Motivated by several claims of spin-orbit-driven spin-liquid physics in hexagonal ${\mathrm{Ba}}_3{\mathrm{Ti}}_{3-x}{\mathrm{Ir}}_x{\mathrm{O}}_9$ hosting ${\mathrm{Ir}}_2{\mathrm{O}}_9$ dimers, we report on resonant inelastic x-ray scattering (RIXS) at the Ir $L_3$ edge for different $x$. We demonstrate that magnetism in ${\mathrm{Ba}}_3{\mathrm{Ti}}_{3-x}{\mathrm{Ir}}_x{\mathrm{O}}_9$ is governed by an unconventional realization of strong disorder, where cation disorder affects the character of the local moments. RIXS interferometry, studying the RIXS intensity over a broad range of transferred momentum $\mathbf{q}$, is ideally suited to assign different excitations to different Ir sites. We find pronounced Ir-Ti site mixing. Both ions are distributed over two crystallographically inequivalent sites, giving rise to a coexistence of quasimolecular singlet states on ${\mathrm{Ir}}_2{\mathrm{O}}_9$ dimers and spin-orbit-entangled $j=1/2$ moments of $5d^5{\mathrm{Ir}}^{4+}$ ions. RIXS reveals different kinds of strong magnetic couplings for different bonding geometries, highlighting the role of cation disorder for the suppression of long-range magnetic order in this family of compounds.

We investigate the influence of large electric fields on the transport properties of nanostructures patterned into the electron gas at the interface between ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$ (100). In these nanostructures, the transport is largely dominated by domain walls between structural domains in the ${\mathrm{SrTiO}}_3$ appearing below a structural phase transition temperature. We find that both positive and negative gate voltages applied in a side-gate configuration can induce persistent changes in the sample that are only reversed by warming through the phase transition. These changes include a resistance increase and a change in magnetoresistance in magnitude and sign. Furthermore, a resistance anomaly during warm-up that has been observed in the past can be further increased by briefly applying a side-gate voltage. These effects are typically observed in nanostructures below a certain size limit. The electric fields also increase this size limit from a few-hundred nm to more than 1 $\mu \mathrm{m}$. All these observations can be consistently explained by a field-induced removal of specific domain-wall types accompanied by an increasing domain size and a reduced number of domain walls in the structures. The results not only show that under certain conditions domain walls can dominate the transport properties even of micron-sized structures, but they also provide an additional tuning knob to induce nonvolatile changes in the transport properties of ${\mathrm{LaAlO}}_3\text{/}{\mathrm{SrTiO}}_3$ interfaces at low temperatures.

Light-matter interactions that are nonlinear with respect to the photon number reveal the quantum nature of coherent states. We characterize how coherent states depart from Gaussian by the emergence of negative values in their Wigner function during the evolution while maintaining their characteristic Poissonian photon statistics. Such states have nonminimum uncertainty yet present a metrological advantage that can reach the Heisenberg limit. Non-Gaussianity of light arises as a general property of nonlinear interactions, which only requires a polarizable media, resonant or dispersive. Our results highlight how useful quantum features can be extracted from the seemingly most classical states of light, a relevant phenomenon for quantum optics applications.

Superconducting optoelectronic loop neurons are a class of circuits potentially conducive to networks for large-scale artificial cognition. These circuits employ superconducting components including single-photon detectors, Josephson junctions, and transformers to achieve neuromorphic functions. To date, all simulations of loop neurons have used first-principles circuit analysis to model the behavior of synapses, dendrites, and neurons. These circuit models are computationally inefficient and leave opaque the relationship between loop neurons and other complex systems. Here we introduce a modeling framework that captures the behavior of the relevant synaptic, dendritic, and neuronal circuits at a phenomenological level without resorting to full circuit equations. Within this compact model, each dendrite is discovered to obey a single nonlinear leaky-integrator ordinary differential equation, while a neuron is modeled as a dendrite with a thresholding element and an additional feedback mechanism for establishing a refractory period. A synapse is modeled as a single-photon detector coupled to a dendrite, where the response of the single-photon detector follows a closed-form expression. We quantify the accuracy of the phenomenological model relative to circuit simulations and find that the approach reduces computational time by a factor of ten thousand while maintaining an accuracy of one part in ten thousand. We demonstrate the use of the model with several basic examples. The net increase in computational efficiency enables future simulation of large networks, while the formulation provides a connection to a large body of work in applied mathematics, computational neuroscience, and physical systems such as spin glasses.

