classification of one-dimensional non-Hermitian (NH) Hamiltonians with separable bands. A ${\mathbb{Z}}_2$ knot invariant, the global biorthogonal Berry phase $Q$ as the sum of the Wilson loop eigenphases, is proved to be equal to the permutation parity of the NH bands. We show the transition between two phases characterized by distinct knots occur through exceptional points and come in two types. We further develop an algorithm to construct the corresponding tight-binding NH Hamiltonian for any desired knot, and propose a scheme to probe the knot structure via quantum quench. The theory and algorithm are demonstrated by model Hamiltonians that feature, for example, the Hopf link, the trefoil knot, the figure-8 knot, and the Whitehead link.

It was recently shown that a scalar field suitably coupled to the Gauss-Bonnet invariant $\mathcal{G}$ can undergo a spin-induced linear tachyonic instability near a Kerr black hole. This instability appears only once the dimensionless spin $j$ is sufficiently large, that is, $j\gtrsim 0.5$. A tachyonic instability is the hallmark of spontaneous scalarization. Focusing, for illustrative purposes, on a class of theories that do exhibit this instability, we show that stationary, rotating black hole solutions do indeed have scalar hair once the spin-induced instability threshold is exceeded, while black holes that lie below the threshold are described by the Kerr solution. Our results provide strong support for spin-induced black hole scalarization.

We construct black hole solutions with spin-induced scalarization in a class of models where a scalar field is quadratically coupled to the topological Gauss-Bonnet term. Starting from the tachyonically unstable Kerr solutions, we obtain families of scalarized black holes such that the scalar field has either even or odd parity, and we investigate their domain of existence. The scalarized black holes can violate the Kerr rotation bound. We identify “critical” families of scalarized black hole solutions such that the expansion of the metric functions and of the scalar field at the horizon no longer allows for real coefficients. For the quadratic coupling considered here, solutions with spin-induced scalarization are entropically favored over Kerr solutions with the same mass and angular momentum.

Deep inelastic scattering of $e^{\pm }$ off protons is sensitive to contributions from “dark photon” exchange. Using HERA data fit to HERA’s parton distribution functions (PDFs), we obtain the model-independent bound $\epsilon \lesssim 0.02$ on the kinetic mixing between hypercharge and the dark photon for dark photon masses $\lesssim 10\mathrm{GeV}$. This slightly improves on the bound obtained from electroweak precision observables. For higher masses, the limit weakens monotonically; $\epsilon \lesssim 1$ for a dark photon mass of 5 TeV. Utilizing PDF sum rules, we demonstrate that the effects of the dark photon cannot be (trivially) absorbed into refit PDFs and, in fact, lead to non–Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (Bjorken $x_B$-independent) scaling violations that could provide a smoking gun in data. The proposed $e^{\pm }p$ collider operating at $\sqrt{s}=1.3\mathrm{TeV}$ (Large Hadron Electron Collider) is anticipated to accumulate ${10}^3$ times the luminosity of HERA, providing substantial improvements in probing the effects of a dark photon: sensitivity to $\epsilon$ well below that probed by electroweak precision data is possible throughout virtually the entire dark photon mass range, as well as being able to probe to much higher dark photon masses, up to 100 TeV.

We report the first measurement of coherent elastic neutrino-nucleus scattering (CEvNS) on argon using a liquid argon detector at the Oak Ridge National Laboratory Spallation Neutron Source. Two independent analyses prefer CEvNS over the background-only null hypothesis with greater than $3\sigma$ significance. The measured cross section, averaged over the incident neutrino flux, is $(2.2\pm 0.7)\times {10}^{-39}{\mathrm{cm}}^2$—consistent with the standard model prediction. The neutron-number dependence of this result, together with that from our previous measurement on CsI, confirms the existence of the CEvNS process and provides improved constraints on nonstandard neutrino interactions.

Investigating the relationship between structure and dynamical processes is a central goal in condensed matter physics. Perhaps the most noted relationship between the two is the phenomenon of de Gennes narrowing, in which relaxation times in liquids are proportional to the scattering structure factor. Here, a similar relationship is discovered during the self-organized ion-beam nanopatterning of silicon using coherent x-ray scattering. However, in contrast to the exponential relaxation of fluctuations in classic de Gennes narrowing, the dynamic surface exhibits a wide range of behaviors as a function of the length scale, with a compressed exponential relaxation at lengths corresponding to the dominant structural motif—self-organized nanoscale ripples. These behaviors are reproduced in simulations of a nonlinear model describing the surface evolution. We suggest that the compressed exponential behavior observed here is due to the morphological persistence of the self-organized surface ripple patterns which form and evolve during ion-beam nanopatterning.

Using x-ray photoelectron spectroscopy of the oxygen $1s$ core level, the ratio between intact (${\mathrm{D}}_2\mathrm{O}$) and dissociated (OD) water in the hydrated stoichiometric ${\mathrm{TiO}}_2(110)$ surface is determined at varying coverage and temperature. In the submonolayer regime, both the ${\mathrm{D}}_2\mathrm{O}:\mathrm{OD}$ ratio and the core-level binding energy of ${\mathrm{D}}_2\mathrm{O}$ ($\mathrm{\Delta }\mathrm{BE}$) decrease with temperature. The observed variations in $\mathrm{\Delta }\mathrm{BE}$ are shown with density functional theory to be governed crucially and solely by the local hydrogen bonding environment, revealing a generally applicable classification and details about adsorption motifs.

We demonstrate ground state tunability for a hybrid artificial spin ice composed of Fe nanomagnets which are subject to site-specific exchange-bias fields, applied in integer multiples of the lattice along one sublattice of the classic square artificial spin ice. By varying this period, three distinct magnetic textures are identified: a striped ferromagnetic phase; an antiferromagnetic phase attainable through an external field protocol alone; and an unconventional ground state with magnetically charged pairs embedded in an antiferromagnetic matrix. Monte Carlo simulations support the results of field protocols and demonstrate that the pinning tunes relaxation timescales and their critical behavior.

Over the past several years, a new generation of quantum simulations has greatly expanded our understanding of charge density wave phase transitions in Hamiltonians with coupling between local phonon modes and the on-site charge density. A quite different, and interesting, case is one in which the phonons live on the bonds, and hence modulate the electron hopping. This situation, described by the Su-Schrieffer-Heeger (SSH) Hamiltonian, has so far only been studied with quantum Monte Carlo in one dimension. Here we present results for the 2D SSH model, show that a bond ordered wave (BOW) insulator is present in the ground state at half filling, and argue that a critical value of the electron-phonon coupling is required for its onset, in contradistinction with the 1D case where BOW exists for any nonzero coupling. We determine the precise nature of the bond ordering pattern, which has hitherto been controversial, and the critical transition temperature, which is associated with a spontaneous breaking of ${\mathcal{Z}}_4$ symmetry.

Target search by active agents in rugged energy landscapes has remained a challenge because standard enhanced sampling methods do not apply to irreversible dynamics. We overcome this nonequilibrium rare-event problem by developing an algorithm generalizing transition-path sampling to active Brownian dynamics. This method is exemplified and benchmarked for a paradigmatic two-dimensional potential with a high barrier. We find that even in such a simple landscape the structure and kinetics of the ensemble of transition paths changes drastically in the presence of activity. Indeed, active Brownian particles reach the target more frequently than passive Brownian particles, following longer and counterintuitive search patterns.