Empirical studies on the landscape of neural networks have shown that low-energy configurations are often found in complex connected structures, where zero-energy paths between pairs of distant solutions can be constructed. Here, we consider the spherical negative perceptron, a prototypical nonconvex neural network model framed as a continuous constraint satisfaction problem. We introduce a general analytical method for computing energy barriers in the simplex with vertex configurations sampled from the equilibrium. We find that in the overparametrized regime the solution manifold displays simple connectivity properties. There exists a large geodesically convex component that is attractive for a wide range of optimization dynamics. Inside this region we identify a subset of atypical high-margin solutions that are geodesically connected with most other solutions, giving rise to a star-shaped geometry. We analytically characterize the organization of the connected space of solutions and show numerical evidence of a transition, at larger constraint densities, where the aforementioned simple geodesic connectivity breaks down.

We present a single-shot method to measure motional states in the number basis. The technique can be applied to systems with at least three nondegenerate energy levels which can be coupled to a linear quantum harmonic oscillator. The method relies on probing an Autler-Townes splitting that arises when a phonon-number changing transition is strongly coupled. We demonstrate the method using a single trapped ion and show that it may be used in a nondemolition fashion to prepare phonon number states. We also show how the Autler-Townes splitting can be used to measure phonon number distributions.

We provide a model capable of accounting for the multiferroicity in certain materials. The model’s base is on free electrons and spin moments coupled within nonrelativistic quantum mechanics. The synergistic interplay between the magnetic and electric degrees of freedom that turns into the multiferroic phenomena occurs at a profound quantum mechanical level, conjured by Berry’s phases and the quantum theory of polarization. Our results highlight the geometrical nature of the multiferroic order parameter that naturally leads to magnetoelectric domain walls, with promising technological potential.

We propose that the dynamics of Kerr black holes is strongly constrained by the principle of gauge symmetry. We initiate the construction of effective field theories for Kerr black holes of any integer quantum spin $s$ using Stückelberg fields, and show that the known three-point Kerr amplitudes are uniquely predicted using massive higher-spin gauge symmetry. This symmetry is argued to be connected to an enhanced range of validity for the Kerr effective field theories. We consider the closely related root-Kerr electromagnetic solution in parallel, for which the dynamical interactions with photons are also constrained by massive higher-spin gauge symmetry. Finally, the spin-$s$ Compton amplitudes are analyzed, and we discuss contact-term constraints at $s=2$ from Ward identities.

Collinear laser spectroscopy was performed on the isomer of the aluminium isotope ${}^{26m}\mathrm{Al}$. The measured isotope shift to ${}^{27}\mathrm{Al}$ in the $3s^{2}3p{}^2{P}_{3/2}^{○}\to 3s^{2}4s{}^2{S}_{1/2}$ atomic transition enabled the first experimental determination of the nuclear charge radius of ${}^{26m}\mathrm{Al}$, resulting in $R_c=3.130(15)\mathrm{fm}$. This differs by 4.5 standard deviations from the extrapolated value used to calculate the isospin-symmetry breaking corrections in the superallowed $\beta$ decay of ${}^{26m}\mathrm{Al}$. Its corrected $\mathcal{F}t$ value, important for the estimation of $V_{ud}$ in the Cabibbo-Kobayashi-Maskawa matrix, is thus shifted by 1 standard deviation to 3071.4(1.0) s.

The phase diagram of an interacting two-dimensional electron system in a high magnetic field is enriched by the varying form of the effective Coulomb interaction, which depends strongly on the Landau level index. While the fractional quantum Hall states that dominate in the lower-energy Landau levels have been explored experimentally in a variety of two-dimensional systems, much less work has been done to explore electron solids owing to their subtle transport signatures and extreme sensitivity to disorder. Here, we use chemical potential measurements to map the phase diagram of electron solid states in $N=2$, $N=3$, and $N=4$ Landau levels in monolayer graphene. Direct comparison between our data and theoretical calculations reveals a cascade of density-tuned phase transitions between electron bubble phases up to two, three, or four electrons per bubble in the $N=2$, 3, and 4 Landau levels, respectively. Finite-temperature measurements are consistent with melting of the solids for $T\approx 1\mathrm{K}$.

