The 100 most-cited articles in Physical Review Letters, 2021

We present the first results of the Fermilab National Accelerator Laboratory (FNAL) Muon g -2 Experiment for the positive muon magnetic anomaly a μ ≡ ðg μ -2Þ=2.The anomaly is determined from the precision measurements of two angular frequencies.Intensity variation of high-energy positrons from muon decays directly encodes the difference frequency ω a between the spin-precession and cyclotron frequencies for polarized muons in a magnetic storage ring.The storage ring magnetic field is measured using nuclear magnetic resonance probes calibrated in terms of the equivalent proton spin precession frequency ω0 p in a spherical water sample at 34.7 °C.The ratio ω a = ω0 p , together with known fundamental constants, determines a μ ðFNALÞ ¼ 116 592 040ð54Þ × 10 -11 (0.46 ppm).The result is 3.3 standard deviations greater than the standard model prediction and is in excellent agreement with the previous Brookhaven National Laboratory (BNL) E821 measurement.After combination with previous measurements of both μ þ and μ -, the new experimental average of a μ ðExpÞ ¼ 116 592 061ð41Þ × 10 -11…

Scaling up to a large number of qubits with high-precision control is essential in the demonstrations of quantum computational advantage to exponentially outpace the classical hardware and algorithmic improvements. Here, we develop a two-dimensional programmable superconducting quantum processor, Zuchongzhi, which is composed of 66 functional qubits in a tunable coupling architecture. To characterize the performance of the whole system, we perform random quantum circuits sampling for benchmarking, up to a system size of 56 qubits and 20 cycles. The computational cost of the classical simulation of this task is estimated to be 2-3 orders of magnitude higher than the previous work on 53-qubit Sycamore processor [Nature 574, 505 (2019)NATUAS0028-083610.1038/s41586-019-1666-5. We estimate that the sampling task finished by Zuchongzhi in about 1.2 h will take the most powerful supercomputer at least 8 yr. Our work establishes an unambiguous quantum computational advantage that is infeasible for classical computation in a reasonable amount of time. The high-precision and programmable…

We present results from an analysis of all data taken by the BICEP2, Keck Array, and BICEP3 CMB polarization experiments up to and including the 2018 observing season. We add additional Keck Array observations at 220 GHz and BICEP3 observations at 95 GHz to the previous 95/150/220 GHz dataset. The Q/U maps now reach depths of 2.8, 2.8, and 8.8 μK_{CMB} arcmin at 95, 150, and 220 GHz, respectively, over an effective area of ≈600 square degrees at 95 GHz and ≈400 square degrees at 150 and 220 GHz. The 220 GHz maps now achieve a signal-to-noise ratio on polarized dust emission exceeding that of Planck at 353 GHz. We take auto- and cross-spectra between these maps and publicly available WMAP and Planck maps at frequencies from 23 to 353 GHz and evaluate the joint likelihood of the spectra versus a multicomponent model of lensed ΛCDM+r+dust+synchrotron+noise. The foreground model has seven parameters, and no longer requires a prior on the frequency spectral index of the dust emission taken from measurements on other regions of the sky. This model is an adequate description of the data at…

We report a precision measurement of the parity-violating asymmetry A_{PV} in the elastic scattering of longitudinally polarized electrons from ^{208}Pb. We measure A_{PV}=550±16(stat)±8(syst) parts per billion, leading to an extraction of the neutral weak form factor F_{W}(Q^{2}=0.00616 GeV^{2})=0.368±0.013. Combined with our previous measurement, the extracted neutron skin thickness is R_{n}-R_{p}=0.283±0.071 fm. The result also yields the first significant direct measurement of the interior weak density of ^{208}Pb: ρ_{W}^{0}=-0.0796±0.0036(exp)±0.0013(theo) fm^{-3} leading to the interior baryon density ρ_{b}^{0}=0.1480±0.0036(exp)±0.0013(theo) fm^{-3}. The measurement accurately constrains the density dependence of the symmetry energy of nuclear matter near saturation density, with implications for the size and composition of neutron stars.

Spin-current generation by electrical means is among the core phenomena driving the field of spintronics. Using ab initio calculations we show that a room-temperature metallic collinear antiferromagnet RuO_{2} allows for highly efficient spin-current generation, arising from anisotropically spin-split bands with conserved up and down spins along the Néel vector axis. The zero net moment antiferromagnet acts as an electrical spin splitter with a 34° propagation angle between spin-up and spin-down currents. The corresponding spin conductivity is a factor of 3 larger than the record value from a survey of 20 000 nonmagnetic spin-Hall materials. We propose a versatile spin-splitter-torque concept circumventing limitations of spin-transfer and spin-orbit torques in present magnetic memory devices.

Laboratory experiments sensitive to the equation of state of neutron rich matter in the vicinity of nuclear saturation density provide the first rung in a "density ladder" that connects terrestrial experiments to astronomical observations. In this context, the neutron skin thickness of ^{208}Pb (R_{skin}^{208}) provides a stringent laboratory constraint on the density dependence of the symmetry energy. In turn, an improved value of R_{skin}^{208} has been reported recently by the PREX collaboration. Exploiting the strong correlation between R_{skin}^{208} and the slope of the symmetry energy L within a specific class of relativistic energy density functionals, we report a value of L=(106±37) MeV-which systematically overestimates current limits based on both theoretical approaches and experimental measurements. The impact of such a stiff symmetry energy on some critical neutron-star observables is also examined.

We report the first dark matter search results using the commissioning data from PandaX-4T. Using a time projection chamber with 3.7 tonne of liquid xenon target and an exposure of 0.63 tonne·year, 1058 candidate events are identified within an approximate nuclear recoil energy window between 5 and 100 keV. No significant excess over background is observed. Our data set a stringent limit to the dark matter-nucleon spin-independent interactions, with a lowest excluded cross section (90% C.L.) of 3.8×10^{-47} cm^{2} at a dark matter mass of 40 GeV/c^{2}.

Kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) exhibit intriguing superconductivity below 0.9∼2.5 K, a charge density wave (CDW) transition around 80∼100 K, and Z_{2} topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the 2×2×2 CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial Z_{2}-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity T_{c} in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our…

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic constraints in neural networks via constraints in the architecture or the loss function. Applied to convective processes for climate modeling, architectural constraints enforce conservation laws to within machine precision without degrading performance. Enforcing constraints also reduces errors in the subsets of the outputs most impacted by the constraints.

We report phase-programmable Gaussian boson sampling (GBS) which produces up to 113 photon detection events out of a 144-mode photonic circuit. A new high-brightness and scalable quantum light source is developed, exploring the idea of stimulated emission of squeezed photons, which has simultaneously near-unity purity and efficiency. This GBS is programmable by tuning the phase of the input squeezed states. The obtained samples are efficiently validated by inferring from computationally friendly subsystems, which rules out hypotheses including distinguishable photons and thermal states. We show that our GBS experiment passes a nonclassicality test based on inequality constraints, and we reveal nontrivial genuine high-order correlations in the GBS samples, which are evidence of robustness against possible classical simulation schemes. This photonic quantum computer, Jiuzhang 2.0, yields a Hilbert space dimension up to ∼10^{43}, and a sampling rate ∼10^{24} faster than using brute-force simulation on classical supercomputers.

Quasi-bound states in the continuum (QBICs) are Fano resonant states with long optical lifetimes controlled by symmetry-breaking perturbations. While conventional Fano responses are limited to linear polarizations and do not support tailored phase control, here we introduce QBICs born of chiral perturbations that encode arbitrary elliptical polarization states and enable geometric phase engineering. We thereby design metasurfaces with ultrasharp spectral features that shape the impinging wave front with near-unity efficiency. Our findings extend Fano resonances beyond their conventional limits, opening opportunities for nanophotonics, classical and quantum optics, and acoustics.

