The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size.

We demonstrate deterministic generation of two distinct collective excitations in one atomic ensemble, and we realize the Hong-Ou-Mandel interference between them. Using Rydberg blockade we create single collective excitations in two different Zeeman levels, and we use stimulated Raman transitions to perform a beam-splitter operation between the excited atomic modes. By converting the atomic excitations into photons, the two-excitation interference is measured by photon coincidence detection with a visibility of 0.89(6). The Hong-Ou-Mandel interference witnesses an entangled NOON state of the collective atomic excitations, and we demonstrate its two times enhanced sensitivity to a magnetic field compared with a single excitation. Our work implements a minimal instance of boson sampling and paves the way for further multimode and multiexcitation studies with collective excitations of atomic ensembles.

We discuss the determination of the strong coupling ${\alpha }_{\overline{\mathrm{MS}}}(m_Z)$ or, equivalently, the QCD $\mathrm{\Lambda }$ parameter. Its determination requires the use of perturbation theory in ${\alpha }_s(\mu )$ in some scheme $s$ and at some energy scale $\mu$. The higher the scale $\mu$, the more accurate perturbation theory becomes, owing to asymptotic freedom. As one step in our computation of the $\mathrm{\Lambda }$ parameter in three-flavor QCD, we perform lattice computations in a scheme that allows us to nonperturbatively reach very high energies, corresponding to ${\alpha }_s=0.1$ and below. We find that (continuum) perturbation theory is very accurate there, yielding a 3% error in the $\mathrm{\Lambda }$ parameter, while data around ${\alpha }_s\approx 0.2$ are clearly insufficient to quote such a precision. It is important to realize that these findings are expected to be generic, as our scheme has advantageous properties regarding the applicability of perturbation theory.

Angle-resolved photoemission spectroscopy has been developed to a very high accuracy. However, effects that depend sensitively on the state of the emitted photoelectron were so far hard to compute for real molecules. We here show that the real-time propagation approach to time-dependent density functional theory allows us to obtain final-state effects consistently from first principles and with an accuracy that allows for the interpretation of experimental data. In a combined theoretical and experimental study we demonstrate that the approach captures three hallmark effects that are beyond the final-state plane-wave approximation: emission perpendicular to the light polarization, circular dichroism in the photoelectron angular distribution, and a pronounced energy dependence of the photoemission intensity.

Supported by a kinetic simulation, we derive an exclusion energy parameter ${\mathcal{E}}_X$ providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.

Self-consistent $GW$ calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through ab initio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7 eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9 eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at $-9.4$ and $-0.5\mathrm{eV}$ with respect to the vacuum level, respectively.

We investigate the nature of Yu-Shiba-Rusinov (YSR) subgap states induced by single manganese (Mn) atoms adsorbed on different surface orientations of superconducting lead (Pb). Depending on the adsorption site, we detect a distinct number and characteristic patterns of YSR states around the Mn atoms. We suggest that the YSR states inherit their properties from the Mn $d$ levels, which are split by the surrounding crystal field. The periodicity of the long-range YSR oscillations allows us to identify a dominant coupling of the $d$ states to the outer Fermi sheet of the two-band superconductor Pb.

The $t_{2g}$ orbitals of an edge-shared transition-metal oxide with a honeycomb lattice structure form dispersionless electronic bands when only hopping mediated by the edge-sharing oxygens is accessible. This is due to the formation of isolated quasimolecular orbitals (QMOs) in each hexagon, introduced recently by Mazin et al. [Phys. Rev. Lett. 109, 197201 (2012)], which stabilizes a band insulating phase for $t_{2g}^5$ systems. However, with the help of the exact diagonalization method to treat the electron kinetics and correlations on an equal footing, we find that the QMOs are fragile against not only the spin-orbit coupling (SOC) but also the Coulomb repulsion. We show that the electronic phase of $t_{2g}^5$ systems can vary from a quasimolecular band insulator to a relativistic $J_{\text{eff}}=1/2$ Mott insulator with increasing the SOC as well as the Coulomb repulsion. The different electronic phases manifest themselves in electronic excitations observed in optical conductivity and resonant inelastic x-ray scattering. Based on our calculations, we assert that the currently known ${\mathrm{Ru}}^{3+}$ and ${\mathrm{Ir}}^{4+}$ based honeycomb systems are far from the quasimolecular band insulator but rather the relativistic Mott insulator.