By preparing two distant emitters in entangled Dicke states via detection of a single photon, the subsequent spatiotemporal photon emission is investigated. Depending on the parity of the established quantum state, emission patterns for the second scattered photon are observed featuring spatial superradiance as well as subradiance. We employ ultrafast single-photon resolving cameras with high spatial resolution disclosing the spatiotemporal emission characteristics. By recording the first photon in one direction and the second photon in another, revealing the spatial two-photon cross-correlation function $g^{\left(2\right)}({\mathbf{r}}_1,{\mathbf{r}}_2)$, we characterize the collective spontaneous emission behavior of two ions in free space. We explain the observed contrast of $g^{\left(2\right)}({\mathbf{r}}_1,{\mathbf{r}}_2)$ considering independently derived experimental parameters. Our results show how the detection of a single photon can profoundly modify the collective spontaneous emission dynamics of an atomic ensemble.

While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. By including interactions in the topologically nontrivial Haldane model, we show that a quarter-filled state emerges with a nonzero Chern number provided the interactions are sufficiently large. We first motivate this result on physical grounds and then by two methods: Analytically by solving exactly a model in which interactions are local in momentum space and then numerically through the corresponding Hubbard model. All methods yield the same result: For sufficiently large interaction strengths, the quarter-filled Haldane model is a ferromagnetic topological Mott insulator with a Chern number of unity. Possible experimental realizations in cold-atom and solid-state systems are discussed.

Three-body recombination is a chemical reaction where the collision of three atoms leads to the formation of a diatomic molecule. In the ultracold regime it is expected that the production rate of a molecule generally decreases with its binding energy $E_b$, however, its precise dependence and the physics governing it have been left unclear so far. Here we present a comprehensive experimental and theoretical study of the energy dependency for three-body recombination of ultracold Rb. For this, we determine production rates for molecules in a state-to-state resolved manner, with the binding energies $E_b$ ranging from 0.02 to 77 $\mathrm{GHz}\times h$. We find that the formation rate approximately scales as $E_b^{-\alpha }$, where $\alpha$ is in the vicinity of 1. The formation rate typically varies only within a factor of two for different rotational angular momenta of the molecular product, apart from a possible centrifugal barrier suppression for low binding energies. In addition to numerical three-body calculations we present a perturbative model which reveals the physical origin of the energy scaling of the formation rate. Furthermore, we show that the scaling law potentially holds universally for a broad range of interaction potentials.

First-principles Hubbard-corrected approximate density functional theory ($\mathrm{DFT}+\mathrm{U}$) is a low-cost, potentially high-throughput method of simulating materials, but it has been hampered by empiricism and inconsistent band gap correction in transition metal oxides (TMOs). $\mathrm{DFT}+\mathrm{U}$ property prediction of non-magnetic systems such as $d^0$ and $d^{10}$ TMOs is typically faced with excessively large calculated Hubbard U values and difficulty in obtaining acceptable band gaps and lattice volumes. Meanwhile, Hund's exchange coupling J is an important but often neglected component of $\mathrm{DFT}+\mathrm{U}$, and the J parameter has proven challenging to directly calculate by means of linear response. In this paper, we provide a revised formula for computing Hund's J using established self-consistent field $\mathrm{DFT}+\mathrm{U}$ codes. For non-magnetic systems, we introduce a non-approximate technique for calculating U and J simultaneously in such codes, at no additional cost. Using unmodified quantum espresso, we assess the resulting values using two different $\mathrm{DFT}+\mathrm{U}$ functionals incorporating J, namely, the widely used $\mathrm{DFT}+(\mathrm{U}-\mathrm{J})$ and the readily available $\mathrm{DFT}+\mathrm{U}+\mathrm{J}$. We assess a test set comprising $\mathrm{Ti}{\mathrm{O}}_2, \mathrm{Zr}{\mathrm{O}}_2, \mathrm{Hf}{\mathrm{O}}_2, {\mathrm{Cu}}_2\mathrm{O}$, and ZnO, and apply the corrections both to metal- and oxygen-centered pseudoatomic subspaces. Starting from the PBE functional, we find that $\mathrm{DFT}+(\mathrm{U}-\mathrm{J})$ is significantly outperformed in band gap accuracy by $\mathrm{DFT}+\mathrm{U}+\mathrm{J}$, the mean-absolute band gap error of which matches that of the hybrid functional HSE06. ZnO, a longstanding challenge case for $\mathrm{DFT}+\mathrm{U}$, is addressed by means of Zn $4s$ instead of Zn $3d$ correction, whereupon the first-principles $\mathrm{DFT}+\mathrm{U}+\mathrm{J}$ band gap error falls to half of that reported for HSE06 yet remains larger than that for PBE0.

