We report on subcycle terahertz light-field emission of electrons from tungsten nanotips under extreme conditions corresponding to a Keldysh parameter ${\gamma }_{\text{K}}\approx {10}^{-4}$. Local peak THz fields up to 40 GV/m are achieved at the apex of an illuminated nanotip, causing subcycle cold-field electron emission and acceleration in the quasistatic field. By simultaneous measurement of the electron bunch charge and energy distribution, we perform a quantitative test of quasistatic Fowler-Nordheim tunneling theory under field conditions that completely suppress the tunnel barrier. Very high bunch charges of $\sim {10}^6$ electrons/pulse are observed, reaching maximum energies of 3.5 keV after acceleration in the local field. The energy distribution and emission current show good agreement with Fowler-Nordheim theory even in this extreme field regime. Application of this theory under such extreme THz field conditions predicts a single-shot electron energy distribution with a spectral purity reaching ${10}^{-4}$. THz field-induced reshaping and sharpening of the nanotip is observed, reducing the tip radius from 120 to 35 nm over roughly ${10}^9$ THz shots. These results indicate THz-driven nanotips in the extreme field limit are promising electron sources for ultrafast electron diffraction and microscopy.

Nonequilibrium properties of correlated quantum matter are being intensively investigated because of the rich interplay between external driving and the many-body correlations. Of particular interest is the nonequilibrium behavior near a quantum critical point (QCP), where the system is delicately balanced between different ground states. We present both an analytical calculation of the nonequilibrium steady-state current in a critical system and experimental results to which the theory is compared. The system is a quantum dot coupled to resistive leads: a spinless resonant level interacting with an Ohmic dissipative environment. A two-channel Kondo-like QCP occurs when the level is on resonance and symmetrically coupled to the leads, conditions achieved by fine tuning using electrostatic gates. We calculate and measure the nonlinear current as a function of bias ($I\text{−}V$ curve) at the critical values of the gate voltages corresponding to the QCP. The quantitative agreement between the experimental data and the theory, with no fitting parameter, is excellent. As our system is fully accessible to both theory and experiment, it provides an ideal setting for addressing nonequilibrium phenomena in correlated quantum matter.

Classical open systems with balanced gain and loss, i.e., parity-time ($\mathcal{PT}$) symmetric systems, have attracted tremendous attention over the past decade. Their exotic properties arise from exceptional point degeneracies of non-Hermitian Hamiltonians that govern their dynamics. In recent years, increasingly sophisticated models of $\mathcal{PT}$ symmetric systems with time-periodic (Floquet) driving, time-periodic gain and loss, and time-delayed coupling have been investigated, and such systems have been realized across numerous platforms comprising optics, acoustics, mechanical oscillators, optomechanics, and electrical circuits. Here, we introduce a $\mathcal{PT}$ symmetric (balanced gain and loss) system with memory and investigate its dynamics analytically and numerically. Our model consists of two coupled $LC$ oscillators with positive and negative resistance, respectively. We introduce memory by replacing either the resistor with a memristor, or the coupling inductor with a meminductor, and investigate the circuit energy dynamics as characterized by $\mathcal{PT}$ symmetric or $\mathcal{PT}$ symmetry broken phases. Due to the resulting nonlinearity, we find that energy dynamics depend on the sign and strength of initial voltages and currents, as well as the distribution of initial circuit energy across its different components. Surprisingly, at strong inputs, the system exhibits self-organized Floquet dynamics, including a $\mathcal{PT}$ symmetry broken phase at vanishingly small dissipation strength. Our results indicate that $\mathcal{PT}$ symmetric systems with memory show a rich landscape.

We present a physical interpretation of machine learning functions, opening up the possibility to control properties of statistical systems via the inclusion of these functions in Hamiltonians. In particular, we include the predictive function of a neural network, designed for phase classification, as a conjugate variable coupled to an external field within the Hamiltonian of a system. Results in the two-dimensional Ising model evidence that the field can induce an order-disorder phase transition by breaking or restoring the symmetry, in contrast with the field of the conventional order parameter which causes explicit symmetry breaking. The critical behavior is then studied by proposing a Hamiltonian-agnostic reweighting approach and forming a renormalization group mapping on quantities derived from the neural network. Accurate estimates of the critical point and of the critical exponents related to the operators that govern the divergence of the correlation length are provided. We conclude by discussing how the method provides an essential step toward bridging machine learning and physics.

Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments. Here, we investigate Hamiltonian lattice gauge theories defined in two-leg ladders. We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local ${\mathbb{Z}}_N$ gauge symmetries. We study its phase diagram based on both an effective low-energy field theory and density matrix renormalization group simulations. For $N\ge 5$, an extended gapless Coulomb phase emerges, which is separated by a Berezinskii-Kosterlitz-Thouless phase transition from the surrounding gapped phase. Besides the traditional confined and Higgs regimes, we also observe a novel quadrupolar region, originated by the ladder geometry.