We present the possibility of x-ray magnetic circular dichroism on ${\mathrm{RuO}}_2$ with collinear antiferromagnetism (AFM). Given that the crystal symmetry breaks the time reversal symmetry when the antiparallel spin aligns along the [100] direction, the expectation vector of the anisotropic magnetic dipole operator $⟨\mathit{t}⟩$ remains uncanceled along the [010] direction. Our Letter reveals that the magnetic dipole ($T_z$) term in the x-ray magnetic circular dichroism is induced by the residual $⟨\mathit{t}⟩$. Because the features of the magnetic moment can be detected via absorption measurements even in the AFM, this technique will be useful for determining the magnetic phase, the Van Vleck–type paramagnet or the excitonic AFM in $(t_{2g}{)}^4$ system.

We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of the ordered phase nucleate and grow. We characterize analytically this self-similar growth and demonstrate that droplets spread ballistically in all directions. Our results imply that, in the thermodynamic limit, discrete-symmetry flocks—and, by extension, continuous-symmetry flocks with rotational anisotropy—are metastable in all dimensions.

The Wigner-Araki-Yanase (WAY) theorem states that additive conservation laws imply the commutativity of exactly implementable projective measurements and the conserved observables of the system. Known proofs of this theorem are only restricted to bounded or discrete-spectrum conserved observables of the system and are not applicable to unbounded and continuous observables like a momentum operator. In this Letter, we present the WAY theorem for possibly unbounded and continuous conserved observables under the Yanase condition, which requires that the probe positive operator-valued measure should commute with the conserved observable of the probe system. As a result of this WAY theorem, we show that exact implementations of the projective measurement of the position under momentum conservation and of the quadrature amplitude using linear optical instruments and photon counters are impossible. We also consider implementations of unitary channels under conservation laws and find that the conserved observable $L_S$ of the system commutes with the implemented unitary $U_S$ if $L_S$ is semibounded, while $U_S^{†}{L}_S{U}_S$ can shift up to possibly nonzero constant factor if the spectrum of $L_S$ is upper and lower unbounded. We give simple examples of the latter case, where $L_S$ is a momentum operator.

Fault-tolerant quantum computing based on surface code has emerged as an attractive candidate for practical large-scale quantum computers to achieve robust noise resistance. To achieve universality, magic states preparation is a commonly approach for introducing non-Clifford gates. Here, we present a hardware-efficient and scalable protocol for arbitrary logical state preparation for the rotated surface code, and further experimentally implement it on the Zuchongzhi 2.1 superconducting quantum processor. An average of $0.8983\pm 0.0002$ logical fidelity at different logical states with distance three is achieved, taking into account both state preparation and measurement errors. In particular, the logical magic states $|A^{\pi /4}{⟩}_L$, $|H{⟩}_L$, and $|T{⟩}_L$ are prepared nondestructively with logical fidelities of $0.8771\pm 0.0009$, $0.9090\pm 0.0009$, and $0.8890\pm 0.0010$, respectively, which are higher than the state distillation protocol threshold, 0.859 (for $H$-type magic state) and 0.827 (for $T$-type magic state). Our work provides a viable and efficient avenue for generating high-fidelity raw logical magic states, which is essential for realizing non-Clifford logical gates in the surface code.