We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix associated with the system, leading to the emergence of waves with a preferred direction. We then create analytical predictions for the specific spatiotemporal patterns observed in individual simulations of time-delayed Kuramoto networks. This approach generalizes to systems with heterogeneous time delays at finite scales, which permits the study of spatiotemporal dynamics in a broad range of applications.

We use entanglement witnesses to detect entanglement in the $XY$ chain in thermal equilibrium and determine the temperature bound below which the state is detected as entangled. We consider the entanglement witness based on the Hamiltonian. Such a witness detects a state as entangled if its energy is smaller than the energy of separable states. We also consider a family of entanglement witnesses related to the entanglement negativity of the state. We test the witnesses in infinite and finite systems. We study how the temperature bounds obtained are influenced by a quantum phase transition or a disorder line in the ground state. Very strong finite-size corrections are observed in the ordered phase due to the presence of a quasidegenerate excitation. We also study the postquench states in the thermodynamic limit after a quench when the parameters of the Hamiltonian are changed suddenly. In the case of the Ising model, we find that the mixed postquench state is detected as entangled by the two methods if the parameters of the Hamiltonian before and after the quench are close to each other. We find that the two witnesses give qualitatively similar results, showing that energy-based entanglement witnesses are efficient in detecting the nearest-neighbor entanglement in spin chains in various circumstances. For other XY models, we find that the negativity-based witnesses also detect states in some parameter regions where the energy-based witness does not, in particular, if the quench is performed from the paramagnetic phase to the ferromagnetic phase and vice versa. The domains in parameter space corresponding to postquench states detected as entangled by the energy-based witness have been determined analytically, which stresses further the utility of our method.

We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit-coupled Rydberg atoms gives rise to disordered quantum phases which are topological and may be candidates for quantum spin liquids. As recently demonstrated by Lienhard et al. [Phys. Rev. X 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of spin excitations which behave as hard-core bosons. Using exact diagonalization (ED), we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms as well as density-density interactions. In mean-field approximation there is a phase transition from a condensate to a ${120}^{\circ }$ phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase emerges close to the mean-field critical point as a result of quantum correlations induced by the density dependence of the complex hopping. We show that without density-density interactions this phase is a genuine disordered one, has large spin chirality, and is characterized by a nontrivial many-body Chern number. The Chern number is found to be robust to disorder. ED simulations of small lattices with up to 30 lattice sites give indications for a nondegenerate ground state with finite spin and collective gaps and thus for a bosonic integer quantum Hall phase, protected by $\mathrm{U}\left(1\right)$ symmetry. On the other hand, while staying finite, the many-body gap varies substantially when different twisted boundary conditions are applied, which points to a gapless phase. For very strong negative nonlinear hopping amplitudes we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin liquid but lies outside the parameter regime experimentally accessible in the Rydberg system.

Many computational problems can be formulated in terms of high-dimensional functions. Simple representations of such functions and resulting computations with them typically suffer from the “curse of dimensionality,” an exponential cost dependence on dimension. Tensor networks provide a way to represent certain classes of high-dimensional functions with polynomial memory. This results in computations where the exponential cost is ameliorated or, in some cases, removed, if the tensor network representation can be obtained. Here, we introduce a direct mapping from the arithmetic circuit of a function to arithmetic circuit tensor networks, avoiding the need to perform any optimization or functional fit. We demonstrate the power of the circuit construction in examples of multivariable integration on the unit hypercube in up to 50 dimensions, where the complexity of integration can be understood from the circuit structure. We find very favorable cost scaling compared with quasi–Monte Carlo integration for these cases and further give an example where efficient quasi–Monte Carlo integration cannot be performed without knowledge of the underlying tensor network circuit structure.

Recently, an unconditional advantage has been demonstrated for the process of charging of a quantum battery in a collisional model [Seah et al., Phys. Rev. Lett. 127, 100601 (2021)]. Motivated by the question of whether such an advantage could be observed experimentally, we consider a model where the battery is described by a quantum harmonic oscillator or a large spin, charged via repeated interactions with a stream of qubit units. For both setups, we show that a quantum protocol can significantly outperform the most general adaptive classical schemes, leading to 90 and 38% higher charging power for the cavity and large spin batteries, respectively. Toward an experimental realization, we also characterize the robustness of this quantum advantage to imperfections (noise and decoherence) considering implementations with state-of-the-art micromasers and hybrid superconducting devices.