The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method, supported by machine learning techniques, that is capable of constructing topological models for a generic lattice without prior knowledge of the phase diagram. By sampling tight-binding parameter vectors from a random distribution, we obtain data sets that we label with the corresponding topological index. This labeled data is then analyzed to extract those parameters most relevant for the topological classification and to find their most likely values. We find that the marginal distributions of the parameters already define a topological model. Additional information is hidden in correlations between parameters. Here we present as a proof of concept the prediction of the Haldane model as the prototypical topological insulator for the honeycomb lattice in Altland-Zirnbauer (AZ) class A. The algorithm is straightforwardly applicable to any other AZ class or lattice, and could be generalized to interacting systems.

We propose a versatile, free-space cavity optomechanics platform built from two photonic crystal membranes, one of which is freely suspended, and designed to form a microcavity less than one wavelength long. This cavity features a series of photonic bound states in the continuum that, in principle, trap light forever and can be favorably used together with evanescent coupling for realizing various types of optomechanical couplings, such as linear or quadratic coupling of either dispersive or dissipative type, by tuning the photonic crystal patterning and cavity length. Crucially, this platform allows for a quantum cooperativity exceeding unity in the ultrastrong single-photon coupling regime, surpassing the performance of conventional Fabry-Pérot–based cavity optomechanical devices in the nonresolved sideband regime. This platform allows for exploring new regimes of the optomechanical interaction, in particular in the framework of pulsed and single-photon optomechanics.

Self-oscillating systems, described in classical dynamics as limit cycles, are emerging as canonical models for driven dissipative nonequilibrium open quantum systems and as key elements in quantum technology. We consider a family of models that interpolates between the classical textbook examples of the Rayleigh and the van der Pol oscillators and follow their transition from the classical to the quantum domain, while properly formulating their corresponding quantum descriptions. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models, applicable to any bosonic system—whether mechanical, optical, or otherwise—that is coupled to its environment via single-boson and double-boson emission and absorption. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature, often misattributed to the quantum van der Pol oscillator. We closely explore the classical to quantum transition of the bifurcation to self-oscillations of this oscillator, while noting changes in the dynamics and identifying features that are uniquely quantum.

In this paper we study the scattering and transfer matrices for electric fields defined with respect to an angular spectrum of plane waves. For these matrices, we derive the constraints that are enforced by conservation of energy, reciprocity, and time reversal symmetry. Notably, we examine the general case of vector fields in three dimensions and allow for evanescent field components. Moreover, we consider fields described by both continuous and discrete angular spectra, the latter being more relevant to practical applications, such as optical scattering experiments. We compare our results to better-known constraints, such as the unitarity of the scattering matrix for far-field modes, and show that previous results follow from our framework as special cases. Finally, we demonstrate our results numerically with a simple example of wave propagation at a planar glass-air interface, including the effects of total internal reflection. Our formalism makes minimal assumptions about the nature of the scattering medium and is thus applicable to a wide range of scattering problems.

In this work, we use ultrafast pump-probe nonresonant and resonant x-ray diffraction to track the periodic lattice distortion and the electronic charge density wave in $1\mathrm{T}\text{−}{\mathrm{TiSe}}_2$ upon optical excitation. We observe a fluence regime in which the periodic lattice deformation is strongly suppressed but the charge density wave related Se $4p$ orbital order remains mostly intact. Complete melting of both structural and electronic order occurs four to five times faster than expected from a purely electronic charge-screening process, strongly suggesting a structurally assisted weakening of excitonic correlations. Our experimental data provide insight on the intricate coupling between structural and electronic order in stabilizing the periodic-lattice-distortion/charge-density-wave state in $1\mathrm{T}\text{−}{\mathrm{TiSe}}_2$. The results further show that electron-phonon coupling can lead to different, energy dependent phase-transition pathways in condensed matter systems, opening different possibilities in the conception of nonequilibrium phenomena at the ultrafast scale.

Unconventional symmetry-breaking phenomena due to nontrivial order parameters attract increasing attention in strongly correlated electron systems. Here, we predict theoretically the occurrence of nanoscale spontaneous spin current, called the spin-loop-current (sLC) order, as a promising origin of the pseudogap and electronic nematicity in cuprates. We reveal that the sLC is driven by the odd-parity electron-hole condensations that are mediated by transverse spin fluctuations around the pseudogap temperature $T^{*}$. At the same temperature, odd-parity magnon pair condensation occurs. The sLC order is “hidden” in that neither internal magnetic field nor charge-density modulation is induced, whereas the predicted sLC with finite wave-number naturally gives the Fermi arc structure. In addition, the fluctuations of sLC order work as attractive pairing interaction between adjacent hot spots, which enlarges the $d$-wave superconducting transition temperature $T_{\mathrm{c}}$. The sLC state will be a key ingredient in understanding the pseudogap, electronic nematicity, as well as superconductivity in cuprates and other strongly correlated metals.