CsV_{3}Sb_{5} is a newly discovered Z_{2} topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at T^{*}=94 K and superconductivity (SC) at T_{c}=2.5 K at ambient pressure. Here, we study the interplay between CDW and SC in CsV_{3}Sb_{5} via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at P_{c1}≈0.6-0.9 GPa before it vanishes completely at P_{c2}≈2 GPa. Correspondingly, T_{c}(P) displays an unusual M-shaped double dome with two maxima around P_{c1} and P_{c2}, respectively, leading to a tripled enhancement of T_{c} to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range P_{c1}≤P≤P_{c2} as evidenced by the broad superconducting transition and reduced superconducting volume fraction.…

Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum approximate optimization algorithms that solve ground state problems from quantum chemistry and binary optimization problems, respectively. They are based on the idea of using a classical computer to train a parametrized quantum circuit. We show that the corresponding classical optimization problems are NP-hard. Moreover, the hardness is robust in the sense that, for every polynomial time algorithm, there are instances for which the relative error resulting from the classical optimization problem can be arbitrarily large assuming that P≠NP. Even for classically tractable systems composed of only logarithmically many qubits or free fermions, we show the optimization to be NP-hard. This elucidates that the classical optimization is intrinsically hard and does not merely inherit the hardness from the ground state problem. Our analysis shows that the training landscape can have many far from optimal…

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII^{''} and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

We perform a comprehensive study of Milky Way (MW) satellite galaxies to constrain the fundamental properties of dark matter (DM). This analysis fully incorporates inhomogeneities in the spatial distribution and detectability of MW satellites and marginalizes over uncertainties in the mapping between galaxies and DM halos, the properties of the MW system, and the disruption of subhalos by the MW disk. Our results are consistent with the cold, collisionless DM paradigm and yield the strongest cosmological constraints to date on particle models of warm, interacting, and fuzzy dark matter. At 95% confidence, we report limits on (i) the mass of thermal relic warm DM, m_{WDM}>6.5 keV (free-streaming length, λ_{fs}≲10h^{-1} kpc), (ii) the velocity-independent DM-proton scattering cross section, σ_{0}<8.8×10^{-29} cm^{2} for a 100 MeV DM particle mass [DM-proton coupling, c_{p}≲(0.3 GeV)^{-2}], and (iii) the mass of fuzzy DM, m_{ϕ}>2.9×10^{-21} eV (de Broglie wavelength, λ_{dB}≲0.5 kpc). These constraints are complementary to other observational and laboratory constraints on DM properties.

Bound states in the continuum (BICs) confine resonances embedded in a continuous spectrum by eliminating radiation loss. Merging multiple BICs provides a promising approach to further reduce the scattering losses caused by fabrication imperfections. However, to date, BIC merging has been limited to only the Γ point, which constrains potential application scenarios such as beam steering and directional vector beams. Here, we propose a new scheme to construct merging BICs at almost an arbitrary point in reciprocal space. Our approach utilizes the topological features of BICs on photonic crystal slabs, and we merge a Friedrich-Wintgen BIC and an accidental BIC. The Q factors of the resulting merging BIC are enhanced for a broad wave vector range compared with both the original Friedrich-Wintgen BIC and the accidental BIC. Since Friedrich-Wintgen BICs and accidental BICs are quite common in the band structure, our proposal provides a general approach to realize off-Γ merging BICs with superhigh Q factors that can substantially enhance nonlinear and quantum effects and boost the…

Motivated by the recent discovery of unconventional charge order, we develop a theory of electronically mediated charge density wave formation in the family of kagome metals AV_{3}Sb_{5} (A=K,Rb,Cs). The intertwining of van Hove filling and sublattice interference suggests a three-fold charge density wave instability at T_{CDW}. From there, the charge order forming below T_{CDW} can unfold into a variety of phases capable of exhibiting orbital currents and nematicity. We develop a Ginzburg Landau formalism to stake out the parameter space of kagome charge order. We find a nematic chiral charge order to be energetically preferred, which shows tentative agreement with experimental evidence.

We analyze the quantum trajectory dynamics of free fermions subject to continuous monitoring. For weak monitoring, we identify a novel dynamical regime of subextensive entanglement growth, reminiscent of a critical phase with an emergent conformal invariance. For strong monitoring, however, the dynamics favors a transition into a quantum Zeno-like area-law regime. Close to the critical point, we observe logarithmic finite size corrections, indicating a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition. This uncovers an unconventional entanglement transition in an elementary, physically realistic model for weak continuous measurements. In addition, we demonstrate that the measurement aspect in the dynamics is crucial for whether or not a phase transition takes place.

We present a new bound on the ultralight axion (ULA) dark matter mass ${m}_{\mathrm{a}}$, using the Lyman-alpha forest to look for suppressed cosmic structure growth: a 95% lower limit ${m}_{\mathrm{a}}>2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }\mathrm{eV}$. This strongly disfavors ($>99.7%$ credibility) the canonical ULA with ${10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}<{m}_{\mathrm{a}}<{10}^{\ensuremath{-}21}\text{ }\text{ }\mathrm{eV}$, motivated by the string axiverse and solutions to possible tensions in the cold dark matter model. We strengthen previous equivalent bounds by about an order of magnitude. We demonstrate the robustness of our results using an optimized emulator of improved hydrodynamical simulations.

The NANOGrav Collaboration has recently published strong evidence for a stochastic common-spectrum process that may be interpreted as a stochastic gravitational wave background. We show that such a signal can be explained by second-order gravitational waves produced during the formation of primordial black holes from the collapse of sizeable scalar perturbations generated during inflation. This possibility has two predictions: (i) the primordial black holes may comprise the totality of the dark matter with the dominant contribution to their mass function falling in the range (10^{-15}÷10^{-11})M_{⊙} and (ii) the gravitational wave stochastic background will be seen as well by the Laser Interferometer Space Antenna experiment.

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…

The discoveries of high-temperature superconductivity in ${\mathrm{H}}_{3}\mathrm{S}$ and ${\mathrm{LaH}}_{10}$ have excited the search for superconductivity in compressed hydrides, finally leading to the first discovery of a room-temperature superconductor in a carbonaceous sulfur hydride. In contrast to rapidly expanding theoretical studies, high-pressure experiments on hydride superconductors are expensive and technically challenging. Here, we experimentally discovered superconductivity in two new phases, $Fm\overline{3}m\text{\ensuremath{-}}{\mathrm{CeH}}_{10}$ (SC-I phase) and $P{6}_{3}/mmc\text{\ensuremath{-}}{\mathrm{CeH}}_{9}$ (SC-II phase) at pressures that are much lower ($<100\text{ }\text{ }\mathrm{GPa}$) than those needed to stabilize other polyhydride superconductors. Superconductivity was evidenced by a sharp drop of the electrical resistance to zero and decreased critical temperature in deuterated samples and in external magnetic field. SC-I has ${T}_{c}=115\text{ }\text{ }\mathrm{K}$ at 95 GPa, showing an expected decrease in further compression due to the decrease…

The recent discovery of AV_{3}Sb_{5} (A=K,Rb,Cs) has uncovered an intriguing arena for exotic Fermi surface instabilities in a kagome metal. Among them, superconductivity is found in the vicinity of multiple van Hove singularities, exhibiting indications of unconventional pairing. We show that the sublattice interference mechanism is central to understanding the formation of superconductivity in a kagome metal. Starting from an appropriately chosen minimal tight-binding model with multiple van Hove singularities close to the Fermi level for AV_{3}Sb_{5}, we provide a random phase approximation analysis of superconducting instabilities. Nonlocal Coulomb repulsion, the sublattice profile of the van Hove bands, and the interaction strength turn out to be the crucial parameters to determine the preferred pairing symmetry. Implications for potentially topological surface states are discussed, along with a proposal for additional measurements to pin down the nature of superconductivity in AV_{3}Sb_{5}.