The cluster structure of the neutron-rich isotope ${}^{10}\mathrm{Be}$ has been probed via the $(p,p\alpha )$ reaction at $150\mathrm{MeV}/\mathrm{nucleon}$ in inverse kinematics and in quasifree conditions. The populated states of ${}^6\mathrm{He}$ residues were investigated through missing mass spectroscopy. The triple differential cross section for the ground-state transition was extracted for quasifree angle pairs $({\theta }_p,{\theta }_{\alpha })$ and compared to distorted-wave impulse approximation reaction calculations performed in a microscopic framework using successively the Tohsaki-Horiuchi-Schuck-Röpke product wave function and the wave function deduced from antisymmetrized molecular dynamics calculations. The remarkable agreement between calculated and measured cross sections in both shape and magnitude validates the molecular structure description of the ${}^{10}\mathrm{Be}$ ground-state, configured as an $\alpha \text{−}\alpha$ core with two valence neutrons occupying $\pi$-type molecular orbitals.

Mixing solutions of oppositely charged macromolecules can result in liquid-liquid phase separation into a polymer-rich coacervate phase and a polymer-poor supernatant phase. Here, we show that charge asymmetry in the constituent polymers can slow down the coarsening dynamics, with an apparent growth exponent that deviates from the well-known $1/3$ for neutral systems and decreases with increasing degrees of charge asymmetry. Decreasing solvent quality accelerates the coarsening dynamics for asymmetric mixtures but slows down the coarsening dynamics for symmetric mixtures. We rationalize these results by examining the interaction potential between merging droplets.

AlphaFold2 (AF) is a promising tool, but is it accurate enough to predict single mutation effects? Here, we report that the localized structural deformation between protein pairs differing by only 1–3 mutations—as measured by the effective strain—is correlated across 3901 experimental and AF-predicted structures. Furthermore, analysis of $\sim 11000$ proteins shows that the local structural change correlates with various phenotypic changes. These findings suggest that AF can predict the range and magnitude of single-mutation effects on average, and we propose a method to improve precision of AF predictions and to indicate when predictions are unreliable.

Current cosmological data exhibit discordance between indirect and some direct inferences of the present-day expansion rate $H_0$. Early dark energy (EDE), which briefly increases the cosmic expansion rate prior to recombination, is a leading scenario for resolving this “Hubble tension” while preserving a good fit to cosmic microwave background (CMB) data. However, this comes at the cost of changes in parameters that affect structure formation in the late-time universe, including the spectral index of scalar perturbations $n_s$. Here, we present the first constraints on axionlike EDE using data from the Lyman-$\alpha$ forest, i.e., absorption lines imprinted in background quasar spectra by neutral hydrogen gas along the line of sight. We consider two independent measurements of the one-dimensional $\mathrm{Ly}\alpha$ forest flux power spectrum from the Sloan Digital Sky Survey (SDSS eBOSS) and from the MIKE/HIRES and X-Shooter spectrographs. We combine these with a baseline dataset comprised of Planck CMB data and baryon acoustic oscillation (BAO) measurements. Combining the eBOSS $\mathrm{Ly}\alpha$ data with the CMB and BAO dataset reduces the 95% confidence level (C.L.) upper bound on the maximum fractional contribution of EDE to the cosmic energy budget $f_{\mathrm{EDE}}$ from 0.07 to 0.03 and constrains $H_0={67.9}_{-0.4}^{+0.4}\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ (68% C.L.), with maximum a posteriori value $H_0=67.9\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$. Similar results are obtained for the MIKE/HIRES and X-Shooter $\mathrm{Ly}\alpha$ data. Our $\mathrm{Ly}\alpha$-based EDE constraints yield $H_0$ values that are in $>4\sigma$ tension with the SH0ES distance-ladder measurement and are driven by the preference of the $\mathrm{Ly}\alpha$ forest data for $n_s$ values lower than those required by EDE cosmologies that fit Planck CMB data. Taken at face value, the $\mathrm{Ly}\alpha$ forest severely constrains canonical EDE models that could resolve the Hubble tension.

