We report on the first Belle search for a light $CP$-odd Higgs boson, $A^0$, that decays into low mass dark matter, $\chi$, in final states with a single photon and missing energy. We search for events produced via the dipion transition $\mathrm{\Upsilon }(2S)\to \mathrm{\Upsilon }(1S){\pi }^{+}{\pi }^{-}$, followed by the on-shell process $\mathrm{\Upsilon }(1S)\to \gamma A^0$ with $A^0\to \chi \chi$, or by the off-shell process $\mathrm{\Upsilon }(1S)\to \gamma \chi \chi$. Utilizing a data sample of $157.3\times {10}^6$ $\mathrm{\Upsilon }(2\mathrm{S})$ decays, we find no evidence for a signal. We set limits on the branching fractions of such processes in the mass ranges $M_{A^0}<8.97\mathrm{GeV}/c^2$ and $M_{\chi }<4.44\mathrm{GeV}/c^2$. We then use the limits on the off-shell process to set competitive limits on WIMP-nucleon scattering in the WIMP mass range below $5\mathrm{GeV}/c^2$.

For translationally invariant one-band lattice models, we exploit the ab initio knowledge of the natural orbitals to simplify reduced density matrix functional theory (RDMFT). Striking underlying features are discovered. First, within each symmetry sector, the interaction functional $\mathcal{F}$ depends only on the natural occupation numbers $\mathit{n}$. The respective sets ${\mathcal{P}}_N^1$ and ${\mathcal{E}}_N^1$ of pure and ensemble $N$-representable one-matrices coincide. Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope ${\mathcal{E}}_N^1\equiv {\mathcal{P}}_N^1$, described by linear constraints $D^{(j)}(\mathit{n})\ge 0$. For smaller systems, it follows as $\mathcal{F}[\mathit{n}]=\sum _{i,i^{\prime }}{\overline{V}}_{i,i^{\prime }}\sqrt{D^{(i)}(\mathit{n})D^{(i^{\prime })}(\mathit{n})}$. This generalizes to systems of arbitrary size by replacing each $D^{(i)}$ by a linear combination of $\{D^{(j)}(\mathit{n})\}$ and adding a nonanalytical term involving the interaction $\widehat{V}$. Third, the gradient $d\mathcal{F}/d\mathit{n}$ is shown to diverge on the boundary $\partial {\mathcal{E}}_N^1$, suggesting that the fermionic exchange symmetry manifests itself within RDMFT in the form of an “exchange force.” All findings hold for systems with a nonfixed particle number as well and $\widehat{V}$ can be any $p$-particle interaction. As an illustration, we derive the exact functional for the Hubbard square.

Structured photons are nowadays an important resource in classical and quantum optics due to the richness of properties they show under propagation, focusing, and in their interaction with matter. Vectorial modes of light in particular, a class of modes where the polarization varies across the beam profile, have already been used in several areas ranging from microscopy to quantum information. One of the key ingredients needed to exploit the full potential of complex light in the quantum domain is the control of quantum interference, a crucial resource in fields like quantum communication, sensing, and metrology. Here we report a tunable Hong-Ou-Mandel interference between vectorial modes of light. We demonstrate how a properly designed spin-orbit device can be used to control quantum interference between vectorial modes of light by simply adjusting the device parameters and no need of interferometric setups. We believe our result can find applications in fundamental research and quantum technologies based on structured light by providing a new tool to control quantum interference in a compact, efficient, and robust way.

We investigate cluster synchronization in experiments with a multilayer network of electronic Colpitts oscillators, specifically a network with two interaction layers. We observe and analytically characterize the appearance of several cluster states as we change coupling in the layers. In this study, we innovatively combine bifurcation analysis and the computation of transverse Lyapunov exponents. We observe four kinds of synchronized states, from fully synchronous to a clustered quasiperiodic state—the first experimental observation of the latter state. Our work is the first to study fundamentally dissimilar kinds of coupling within an experimental multilayer network.

It has so far remained a major challenge to quantitatively predict the boson peak, a THz vibrational anomaly universal for glasses, from features in the amorphous structure. Using molecular dynamics simulations of a model ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$ glass, we decompose the boson peak to contributions from atoms residing in different types of Voronoi polyhedra. We then introduce a microscopic structural parameter to depict the “orientational order,” using the vector pointing from the center atom to the farthest vertex of its Voronoi coordination polyhedron. This order parameter represents the most probable direction of transverse vibration at low frequencies. Its magnitude scales linearly with the boson peak intensity, and its spatial distribution accounts for the quasilocalized modes. This correlation is shown to be universal for different types of glasses.