Pancharatnam-Berry geometric phase has attracted enormous interest in subwavelength optics and electromagnetics during the past several decades. Traditional theory predicts that the geometric phase is equal to twice the rotation angle of anisotropic elements. Here, we show that high-order geometric phases equal to multiple times the rotation angle could be achieved by meta-atoms with highfold rotational symmetries. As a proof of concept, the broadband angular spin Hall effect of light and optical vortices is experimentally demonstrated by using plasmonic metasurfaces consisting of space-variant nanoapertures with C2, C3, and C5 rotational symmetries. The results provide a fundamentally new understanding of the geometric phase as well as light-matter interaction in nanophotonics.

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 3σ significance. The measured cross section, averaged over the incident neutrino flux, is (2.2±0.7)×10^{-39} 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.

Pulsar timing data used to provide upper limits on a possible stochastic gravitational wave background (SGWB). However, the NANOGrav Collaboration has recently reported strong evidence for a stochastic common-spectrum process, which we interpret as a SGWB in the framework of cosmic strings. The possible NANOGrav signal would correspond to a string tension Gμ∈(4×10^{-11},10^{-10}) at the 68% confidence level, with a different frequency dependence from supermassive black hole mergers. The SGWB produced by cosmic strings with such values of Gμ would be beyond the reach of LIGO, but could be measured by other planned and proposed detectors such as SKA, LISA, TianQin, AION-1 km, AEDGE, Einstein Telescope, and Cosmic Explorer.

We study the performance of classical and quantum machine learning (ML) models in predicting outcomes of physical experiments. The experiments depend on an input parameter x and involve execution of a (possibly unknown) quantum process E. Our figure of merit is the number of runs of E required to achieve a desired prediction performance. We consider classical ML models that perform a measurement and record the classical outcome after each run of E, and quantum ML models that can access E coherently to acquire quantum data; the classical or quantum data are then used to predict the outcomes of future experiments. We prove that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model. In contrast, for achieving an accurate prediction on all inputs, we prove that the exponential quantum advantage is possible. For example, to predict the expectations of all Pauli observables in an n-qubit system ρ, classical ML models require 2^{Ω(n)} copies of ρ, but we present a quantum…

We demonstrate unprecedented accuracy for rapid gravitational wave parameter estimation with deep learning. Using neural networks as surrogates for Bayesian posterior distributions, we analyze eight gravitational wave events from the first LIGO-Virgo Gravitational-Wave Transient Catalog and find very close quantitative agreement with standard inference codes, but with inference times reduced from O(day) to 20 s per event. Our networks are trained using simulated data, including an estimate of the detector noise characteristics near the event. This encodes the signal and noise models within millions of neural-network parameters and enables inference for any observed data consistent with the training distribution, accounting for noise nonstationarity from event to event. Our algorithm-called "DINGO"-sets a new standard in fast and accurate inference of physical parameters of detected gravitational wave events, which should enable real-time data analysis without sacrificing accuracy.

Detecting the orientation of the Néel vector is a major research topic in antiferromagnetic spintronics. Here we recognize the intrinsic nonlinear Hall effect, which is independent of the relaxation time, as a prominent contribution to the time-reversal-odd second order conductivity and can be used to detect the reversal of the Néel vector. In contrast, the Berry-curvature-dipole-induced nonlinear Hall effect depends linearly on relaxation time and is time-reversal even. We study the intrinsic nonlinear Hall effect in an antiferromagnetic metal: tetragonal CuMnAs, and show that its nonlinear Hall conductivity can reach the order of mA/V^{2}. The dependence on the chemical potential of such nonlinear Hall conductivity can be qualitatively explained by a tilted massive Dirac model. Moreover, we demonstrate its strong temperature dependence and briefly discuss its competition with the second order Drude conductivity. Finally, a complete survey of magnetic point groups is presented, providing guidelines for finding more antiferromagnetic materials with the intrinsic nonlinear Hall…

The North American Nanohertz Observatory for Gravitational Waves has recently reported strong evidence for a stochastic common-spectrum process affecting the pulsar timing residuals in its 12.5-year data set. We demonstrate that this process admits an interpretation in terms of a stochastic gravitational-wave background emitted by a cosmic-string network in the early Universe. We study stable Nambu-Goto strings in dependence of their tension Gμ and loop size α and show that the entire viable parameter space will be probed by an array of future experiments.

We report the results from a haloscope search for axion dark matter in the 3.3-4.2 μeV mass range. This search excludes the axion-photon coupling predicted by one of the benchmark models of "invisible" axion dark matter, the Kim-Shifman-Vainshtein-Zakharov model. This sensitivity is achieved using a large-volume cavity, a superconducting magnet, an ultra low noise Josephson parametric amplifier, and sub-Kelvin temperatures. The validity of our detection procedure is ensured by injecting and detecting blind synthetic axion signals.

We present the first experimental realization of a time crystal stabilized by dissipation. The central signature in our implementation in a driven open atom-cavity system is a period doubled switching between distinct checkerboard density wave patterns, induced by the interplay between controlled cavity dissipation, cavity-mediated interactions, and external driving. We demonstrate the robustness of this dynamical phase against system parameter changes and temporal perturbations of the driving.

Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G^{4}). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G^{3}) via its relation to the tail effect.

We predict the limits of existence of atomic nuclei, the proton and neutron drip lines, from the light through medium-mass regions. Starting from a chiral two- and three-nucleon interaction with good saturation properties, we use the valence-space in-medium similarity renormalization group to calculate ground-state and separation energies from helium to iron, nearly 700 isotopes in total. We use the available experimental data to quantify the theoretical uncertainties for our ab initio calculations towards the drip lines. Where the drip lines are known experimentally, our predictions are consistent within the estimated uncertainty. For the neutron-rich sodium to chromium isotopes, we provide predictions to be tested at rare-isotope beam facilities.

Flatbands appear in many condensed matter systems, including the two-dimensional electron gas in a high magnetic field, correlated materials, and moiré heterostructures. They are characterized by intrinsic geometric properties such as the Berry curvature and Fubini-Study metric. The influence of the band geometry on electron-electron interaction is difficult to understand analytically because the geometry is in general nonuniform in momentum space. In this work, we study the topological flatband of Chern number C=1 with a momentum-dependent but positive definite Berry curvature that fluctuates in sync with Fubini-Study metric. We derive an exact correspondence between such ideal flatbands and Landau levels and show that the band geometry fluctuation gives rise to a new type of interaction in the corresponding Landau levels that depends on the center of mass of two particles. We characterize such interactions by generalizing the usual Haldane pseudopotentials. This mapping gives exact zero-energy ground states for short-ranged repulsive generalized pseudopotentials in flatbands, in…

The superconductivity of a kagome superconductor CsV_{3}Sb_{5} is studied by scanning tunneling microscopy and spectroscopy at ultralow temperature with high resolution. Two kinds of superconducting gaps with multiple sets of coherent peaks and residual zero-energy density of states (DOS) are observed on both half-Cs and Sb surfaces, implying multiband superconductivity. In addition, in-gap states can be induced by magnetic impurities but not by nonmagnetic impurities, suggesting a sign-preserving or s-wave superconducting order parameter. Moreover, the interplay between charge density waves (CDW) and superconductivity differs on various bands, resulting in different density-of-states distributions. Our results suggest that the superconducting gap is likely isotropic on the sections of Fermi surface that play little roles in CDW, and the superconducting gaps on the sections of Fermi surface with anisotropic CDW gaps are likely anisotropic as well. The residual spectral weights at zero energy are attributed to the extremely small superconducting gap on the tiny oval Fermi pockets.…

We show that the recent NANOGrav result can be interpreted as a stochastic gravitational wave signal associated to formation of primordial black holes from high-amplitude curvature perturbations. The indicated amplitude and power of the gravitational wave spectrum agrees well with formation of primordial seeds for supermassive black holes.

We report, for the first time, the long-awaited detection of diffuse gamma rays with energies between 100 TeV and 1 PeV in the Galactic disk. Particularly, all gamma rays above 398 TeV are observed apart from known TeV gamma-ray sources and compatible with expectations from the hadronic emission scenario in which gamma rays originate from the decay of π^{0}'s produced through the interaction of protons with the interstellar medium in the Galaxy. This is strong evidence that cosmic rays are accelerated beyond PeV energies in our Galaxy and spread over the Galactic disk.