The control of guided water wave propagation based on the Autler-Townes splitting resonance concept is demonstrated experimentally, numerically, and theoretically. Complete wave absorption is achieved using an asymmetric pointlike scatterer made of two closely spaced resonant side channels connected to a guide and designed so that its energy leakage is in perfect balance with the inherent viscous losses in the system. We demonstrate that the nature of the resonators and guide junction completely controls the positions of the wave numbers at the reflection and transmission zeros on the real axis; the asymmetry of the resonators completely controls their positions on the imaginary axis. Thus, by adjusting these two independent parameters, we obtain a zero reflection and transmission.

Bayesian methods are used to constrain the density dependence of the QCD equation of state (EOS) for dense nuclear matter using the data of mean transverse kinetic energy and elliptic flow of protons from heavy ion collisions (HICs), in the beam energy range $\sqrt{s_{\mathrm{NN}}}=2–10\mathrm{GeV}$. The analysis yields tight constraints on the density dependent EOS up to 4 times the nuclear saturation density. The extracted EOS yields good agreement with other observables measured in HIC experiments and constraints from astrophysical observations both of which were not used in the inference. The sensitivity of inference to the choice of observables is also discussed.

High harmonic generation (HHG) has become a core pillar of attosecond science. Traditionally described with field-based models, HHG can also be viewed in a parametric picture, which predicts all properties of the emitted photons, but not the nonperturbative efficiency of the process. Driving HHG with two noncollinear beams and deriving analytically the corresponding yield scaling laws for any intensity ratio, we herein reconcile the two interpretations, introducing a generalized photonic description of HHG. It is in full agreement with field-based simulations and experimental data, opening the route to smart engineering of HHG with multiple driving beams.

Damage caused by freezing wet, porous materials is a widespread problem but is hard to predict or control. Here, we show that polycrystallinity significantly speeds up the stress buildup process that underpins this damage. Unfrozen water in grain-boundary grooves feeds ice growth at temperatures below the freezing temperature, leading to fast stress buildup. These stresses can build up to levels that can easily break many brittle materials. The dynamics of the process are very variable, which we ascribe to local differences in ice-grain orientation and to the surprising mobility of many grooves—which further accelerates stress buildup. Our Letter will help understand how freezing damage occurs and in developing accurate models and effective damage-mitigation strategies.

The changes in mean-squared charge radii of neutron-deficient gold nuclei have been determined using the in-source, resonance-ionization laser spectroscopy technique, at the ISOLDE facility (CERN). From these new data, nuclear deformations are inferred, revealing a competition between deformed and spherical configurations. The isotopes ${}^{180,181,182}\mathrm{Au}$ are observed to possess well-deformed ground states and, when moving to lighter masses, a sudden transition to near-spherical shapes is seen in the extremely neutron-deficient nuclides, ${}^{176,177,179}\mathrm{Au}$. A case of shape coexistence and shape staggering is identified in ${}^{178}\mathrm{Au}$ which has a ground and isomeric state with different deformations. These new data reveal a pattern in ground-state deformation unique to the gold isotopes, whereby, when moving from the heavy to light masses, a plateau of well-deformed isotopes exists around the neutron midshell, flanked by near-spherical shapes in the heavier and lighter isotopes—a trend hitherto unseen elsewhere in the nuclear chart. The experimental charge radii are compared to those from Hartree-Fock-Bogoliubov calculations using the D1M Gogny interaction and configuration mixing between states of different deformation. The calculations are constrained by the known spins, parities, and magnetic moments of the ground states in gold nuclei and show a good agreement with the experimental results.

We report the preparation and observation of single atoms of dysprosium in arrays of optical tweezers with a wavelength of 532 nm, imaged on the intercombination line at 626 nm. We use the anisotropic light shift specific to lanthanides and in particular a large difference in tensor and vector polarizabilities between the ground and excited states to tune the differential light shift and produce tweezers in near-magic or magic polarization. This allows us to find a regime where single atoms can be trapped and imaged. Using the tweezer array toolbox to manipulate lanthanides will open new research directions for quantum physics studies by taking advantage of their rich spectrum, large spin, and magnetic dipole moment.