With spin-orbit coupling, both local-moment magnetism and itinerant electrons are expected to behave anisotropically in spin space, but such effects’ influence on the formation of unconventional superconductivity has been hitherto unexplored. Here, in an iron-based superconductor, ${\mathrm{Sr}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$, we report spectroscopic evidence that itinerant electrons “prefer” to be assisted by $c$-axis polarized magnetic excitations in their formation of superconducting Cooper pairs, against the polarization of the local-moment excitations. Our result naturally explains why the superconductivity competes strongly with the tetragonal magnetic phase in this material, and provides a fresh view on how to make a good superconductor out of a magnetic “Hund’s metal.”

We study the critical breakdown of two-dimensional quantum magnets in the presence of algebraically decaying long-range interactions by investigating the transverse-field Ising model on the square and triangular lattice. This is achieved technically by combining perturbative continuous unitary transformations with classical Monte Carlo simulations to extract high-order series for the one-particle excitations in the high-field quantum paramagnet. We find that the unfrustrated systems change from mean-field to nearest-neighbor universality with continuously varying critical exponents. In the frustrated case on the square lattice the system remains in the universality class of the nearest-neighbor model independent of the long-range nature of the interaction, while we argue that the quantum criticality for the triangular lattice is terminated by a first-order phase transition line.

We study a particle immersed in a heat bath, in the presence of an external force which decays at least as rapidly as $1/x$, e.g., a particle interacting with a surface through a Lennard-Jones or a logarithmic potential. As time increases, our system approaches a non-normalizable Boltzmann state. We study observables, such as the energy, which are integrable with respect to this asymptotic thermal state, calculating both time and ensemble averages. We derive a useful canonical-like ensemble which is defined out of equilibrium, using a maximum entropy principle, where the constraints are normalization, finite averaged energy, and a mean-squared displacement which increases linearly with time. Our work merges infinite-ergodic theory with Boltzmann-Gibbs statistics, thus extending the scope of the latter while shedding new light on the concept of ergodicity.

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons is injection locked by the external drive at long timescales, but exhibits an unexpected suppression of the fast timing jitter. Counterintuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long timescale stability of the Kerr frequency comb’s repetition rate is improved by more than 4 orders of magnitude, the purified microwave signal shows a reduction of the phase noise by 30 dB at offset frequencies above 10 kHz.

We investigate the impact of liquid drops on deep pools of aqueous glycerol solutions with variable pool viscosity and air pressure both experimentally and numerically. With this approach, we are able to address drop impacts on substrates that continuously transition from low-viscosity liquids to almost solids. We show that the generic corolla spreading out from the impact point consists of two distinct sheets, namely an ejecta sheet fed by the drop liquid and a second sheet fed by the substrate liquid, which evolve on separated timescales. These two sheets contribute to a varying extent to the corolla overall dynamics and splashing, depending on the viscosity ratio between the two liquids.

We investigate the electronic structure of the flat bands induced by moiré superlattices and electric fields in nearly aligned $ABC$ trilayer graphene (TLG) boron-nitride (BN) interfaces where Coulomb effects can lead to correlated gapped phases. Our calculations indicate that valley-spin resolved isolated superlattice flat bands that carry a finite Chern number $C=3$ proportional to the layer number can appear near charge neutrality for appropriate perpendicular electric fields and twist angles. When the degeneracy of the bands is lifted by Coulomb interactions, these topological bands can lead to anomalous quantum Hall phases that embody orbital and spin magnetism. Narrow bandwidths of $\sim 10\mathrm{meV}$ achievable for a continuous range of twist angles $\theta \lesssim 0.6°$ with moderate interlayer potential differences of $\sim 50\mathrm{meV}$ make the TLG-BN systems a promising platform for the study of electric-field tunable Coulomb-interaction-driven spontaneous Hall phases.