We propose a relativistic gravitational theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed cosmic microwave background and matter power spectra on linear cosmological scales. We show that its action expanded to second order is free of ghost instabilities and discuss its possible embedding in a more fundamental theory.

Advanced LIGO-Virgo have reported a short gravitational-wave signal (GW190521) interpreted as a quasicircular merger of black holes, one at least populating the pair-instability supernova gap, that formed a remnant black hole of ${M}_{f}\ensuremath{\sim}142\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ at a luminosity distance of ${d}_{L}\ensuremath{\sim}5.3\text{ }\text{ }\mathrm{Gpc}$. With barely visible pre-merger emission, however, GW190521 merits further investigation of the pre-merger dynamics and even of the very nature of the colliding objects. We show that GW190521 is consistent with numerically simulated signals from head-on collisions of two (equal mass and spin) horizonless vector boson stars (aka Proca stars), forming a final black hole with ${M}_{f}=23{1}_{\ensuremath{-}17}^{+13}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, located at a distance of ${d}_{L}=57{1}_{\ensuremath{-}181}^{+348}\text{ }\text{ }\mathrm{Mpc}$. This provides the first demonstration of close degeneracy between these two theoretical models, for a real gravitational-wave event. The favored mass for…

It was recently shown that a scalar field suitably coupled to the Gauss-Bonnet invariant 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≳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.

Nonmonotonic variation with collision energy (sqrt[s_{NN}]) of the moments of the net-baryon number distribution in heavy-ion collisions, related to the correlation length and the susceptibilities of the system, is suggested as a signature for the quantum chromodynamics critical point. We report the first evidence of a nonmonotonic variation in the kurtosis times variance of the net-proton number (proxy for net-baryon number) distribution as a function of sqrt[s_{NN}] with 3.1 σ significance for head-on (central) gold-on-gold (Au+Au) collisions measured solenoidal tracker at Relativistic Heavy Ion Collider. Data in noncentral Au+Au collisions and models of heavy-ion collisions without a critical point show a monotonic variation as a function of sqrt[s_{NN}].

Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalous Hall transport in magnets, an intrinsic effect can appear at the second order to the applied electric field. We show that this intrinsic second-order anomalous Hall effect is associated with an intrinsic band geometric property-the dipole moment of Berry-connection polarizability (BCP) in momentum space. The effect has scaling relation and symmetry constraints that are distinct from the previously studied extrinsic contributions. Particularly, in antiferromagnets with PT symmetry, the intrinsic effect dominates. Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the effect in the antiferromagnet Mn_{2}Au. We show that the BCP dipole and the resulting intrinsic second-order conductivity are pronounced around band near degeneracies. Importantly, the intrinsic response exhibits sensitive…

Systems with non-Hermitian skin effects are very sensitive to the imposed boundary conditions and lattice size, and thus an important question is whether non-Hermitian skin effects can survive when deviating from the open boundary condition. To unveil the origin of boundary sensitivity, we present exact solutions for one-dimensional non-Hermitian models with generalized boundary conditions and study rigorously the interplay effect of lattice size and boundary terms. Besides the open boundary condition, we identify the existence of non-Hermitian skin effect when one of the boundary hopping terms vanishes. Apart from this critical line on the boundary parameter space, we find that the skin effect is fragile under any tiny boundary perturbation in the thermodynamic limit, although it can survive in a finite size system. Moreover, we demonstrate that the non-Hermitian Su-Schreieffer-Heeger model exhibits a new phase diagram in the boundary critical line, which is different from either open or periodical boundary case.

Recently, a new family of symmetry-protected higher-order topological insulators has been proposed and was shown to host lower-dimensional boundary states. However, with the existence of the strong disorder in the bulk, the crystal symmetry is broken, and the associated corner states are disappeared. It is well known that the emergence of robust edge states and quantized transport can be induced by adding sufficient disorders into a topologically trivial insulator, that is the so-called topological Anderson insulator. The question is whether disorders can also cause the higher-order topological phase. This is not known so far, because interactions between disorders and the higher-order topological phases are completely different from those with the first-order topological system. Here, we demonstrate theoretically that the disorder-induced higher-order topological corner state and quantized fraction corner charge can appear in a modified Haldane model. In experiments, we construct the classical analog of such higher-order topological Anderson insulators using electric circuits and…

The high temperatures and strong magnetic fields of the solar corona form streams of solar wind that expand through the Solar System into interstellar space. At 09:33 UT on 28 April 2021 Parker Solar Probe entered the magnetized atmosphere of the Sun 13 million km above the photosphere, crossing below the Alfvén critical surface for five hours into plasma in casual contact with the Sun with an Alfvén Mach number of 0.79 and magnetic pressure dominating both ion and electron pressure. The spectrum of turbulence below the Alfvén critical surface is reported. Magnetic mapping suggests the region was a steady flow emerging on rapidly expanding coronal magnetic field lines lying above a pseudostreamer. The sub-Alfvénic nature of the flow may be due to suppressed magnetic reconnection at the base of the pseudostreamer, as evidenced by unusually low densities in this region and the magnetic mapping.

Exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce, are ubiquitous and unique features of non-Hermitian systems. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of two real parameters, which is less than the three parameters needed to generically find ordinary Hermitian eigenvalue degeneracies. Higher-order EPs generically require more fine-tuning, and are thus assumed to play a much less prominent role. Here, however, we illuminate how physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer. More saliently, third-order EPs generically require only two real tuning parameters in the presence of either a parity-time (PT) symmetry or a generalized chiral symmetry. Remarkably, we find that these different symmetries yield topologically distinct types of EPs. We illustrate our findings in simple models, and show how third-order EPs with a generic ∼k^{1/3} dispersion are protected by PT symmetry, while third-order EPs with a ∼k^{1/2} dispersion are protected by the…

We introduce a new class of primitive building blocks for realizing quantum logic elements based on nanoscale magnetization textures called skyrmions. In a skyrmion qubit, information is stored in the quantum degree of helicity, and the logical states can be adjusted by electric and magnetic fields, offering a rich operation regime with high anharmonicity. By exploring a large parameter space, we propose two skyrmion qubit variants depending on their quantized state. We discuss appropriate microwave pulses required to generate single-qubit gates for quantum computing, and skyrmion multiqubit schemes for a scalable architecture with tailored couplings. Scalability, controllability by microwave fields, operation time scales, and readout by nonvolatile techniques converge to make the skyrmion qubit highly attractive as a logical element of a quantum processor.

Parity-time (PT)-symmetric Hamiltonians have widespread significance in non-Hermitian physics. A PT-symmetric Hamiltonian can exhibit distinct phases with either real or complex eigenspectrum, while the transition points in between, the so-called exceptional points, give rise to a host of critical behaviors that holds great promise for applications. For spatially periodic non-Hermitian systems, PT symmetries are commonly characterized and observed in line with the Bloch band theory, with exceptional points dwelling in the Brillouin zone. Here, in nonunitary quantum walks of single photons, we uncover a novel family of exceptional points beyond this common wisdom. These "non-Bloch exceptional points" originate from the accumulation of bulk eigenstates near boundaries, known as the non-Hermitian skin effect, and inhabit a generalized Brillouin zone. Our finding opens the avenue toward a generalized PT-symmetry framework, and reveals the intriguing interplay between PT symmetry and non-Hermitian skin effect.

Using the recently established formalism of a worldline quantum field theory description of the classical scattering of two spinless black holes, we compute the far-field time-domain waveform of the gravitational waves produced in the encounter at leading order in the post-Minkowskian (weak field but generic velocity) expansion. We reproduce the previous results of Kovacs and Thorne in a highly economic way. Then, using the waveform, we extract the leading-order total radiated angular momentum and energy (including differential results). Our work may enable crucial improvements of gravitational-wave predictions in the regime of large relative velocities.