The embryogenesis of the small nematode Caenorhabditis elegans is a remarkably robust self-organization phenomenon. Cell migration trajectories in the early embryo, for example, are well explained by mechanical cues that push cells into positions where they experience the least repulsive forces. Yet, how this mechanically guided progress in development is properly timed has remained elusive so far. Here, we show that cell volumes and division times are strongly anticorrelated during the early embryogenesis of C. elegans with significant differences between somatic cells and precursors of the germline. Our experimental findings are explained by a simple model that in conjunction with mechanical guidance can account for the fail-safe early embryogenesis of C. elegans.

It is commonly believed that quantum isolated systems satisfying the eigenstate thermalization hypothesis (ETH) are diffusive. We show that this assumption is too restrictive since there are systems that are asymptotically in a thermal state yet exhibit anomalous, subdiffusive thermalization. We show that such systems satisfy a modified version of the ETH ansatz and derive a general connection between the scaling of the variance of the off-diagonal matrix elements of local operators, written in the eigenbasis of the Hamiltonian, and the dynamical exponent. We find that for subdiffusively thermalizing systems the variance scales more slowly with system size than expected for diffusive systems. We corroborate our findings by numerically studying the distribution of the coefficients of the eigenfunctions and the off-diagonal matrix elements of local operators of the random field Heisenberg chain, which has anomalous transport in its thermal phase. Surprisingly, this system also has non-Gaussian distributions of the eigenfunctions, thus, directly violating Berry’s conjecture.

Achieving error rates that meet or exceed the fault-tolerance threshold is a central goal for quantum computing experiments, and measuring these error rates using randomized benchmarking is now routine. However, direct comparison between measured error rates and thresholds is complicated by the fact that benchmarking estimates average error rates while thresholds reflect worst-case behavior when a gate is used as part of a large computation. These two measures of error can differ by orders of magnitude in the regime of interest. Here we facilitate comparison between the experimentally accessible average error rates and the worst-case quantities that arise in current threshold theorems by deriving relations between the two for a variety of physical noise sources. Our results indicate that it is coherent errors that lead to an enormous mismatch between average and worst case, and we quantify how well these errors must be controlled to ensure fair comparison between average error probabilities and fault-tolerance thresholds.

We report a detailed simulation and classical density functional theory study of the drying transition in a realistic model fluid at a smooth substrate. This transition (in which the contact angle $\theta \to 180°$) is shown to be critical for both short-ranged and long-ranged substrate-fluid interaction potentials. In the latter case critical drying occurs at exactly zero attractive substrate strength. This observation permits the accurate elucidation of the character of the transition via a finite-size scaling analysis of the density probability function. We find that the critical exponent ${\nu }_{\parallel }$ that controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall, is over twice as large as predicted by mean field and renormalization group calculations. We suggest a reason for the discrepancy. Our findings shed new light on fluctuation phenomena in fluids near hydrophobic and solvophobic interfaces.

The physical properties of epitaxial films can fundamentally differ from those of bulk single crystals even above the critical thickness. By a combination of nonresonant x-ray magnetic scattering, neutron diffraction and vector-mapped x-ray magnetic linear dichroism photoemission electron microscopy, we show that epitaxial (111)-${\text{BiFeO}}_3$ films support submicron antiferromagnetic domains, which are magnetoelastically coupled to a coherent crystallographic monoclinic twin structure. This unique texture, which is absent in bulk single crystals, should enable control of magnetism in ${\text{BiFeO}}_3$ film devices via epitaxial strain.

One of the most intriguing aspects of quantum mechanics is the impossibility of measuring at the same time observables corresponding to noncommuting operators, because of quantum uncertainty. This impossibility can be partially relaxed when considering joint or sequential weak value evaluation. Indeed, weak value measurements have been a real breakthrough in the quantum measurement framework that is of the utmost interest from both a fundamental and an applicative point of view. In this Letter, we show how we realized for the first time a sequential weak value evaluation of two incompatible observables using a genuine single-photon experiment. These (sometimes anomalous) sequential weak values revealed the single-operator weak values, as well as the local correlation between them.