We consider the ground-state energy and the spectrum of the low-energy excitations of a Majorana island formed of topological superconductors connected by a single-mode junction of arbitrary transmission. Coulomb blockade results in $e$-periodic modulation of the energies with the gate-induced charge. We find the amplitude of modulation as a function of reflection coefficient $\mathcal{R}$. The amplitude scales as $\sqrt{\mathcal{R}}$ in the limit $\mathcal{R}\to 0$. At larger $\mathcal{R}$, the dependence of the amplitude on the Josephson and charging energies is similar to that of a conventional-superconductor Cooper-pair box. The crossover value of $\mathcal{R}$ is small and depends on the ratio of the charging energy to superconducting gap.

Partial disorder—the microscopic coexistence of long-range magnetic order and disorder—is a rare phenomenon that has been experimentally and theoretically reported in some Ising- or easy plane-spin systems, driven by entropic effects at finite temperatures. Here, we present an analytical and numerical analysis of the $S=1/2$ Heisenberg antiferromagnet on the $\sqrt{3}\times \sqrt{3}$-distorted triangular lattice, which shows that its quantum ground state has partial disorder in the weakly frustrated regime. This state has a 180° Néel ordered honeycomb subsystem coexisting with disordered spins at the hexagon center sites. These central spins are ferromagnetically aligned at short distances, as a consequence of a Casimir-like effect originated by the zero-point quantum fluctuations of the honeycomb lattice.

We studied the magnetic ordering of thin films and bulk crystals of rutile ${\mathrm{RuO}}_2$ using resonant x-ray scattering across the Ru $L_2$ absorption edge. Combining polarization analysis and azimuthal angle dependence of the magnetic Bragg signal, we have established the presence and characteristic of collinear antiferromagnetism in ${\mathrm{RuO}}_2$ with $T_N>300\mathrm{K}$. In addition to revealing a spin-ordered ground state in the simplest ruthenium oxide compound, the persistence of magnetic order even in nanometer-thick films lays the ground for potential applications of ${\mathrm{RuO}}_2$ in antiferromagnetic spintronics.

We present a link between parametrizations of alternative theories of gravity on large and small scales in cosmology. This relationship is established using theoretical consistency conditions only. We find that in both limits the “slip” and “effective Newton’s constant” can be written in terms of a set of four functions of time, two of which are direct generalizations of the $\alpha$ and $\gamma$ parameters from post-Newtonian physics. This generalizes previous work that has constructed frameworks for testing gravity on small scales, and is to the best of our knowledge the first time that a link between parametrizations of gravity on such very different scales has been established. We expect our result to facilitate the imposition of observational constraints, by drastically reducing the number of functional degrees of freedom required to consistently test gravity on multiple scales in cosmology.

We study lasing at the high-symmetry points of the Brillouin zone in a honeycomb plasmonic lattice. We use symmetry arguments to define singlet and doublet modes at the $K$ points of the reciprocal space. We experimentally demonstrate lasing at the $K$ points that is based on plasmonic lattice modes and two-dimensional feedback. By comparing polarization properties to $T$-matrix simulations, we identify the lasing mode as one of the singlets with an energy minimum at the $K$ point enabling feedback. Our results offer prospects for studies of topological lasing in radiatively coupled systems.

The charge density wave (CDW) in ${\mathrm{ZrTe}}_3$ is quenched in samples with a small amount of Te isoelectronically substituted by Se. Using angle-resolved photoemission spectroscopy we observe subtle changes in the electronic band dispersions and Fermi surfaces upon Se substitution. The scattering rates are substantially increased, in particular for the large three-dimensional Fermi surface sheet. The quasi-one-dimensional band is unaffected by the substitution and still shows a gap at low temperature, which starts to open from room temperature. Long-range order is, however, absent in the electronic states as in the periodic lattice distortion. The competition between superconductivity and the CDW is thus linked to the suppression of long-range order of the CDW.

Ultracold atoms in optical lattices provide clean, tunable, and well-isolated realizations of paradigmatic quantum lattice models. With the recent advent of quantum-gas microscopes, they now also offer the possibility to measure the occupations of individual lattice sites. What, however, has not yet been achieved is to measure those elements of the single-particle density matrix, which are off- diagonal in the occupation basis. Here, we propose a scheme to access these basic quantities both for fermions as well as hard-core bosons and investigate its accuracy and feasibility. The scheme relies on the engineering of a large effective tunnel coupling between distant lattice sites and a protocol that is based on measuring site occupations after two subsequent quenches.