We compare two optical clocks based on the ${^{2}S}_{1/2}(F=0)\ensuremath{\rightarrow}{^{2}D}_{3/2}(F=2)$ electric quadrupole (E2) and the ${^{2}S}_{1/2}(F=0)\ensuremath{\rightarrow}{^{2}F}_{7/2}(F=3)$ electric octupole (E3) transition of ${^{171}\mathrm{Yb}}^{+}$ and measure the frequency ratio ${\ensuremath{\nu}}_{\mathrm{E}3}/{\ensuremath{\nu}}_{\mathrm{E}2}=0.932829404530965376(32)$, improving upon previous measurements by an order of magnitude. Using two caesium fountain clocks, we find ${\ensuremath{\nu}}_{E3}=642121496772645.10(8)\text{ }\text{ }\mathrm{Hz}$, the most accurate determination of an optical transition frequency to date. Repeated measurements of both quantities over several years are analyzed for potential violations of local position invariance. We improve by factors of about 20 and 2 the limits for fractional temporal variations of the fine structure constant $\ensuremath{\alpha}$ to $1.0(1.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}18}/\mathrm{yr}$ and of the proton-to-electron mass ratio $\ensuremath{\mu}$ to…

The neutrino floor is a theoretical lower limit on WIMP-like dark matter models that are discoverable in direct detection experiments. It is commonly interpreted as the point at which dark matter signals become hidden underneath a remarkably similar-looking background from neutrinos. However, it has been known for some time that the neutrino floor is not a hard limit, but can be pushed past with sufficient statistics. As a consequence, some have recently advocated for calling it the "neutrino fog" instead. The downside of current methods of deriving the neutrino floor are that they rely on arbitrary choices of experimental exposure and energy threshold. Here we propose to define the neutrino floor as the boundary of the neutrino fog, and develop a calculation free from these assumptions. The technique is based on the derivative of a hypothetical experimental discovery limit as a function of exposure, and leads to a neutrino floor that is only influenced by the systematic uncertainties on the neutrino flux normalizations. Our floor is broadly similar to those found in the literature,…

Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn_{6}Sn_{6} manifest the quantum transport properties analogical to those in the quantum-limit Chern magnet TbMn_{6}Sn_{6}. The topological transport in the family, including quantum oscillations with nontrivial Berry phase and large anomalous Hall effect arising from Berry curvature field, points to the existence of Chern gapped Dirac fermions. Our observation demonstrates a close relationship between rare-earth magnetism and topological electron structure, indicating the rare-earth elements can effectively engineer the Chern quantum phase in kagome magnets.

We propose tunable chiral bound states in a system composed of superconducting giant atoms and a Josephson photonic-crystal waveguide (PCW), with no analog in other quantum setups. The chiral bound states arise due to interference in the nonlocal coupling of a giant atom to multiple points of the waveguide. The chirality can be tuned by changing either the atom-waveguide coupling or the external bias of the PCW. Furthermore, the chiral bound states can induce directional dipole-dipole interactions between multiple giant atoms coupling to the same waveguide. Our proposal is ready to be implemented in experiments with superconducting circuits, where it can be used as a tunable toolbox to realize topological phase transitions and quantum simulations.

The symmetry energy and its density dependence are crucial inputs for many nuclear physics and astrophysics applications, as they determine properties ranging from the neutron-skin thickness of nuclei to the crust thickness and the radius of neutron stars. Recently, PREX-II reported a value of $0.283\ifmmode\pm\else\textpm\fi{}0.071\text{ }\text{ }\mathrm{fm}$ for the neutron-skin thickness of $^{208}\mathrm{Pb}$, implying a slope parameter $L=106\ifmmode\pm\else\textpm\fi{}37\text{ }\text{ }\mathrm{MeV}$, larger than most ranges obtained from microscopic calculations and other nuclear experiments. We use a nonparametric equation of state representation based on Gaussian processes to constrain the symmetry energy ${S}_{0}$, $L$, and ${R}_{\mathrm{skin}}^{^{208}\mathrm{Pb}}$ directly from observations of neutron stars with minimal modeling assumptions. The resulting astrophysical constraints from heavy pulsar masses, LIGO/Virgo, and NICER clearly favor smaller values of the neutron skin and $L$, as well as negative symmetry incompressibilities. Combining astrophysical data with…

We propose a method for the fast generation of nonclassical ground states of the Rabi model in the ultrastrong and deep-strong coupling regimes via the shortcuts-to-adiabatic (STA) dynamics. The time-dependent quantum Rabi model is simulated by applying parametric amplification to the Jaynes-Cummings model. Using experimentally feasible parametric drive, this STA protocol can generate large-size Schrödinger cat states, through a process that is ∼10 times faster compared to adiabatic protocols. Such fast evolution increases the robustness of our protocol against dissipation. Our method enables one to freely design the parametric drive, so that the target state can be generated in the lab frame. A largely detuned light-matter coupling makes the protocol robust against imperfections of the operation times in experiments.

We search for gravitational-wave signals produced by cosmic strings in the Advanced LIGO and Virgo full O3 dataset. Search results are presented for gravitational waves produced by cosmic string loop features such as cusps, kinks, and, for the first time, kink-kink collisions. A template-based search for short-duration transient signals does not yield a detection. We also use the stochastic gravitational-wave background energy density upper limits derived from the O3 data to constrain the cosmic string tension Gμ as a function of the number of kinks, or the number of cusps, for two cosmic string loop distribution models. Additionally, we develop and test a third model that interpolates between these two models. Our results improve upon the previous LIGO-Virgo constraints on Gμ by 1 to 2 orders of magnitude depending on the model that is tested. In particular, for the one-loop distribution model, we set the most competitive constraints to date: Gμ≲4×10^{-15}. In the case of cosmic strings formed at the end of inflation in the context of grand unified theories, these results challenge…

Using combined data from the Relativistic Heavy Ion and Large Hadron Colliders, we constrain the shear and bulk viscosities of quark-gluon plasma (QGP) at temperatures of ∼150-350 MeV. We use Bayesian inference to translate experimental and theoretical uncertainties into probabilistic constraints for the viscosities. With Bayesian model averaging we propagate an estimate of the model uncertainty generated by the transition from hydrodynamics to hadron transport in the plasma's final evolution stage, providing the most reliable phenomenological constraints to date on the QGP viscosities.

Abstract To mitigate the COVID-19 pandemic, it is key to slow down the spreading of the life-threatening coronavirus (SARS-CoV-2). This spreading mainly occurs through virus-laden droplets expelled at speaking, screaming, shouting, singing, coughing, sneezing, or even breathing [1–7]. To reduce infections through such respiratory droplets, authorities all over the world have introduced the so-called “2-meter distance rule” or “6-foot rule”. However, there is increasing empirical evidence, e.g. through the analysis of super-spreading events [6, 8–11], that airborne transmission of the coronavirus over much larger distances plays a major role [1–3, 7, 12–15], with tremendous implications for the risk assessment of coronavirus transmission. It is key to better and fundamentally understand the environmental ambient conditions under which airborne transmission of the coronavirus is likely to occur, in order to be able to control and adapt them. Here we employ direct numerical simulations of a typical respiratory aerosol in a turbulent jet of the respiratory event within a…

We study the spin polarization generated by the hydrodynamic gradients. In addition to the widely studied thermal vorticity effects, we identify an undiscovered contribution from the fluid shear. This shear-induced polarization (SIP) can be viewed as the fluid analog of strain-induced polarization observed in elastic and nematic materials. We obtain the explicit expression for SIP using the quantum kinetic equation and linear response theory. Based on a realistic hydrodynamic model, we compute the differential spin polarization along both the beam direction z[over ^] and the out-plane direction y[over ^] in noncentral heavy-ion collisions at sqrt[s_{NN}]=200 GeV, including both SIP and thermal vorticity effects. We find that SIP contribution always shows the same azimuthal angle dependence as experimental data and competes with thermal vorticity effects. In the scenario that Λ inherits and memorizes the spin polarization of a strange quark, SIP wins the competition, and the resulting azimuthal angle dependent spin polarization P_{y} and P_{z} agree qualitatively with the…

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-André model, with an energy-dependent self-duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing low and high energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model's tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of high energy states due to screening. This study paves the way for quantitative studies of interaction effects…

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.

The first observation of exotic states with a new quark content cc[over ¯]us[over ¯] decaying to the J/ψK^{+} final state is reported with high significance from an amplitude analysis of the B^{+}→J/ψϕK^{+} decay. The analysis is carried out using proton-proton collision data corresponding to a total integrated luminosity of 9 fb^{-1} collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV. The most significant state, Z_{cs}(4000)^{+}, has a mass of 4003±6_{-14}^{+4} MeV, a width of 131±15±26 MeV, and spin parity J^{P}=1^{+}, where the quoted uncertainties are statistical and systematic, respectively. A new 1^{+} X(4685) state decaying to the J/ψϕ final state is also observed with high significance. In addition, the four previously reported J/ψϕ states are confirmed and two more exotic states, Z_{cs}(4220)^{+} and X(4630), are observed with significance exceeding 5 standard deviations.

The polarization singularity in momentum space has recently been discovered as a new class of topological signatures of Bloch modes in photonic crystal slabs concerning the far-field radiations, beyond its near-field description with widely explored topological band theory. Bound states in the continuum (BICs) in photonic crystal slabs are demonstrated as vortex eigenpolarization singularities in momentum space and the circular polarization points (C points) are also obtained based on BICs, opening up more possibilities for exotic light scattering and various topological phenomena of singular optics. Here, focusing on the nondegenerate bands, we report the generation to annihilation of two pairs of C points in momentum space in the photonic crystal slabs with inversion symmetry but broken up-down mirror symmetry. Interestingly, as the C points evolve with the structure parameter, we find two merging processes of C points, where an accidental at-Γ BIC and unidirectional radiative resonances with leaky channels of drastically different radiative lifetime emerge. The whole evolution is…

The dynamics of entanglement in "hybrid" nonunitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply postselection on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of nonunitary circuits by taking advantage of spacetime duality. This method maps the purification dynamics of a mixed state under nonunitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code…

Detection mechanisms for low mass bosonic dark matter candidates, such as the axion or hidden photon, leverage potential interactions with electromagnetic fields, whereby the dark matter (of unknown mass) on rare occasion converts into a single photon. Current dark matter searches operating at microwave frequencies use a resonant cavity to coherently accumulate the field sourced by the dark matter and a near standard quantum limited (SQL) linear amplifier to read out the cavity signal. To further increase sensitivity to the dark matter signal, sub-SQL detection techniques are required. Here we report the development of a novel microwave photon counting technique and a new exclusion limit on hidden photon dark matter. We operate a superconducting qubit to make repeated quantum nondemolition measurements of cavity photons and apply a hidden Markov model analysis to reduce the noise to 15.7 dB below the quantum limit, with overall detector performance limited by a residual background of real photons. With the present device, we perform a hidden photon search and constrain the kinetic…

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 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.

We show that the inclusion of a recently found additional term of the spin polarization vector at local equilibrium which is linear in the symmetrized gradients of the velocity field, and the assumption of hadron production at constant temperature restore the quantitative agreement between hydrodynamic model predictions and local polarization measurements in relativistic heavy ion collisions at sqrt[s_{NN}]=200 GeV. The longitudinal component of the spin polarization vector turns out to be very sensitive to the temperature value, with a good fit around 155 MeV. The implications of this finding are discussed.

The new physics of magic-angle twisted bilayer graphene (TBG) motivated extensive studies of flat bands hosted by moiré superlattices in van der Waals structures, inspiring the investigations into their photonic counterparts with potential applications including Bose-Einstein condensation. However, correlation between photonic flat bands and bilayer photonic moiré systems remains unexplored, impeding further development of moiré photonics. In this work, we formulate a coupled-mode theory for low-angle twisted bilayer honeycomb photonic crystals as a close analogy of TBG, discovering magic-angle photonic flat bands with a non-Anderson-type localization. Moreover, the interlayer separation constitutes a convenient degree of freedom in tuning photonic moiré bands without high pressure. A phase diagram is constructed to correlate the twist angle and separation dependencies to the photonic magic angles. Our findings reveal a salient correspondence between fermionic and bosonic moiré systems and pave the avenue toward novel applications through advanced photonic band or state engineering.

In van der Waals (vdW) heterostructures formed by stacking two monolayers of transition metal dichalcogenides, multiple exciton resonances with highly tunable properties are formed and subject to both vertical and lateral confinement. We investigate how a unique control knob, the twist angle between the two monolayers, can be used to control the exciton dynamics. We observe that the interlayer exciton lifetimes in MoSe_{2}/WSe_{2} twisted bilayers (TBLs) change by one order of magnitude when the twist angle is varied from 1° to 3.5°. Using a low-energy continuum model, we theoretically separate two leading mechanisms that influence interlayer exciton radiative lifetimes. The shift to indirect transitions in the momentum space with an increasing twist angle and the energy modulation from the moiré potential both have a significant impact on interlayer exciton lifetimes. We further predict distinct temperature dependence of interlayer exciton lifetimes in TBLs with different twist angles, which is partially validated by experiments. While many recent studies have highlighted how the…

We report a study of the processes of e^{+}e^{-}→K^{+}D_{s}^{-}D^{*0} and K^{+}D_{s}^{*-}D^{0} based on e^{+}e^{-} annihilation samples collected with the BESIII detector operating at BEPCII at five center-of-mass energies ranging from 4.628 to 4.698 GeV with a total integrated luminosity of 3.7 fb^{-1}. An excess of events over the known contributions of the conventional charmed mesons is observed near the D_{s}^{-}D^{*0} and D_{s}^{*-}D^{0} mass thresholds in the K^{+} recoil-mass spectrum for events collected at sqrt[s]=4.681 GeV. The structure matches a mass-dependent-width Breit-Wigner line shape, whose pole mass and width are determined as (3982.5_{-2.6}^{+1.8}±2.1) MeV/c^{2} and (12.8_{-4.4}^{+5.3}±3.0) MeV, respectively. The first uncertainties are statistical and the second are systematic. The significance of the resonance hypothesis is estimated to be 5.3 σ over the contributions only from the conventional charmed mesons. This is the first candidate for a charged hidden-charm tetraquark with strangeness, decaying into D_{s}^{-}D^{*0} and D_{s}^{*-}D^{0}. However, the…

We employ electric circuit networks to study topological states of matter in non-Hermitian systems enriched by parity-time symmetry PT and chiral symmetry anti-PT (APT). The topological structure manifests itself in the complex admittance bands which yields excellent measurability and signal to noise ratio. We analyze the impact of PT-symmetric gain and loss on localized edge and defect states in a non-Hermitian Su-Schrieffer-Heeger (SSH) circuit. We realize all three symmetry phases of the system, including the APT-symmetric regime that occurs at large gain and loss. We measure the admittance spectrum and eigenstates for arbitrary boundary conditions, which allows us to resolve not only topological edge states, but also a novel PT-symmetric Z_{2} invariant of the bulk. We discover the distinct properties of topological edge states and defect states in the phase diagram. In the regime that is not PT symmetric, the topological defect state disappears and only reemerges when APT symmetry is reached, while the topological edge states always prevail and only experience a shift in…

We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example, when some of the Pauli observables have high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.

The Center for Axion and Precision Physics Research at the Institute for Basic Science is searching for axion dark matter using ultralow temperature microwave resonators. We report the exclusion of the axion mass range 10.7126-10.7186 μeV with near Kim-Shifman-Vainshtein-Zakharov (KSVZ) coupling sensitivity and the range 10.16-11.37 μeV with about 9 times larger coupling at 90% confidence level. This is the first axion search result in these ranges. It is also the first with a resonator physical temperature of less than 40 mK.

Quantum criticality, as a fascinating quantum phenomenon, may provide significant advantages for quantum sensing. Here we propose a dynamic framework for quantum sensing with a family of Hamiltonians that undergo quantum phase transitions (QPTs). By giving the formalism of the quantum Fisher information (QFI) for quantum sensing based on critical quantum dynamics, we demonstrate its divergent feature when approaching the critical point. We illustrate the basic principle and the details of experimental implementation using quantum Rabi model. The framework is applicable to a variety of examples and does not rely on the stringent requirement for particular state preparation or adiabatic evolution. It is expected to provide a route towards the implementation of criticality-enhanced quantum sensing.

Recently, spatiotemporal optical vortex pulses carrying a purely transverse intrinsic orbital angular momentum were generated experimentally [Optica 6, 1547 (2019)OPTIC82334-253610.1364/OPTICA.6.001547; Nat. Photonics 14, 350 (2020)NPAHBY1749-488510.1038/s41566-020-0587-z]. However, an accurate theoretical analysis of such states and their angular-momentum properties remains elusive. Here, we provide such analysis, including scalar and vector spatiotemporal Bessel-type solutions as well as description of their propagational, polarization, and angular-momentum properties. Most importantly, we calculate both local densities and integral values of the spin and orbital angular momenta, and predict observable spin-orbit interaction phenomena related to the coupling between the transverse spin and orbital angular momentum. Our analysis is readily extended to spatiotemporal vortex pulses of other natures (e.g., acoustic).

High-pressure chemistry is known to inspire the creation of unexpected new classes of compounds with exceptional properties. Here, we employ the laser-heated diamond anvil cell technique for synthesis of a Dirac material BeN_{4}. A triclinic phase of beryllium tetranitride tr-BeN_{4} was synthesized from elements at ∼85 GPa. Upon decompression to ambient conditions, it transforms into a compound with atomic-thick BeN_{4} layers interconnected via weak van der Waals bonds and consisting of polyacetylene-like nitrogen chains with conjugated π systems and Be atoms in square-planar coordination. Theoretical calculations for a single BeN_{4} layer show that its electronic lattice is described by a slightly distorted honeycomb structure reminiscent of the graphene lattice and the presence of Dirac points in the electronic band structure at the Fermi level. The BeN_{4} layer, i.e., beryllonitrene, represents a qualitatively new class of 2D materials that can be built of a metal atom and polymeric nitrogen chains and host anisotropic Dirac fermions.

It is highly nontrivial to what extent we can deduce the relaxation behavior of a quantum dissipative system from the spectral gap of the Liouvillian that governs the time evolution of the density matrix. We investigate the relaxation processes of a quantum dissipative system that exhibits the Liouvillian skin effect, which means that the eigenmodes of the Liouvillian are localized exponentially close to the boundary of the system, and find that the timescale for the system to reach a steady state depends not only on the Liouvillian gap $\mathrm{\ensuremath{\Delta}}$, but also on the localization length $\ensuremath{\xi}$ of the eigenmodes. In particular, we show that the longest relaxation time $\ensuremath{\tau}$ that is maximized over initial states and local observables is given by $\ensuremath{\tau}\ensuremath{\sim}{\mathrm{\ensuremath{\Delta}}}^{\ensuremath{-}1}(1+L/\ensuremath{\xi})$ with $L$ being the system size. This implies that the longest relaxation time can diverge for $L\ensuremath{\rightarrow}\ensuremath{\infty}$ without gap closing.

We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in ℏ, it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudogauge, the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes in global equilibrium and that the spin potential is, then, equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

Including prior knowledge is important for effective machine learning models in physics and is usually achieved by explicitly adding loss terms or constraints on model architectures. Prior knowledge embedded in the physics computation itself rarely draws attention. We show that solving the Kohn-Sham equations when training neural networks for the exchange-correlation functional provides an implicit regularization that greatly improves generalization. Two separations suffice for learning the entire one-dimensional H_{2} dissociation curve within chemical accuracy, including the strongly correlated region. Our models also generalize to unseen types of molecules and overcome self-interaction error.

Symmetry and topology govern many electronic, magnetic, and photonic phenomena in condensed matter physics and optics, resulting in counterintuitive skyrmion, meron, and other phenomena important for modern technologies. Here we demonstrate photonic spin lattices as a new topological construct governed by the spin-orbit coupling in an optical field. The symmetry of the electromagnetic field in the presence of the spin-orbit interaction may result in only two types of photonic spin lattices: either hexagonal spin-skyrmion or square spin-meron lattices. We show that these spin structures correspond to the lowest energy of the electromagnetic field configuration, therefore, energetically stable. We further show that in the absence of spin-orbit coupling these spin topologies are degenerated in dynamic field skyrmions, unifying the description of electromagnetic field topologies. The results provide a new understanding of electromagnetic field topology and its transformations as well as new opportunities for applications in quantum technologies, spin optics, and topological photonics.

The magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schrödinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even or odd cat states by performing local non-Gaussian operations on the optical mode that is entangled with the magnon mode through pulsed optomagnonic interaction. By evaluating key properties of the resulting cat states, we show that for experimentally feasible parameters, they are generated with both high fidelity and nonclassicality, as well as with a size large enough to be useful for quantum technologies. Furthermore, the effects of experimental imperfections such as the error of projective measurements and dark count when performing single-photon operations have been…

We analyze scattering properties of twisted bilayer photonic crystal slabs through a high-dimensional plane wave expansion method. The method is applicable for arbitrary twist angles and does not suffer from the limitations of the commonly used supercell approximation. We show strongly tunable resonance properties of this system which can be accounted for semianalytically from a correspondence relation to a simpler structure. We also observe strongly tunable resonant chiral behavior in this system. Our work provides the theoretical foundation for predicting and understanding the rich optical physics of twisted multilayer photonic crystal systems.

The measurement of the energy spectrum of cosmic ray helium nuclei from 70 GeV to 80 TeV using 4.5 years of data recorded by the Dark Matter Particle Explorer (DAMPE) is reported in this work. A hardening of the spectrum is observed at an energy of about 1.3 TeV, similar to previous observations. In addition, a spectral softening at about 34 TeV is revealed for the first time with large statistics and well controlled systematic uncertainties, with an overall significance of 4.3σ. The DAMPE spectral measurements of both cosmic protons and helium nuclei suggest a particle charge dependent softening energy, although with current uncertainties a dependence on the number of nucleons cannot be ruled out.

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multimodal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity, using orders of magnitude fewer iterative steps, and less data, than both accelerated projected-gradient-based and iterative maximum-likelihood estimation. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pretrained on similar quantum states.

We present a measurement of ${R}_{{K}^{*}}$, the branching fraction ratio $\mathcal{B}(B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})/\mathcal{B}(B\ensuremath{\rightarrow}{K}^{*}{e}^{+}{e}^{\ensuremath{-}})$, for both charged and neutral $B$ mesons. The ratio for the charged case ${R}_{{K}^{*+}}$ is the first measurement ever performed. In addition, we report absolute branching fractions for the individual modes in bins of the squared dilepton invariant mass ${q}^{2}$. The analysis is based on a data sample of $711\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, containing $772\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }B\overline{B}$ events, recorded at the $\mathrm{\ensuremath{\Upsilon}}(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy ${e}^{+}{e}^{\ensuremath{-}}$ collider. The obtained results are consistent with standard model expectations.

Entanglement generation in trapped-ion systems has relied thus far on two distinct but related geometric phase gate techniques: Mølmer-Sørensen and light-shift gates. We recently proposed a variant of the light-shift scheme where the qubit levels are separated by an optical frequency [B. C. Sawyer and K. R. Brown, Phys. Rev. A 103, 022427 (2021)PLRAAN2469-992610.1103/PhysRevA.103.022427]. Here we report an experimental demonstration of this entangling gate using a pair of ^{40}Ca^{+} ions in a cryogenic surface-electrode ion trap and a commercial, high-power, 532 nm Nd:YAG laser. Generating a Bell state in 35 μs, we directly measure an infidelity of 6(3)×10^{-4} without subtraction of experimental errors. The 532 nm gate laser wavelength suppresses intrinsic photon scattering error to ∼1×10^{-5}.

A significant problem for current quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model often appropriately describes average noise for large circuits involving many qubits and gates. We present a method to mitigate the depolarizing noise by first estimating its rate with a noise-estimation circuit and then correcting the output of the target circuit using the estimated rate. The method is experimentally validated on a simulation of the Heisenberg model. We find that our approach in combination with readout-error correction, randomized compiling, and zero-noise extrapolation produces close to exact results even for circuits containing hundreds of CNOT gates. We also show analytically that zero-noise extrapolation is improved when it is applied to the output of our method.

Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems and their dynamics and interaction. Since the inception of quantum theory, it has been debated whether complex numbers are essential or whether an alternative consistent formulation is possible using real numbers only. Here, we attack this long-standing problem theoretically and experimentally, using the powerful tools of quantum resource theories. We show that, under reasonable assumptions, quantum states are easier to create and manipulate if they only have real elements. This gives an operational meaning to the resource theory of imaginarity. We identify and answer several important questions, which include the state-conversion problem for all qubit states and all pure states of any dimension and the approximate imaginarity distillation for all quantum states. As an application, we show that imaginarity plays a crucial role in state discrimination, that is, there exist real quantum states that can be perfectly distinguished via…

We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordström black holes. They also possess a finite mass M and electric charge Q_{e}, with Q_{e}/M>1. An exact wormhole solution with ungauged, massless fermions is also reported.

We study the timescale of random telegraph noise (RTN) of nanomagnets in stochastic magnetic tunnel junctions (MTJs). From analytical and numerical calculations based on the Landau-Lifshitz-Gilbert and the Fokker-Planck equations, we reveal mechanisms governing the relaxation time of perpendicular easy-axis MTJs (p-MTJs) and in-plane easy-axis MTJs (i-MTJs), showing that i-MTJs can be made to have faster RTN. Superparamagnetic i-MTJs with small in-plane anisotropy and sizable perpendicular effective anisotropy show relaxation times down to 8 ns at negligible bias current, which is more than 5 orders of magnitude shorter than that of typical stochastic p-MTJs and about 100 times faster than the shortest time of i-MTJs reported so far. The findings give a new insight and foundation in developing stochastic MTJs for high-performance probabilistic computers.

The discovery of magic angle twisted bilayer graphene has unveiled a rich variety of superconducting, magnetic, and topologically nontrivial phases. Here, we show that the zero-field states at odd integer filling factors in h-BN nonaligned devices are consistent with symmetry broken Chern insulators, as is evidenced by the observation of the anomalous Hall effect near moiré cell filling factor ν=+1. The corresponding Chern insulator has a Chern number C=±1 and a relatively high Curie temperature of T_{c}≈4.5 K. In a perpendicular magnetic field above B>0.5 T we observe a transition of the ν=+1 Chern insulator from Chern number C=±1 to C=3, characterized by a quantized Hall plateau with R_{yx}=h/3e^{2}. These observations demonstrate that interaction-induced symmetry breaking leads to zero-field ground states that include almost degenerate and closely competing Chern insulators, and that states with larger Chern numbers couple most strongly to the B field. In addition, the device reveals strong superconducting phases with critical temperatures of up to T_{c}≈3.5 K. By providing the…

We report an improved measurement of the free neutron lifetime τ_{n} using the UCNτ apparatus at the Los Alamos Neutron Science Center. We count a total of approximately 38×10^{6} surviving ultracold neutrons (UCNs) after storing in UCNτ's magnetogravitational trap over two data acquisition campaigns in 2017 and 2018. We extract τ_{n} from three blinded, independent analyses by both pairing long and short storage time runs to find a set of replicate τ_{n} measurements and by performing a global likelihood fit to all data while self-consistently incorporating the β-decay lifetime. Both techniques achieve consistent results and find a value τ_{n}=877.75±0.28_{stat}+0.22/-0.16_{syst} s. With this sensitivity, neutron lifetime experiments now directly address the impact of recent refinements in our understanding of the standard model for neutron decay.

Implementation of high-fidelity 2-qubit operations is a key ingredient for scalable quantum error correction. In superconducting qubit architectures, tunable buses have been explored as a means to higher-fidelity gates. However, these buses introduce new pathways for leakage. Here we present a modified tunable bus architecture appropriate for fixed-frequency qubits in which the adiabaticity restrictions on gate speed are reduced. We characterize this coupler on a range of 2-qubit devices, achieving a maximum gate fidelity of 99.85%. We further show the calibration is stable over one day.

In this Letter, we introduce a novel scheme for extrapolating the equation of state of QCD to finite chemical potential that features considerably improved convergence properties and allows us to extend its reach to unprecedentedly high baryonic chemical potentials. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to μ_{B}/T≤3.5. This novel expansion does not suffer from the shortcomings that characterize the traditional Taylor expansion method, such as difficulties inherent in performing such an expansion with a limited number of coefficients and the poor signal-to-noise ratio that affects Taylor coefficients determined from lattice calculations.

Improving two-qubit gate performance and suppressing cross talk are major, but often competing, challenges to achieving scalable quantum computation. In particular, increasing the coupling to realize faster gates has been intrinsically linked to enhanced cross talk due to unwanted two-qubit terms in the Hamiltonian. Here, we demonstrate a novel coupling architecture for transmon qubits that circumvents the standard relationship between desired and undesired interaction rates. Using two fixed frequency coupling elements to tune the dressed level spacings, we demonstrate an intrinsic suppression of the static ZZ while maintaining large effective coupling rates. Our architecture reveals no observable degradation of qubit coherence (T_{1},T_{2}>100 μs) and, over a factor of 6 improvement in the ratio of desired to undesired coupling. Using the cross-resonance interaction, we demonstrate a 180 ns single-pulse controlled not (cnot) gate, and measure a cnot fidelity of 99.77(2)% from interleaved randomized benchmarking.

The understanding of heavy ion collisions and its quark-gluon plasma (QGP) formation requires a complicated interplay of rich physics in a wealth of experimental data. In this work we compare for identified particles the transverse momentum dependence of both the yields and the anisotropic flow coefficients for both PbPb and pPb collisions. We do this in a global model fit including a free streaming prehydrodynamic phase with variable velocity v_{fs}, thereby widening the scope of initial conditions. During the hydrodynamic phase we vary three second order transport coefficients. The free streaming velocity has a preference slightly below the speed of light. In this extended model the QGP bulk viscosity is small and even consistent with zero.

Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.

By generating a Brillouin laser in an optical microresonator, we realize a soliton Kerr microcomb through exciting the Kerr frequency comb using the generated Brillouin laser in the same cavity. The intracavity Brillouin laser pumping scheme enables us to access the soliton states with a blue-detuned input pump. Because of the ultranarrow linewidth and the low-noise properties of the generated Brillouin laser, the observed soliton microcomb exhibits narrow-linewidth comb lines and stable repetition rate. Also, we demonstrate a low-noise microwave signal with phase noise of -49 dBc/Hz at 10 Hz, -130 dBc/Hz at 10 kHz, and -149 dBc/Hz at 1 MHz offsets for a 10.43 GHz carrier with only a free-running input pump. The easy operation of the Brillouin-Kerr soliton microcomb with excellent performance makes our scheme promising for practical applications.

We have theoretically and experimentally achieved large-area one-way transport by using heterostructures consisting of a domain of an ordinary photonic crystal sandwiched between two domains of magnetic photonic crystals. The nonmagnetized domain carries two orthogonal one-way waveguide states which have amplitude uniformly distributed over a large area. We show that such one-way waveguide states can be used to abruptly narrow the beam width of an extended state to concentrate energy, and the transport is robust against different kinds of defects and imperfections. They are also immune to the Anderson-type localization when large randomness is introduced.