In ionic Raman scattering, infrared-active phonons mediate a scattering process that results in the creation or destruction of a Raman-active phonon. This mechanism relies on nonlinear interactions between phonons and has in recent years been associated with a variety of emergent lattice-driven phenomena in complex transition-metal oxides, but the underlying mechanism is often obscured by the presence of multiple coupled order parameters in play. Here, we use time-resolved spectroscopy to compare coherent phonons generated by ionic Raman scattering with those created by more conventional electronic Raman scattering on the nonmagnetic and non-strongly-correlated wide-band-gap insulator ${\mathrm{LaAlO}}_3$. We find that the oscillatory amplitude of the low-frequency Raman-active $E_g$ mode exhibits a sharp peak when we tune our pump frequency into resonance with the high-frequency infrared-active $E_u$ mode, consistent with first-principles calculations. Our results suggest that ionic Raman scattering can strongly dominate electronic Raman scattering in wide-band-gap insulating materials. We also see evidence of competing scattering channels at fluences above $28\mathrm{mJ}/{\mathrm{cm}}^2$ that alter the measured amplitude of the coherent phonon response.

Ab initio molecular dynamics (AIMD) is a powerful tool to predict properties of molecular and condensed matter systems. However, the quality of this procedure relies on the availability of rigorous electronic structure calculations. The development of quantum processors has shown great potential for the efficient evaluation of accurate ground and excited state energies of molecular systems, opening up new avenues for molecular dynamics simulations. In this work, we address the use of variational quantum algorithms for the calculation of accurate atomic forces to be used in AIMD. In particular, we provide solutions for the alleviation of the statistical noise associated with the measurements of the expectation values of energies and forces, as well as schemes for the mitigation of the hardware noise sources (in particular, gate infidelities, qubit decoherence, and readout errors). Despite the relative large error in the calculation of the potential energy, our results show that the proposed algorithms can provide accurate MD trajectories in the microcanonical (constant energy) ensemble. Furthermore, exploiting the intrinsic noise associated to the quantum measurement process, we also propose a Langevin dynamics algorithm for the simulation of canonical, i.e., constant temperature, dynamics. Both algorithms (microcanonical and canonical) are applied to the simulation of simple molecular systems such as ${\mathrm{H}}_2$ and ${\mathrm{H}}_3^{+}$. Finally, we also provide results for the dynamics of ${\mathrm{H}}_2$ obtained with IBM quantum computer ibmq_athens.

We study seasonal epidemic spreading in a susceptible-infected-removed-susceptible model on small-world graphs. We derive a mean-field description that accurately captures the salient features of the model, most notably a phase transition between annual and biennial outbreaks. A numerical scaling analysis exhibits a diverging autocorrelation time in the thermodynamic limit, which confirms the presence of a classical discrete time crystalline phase. We derive the phase diagram of the model both from mean-field theory and from numerics. Our paper demonstrates that small worldness and non-Markovianity can stabilize a classical discrete time crystal, and links recent efforts to understand such dynamical phases of matter to the century-old problem of biennial epidemics.

Understanding the limits to the spin coherence of the nitrogen-vacancy (NV) center in diamond is vital to realizing the full potential of this quantum system. We show that relaxation on the $|m_s=-1\rangle \leftrightarrow |m_s=+1\rangle$ transition occurs approximately twice as fast as relaxation on the $|m_s=0\rangle \leftrightarrow |m_s=\pm 1\rangle$ transitions under ambient conditions in native NVs in high-purity bulk diamond. The rates we observe are independent of NV concentration over four orders of magnitude, indicating they are limited by spin-phonon interactions. We find that the maximum theoretically achievable coherence time for an NV at 295 K is limited to 6.8(2) ms. Finally, we present a theoretical analysis of our results that suggests Orbach-like relaxation from quasilocalized phonons or contributions due to higher-order terms in the spin-phonon Hamiltonian are the dominant mechanism behind $|m_s=-1\rangle \leftrightarrow |m_s=+1\rangle$ relaxation, motivating future measurements of the temperature dependence of this relaxation rate.

With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message-passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targeted. Analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic.

The observation of abundant topological properties in optical platforms has attracted people's attention due to their great advantages in fundamental topological research and practical applications. Here, we use a double Su-Schrieffer-Heeger (SSH) chain structure composed of split ring resonators (SRRs) to mimic a Kitaev model. By properly tuning the orientation angles of the slits of the SRRs, we can ingeniously design the complex coupling distribution. We experimentally measure the topological phase transition of the double SSH model by adjusting the distance between the two chains and observe the topological bound states in the topological nontrivial phase. Importantly, inserting a trivial structure into the topological chain, we show the coupling of two topological bound states. By increasing the length of the inserted trivial chain, we observe that two topological bound states gradually approach each other and degenerate in the critical state. In addition, we theoretically study the controllable topological bound states and exceptional point physics formed by topological bound states. Our findings not only clearly show the establishing process of the photonic bound states in a double SSH chain, but also may facilitate some applications such as sensors, energy transfer, and switch with topological protection.

Density functional theory modeling was performed to determine the effect of humidity and ${\mathrm{H}}_2/{\mathrm{O}}_2$ gas pressure on the defect chemistry, hydrogen solubility and diffusivity, and on cation transport in tetragonal bulk $\mathrm{Zr}{\mathrm{O}}_2$, for the temperature range $400–1200{}^{\circ }\mathrm{C}$. The main goal of this study is to identify the stable defect complexes and hydrogen-related defect species relevant to bulk cation transport kinetics at various gas pressure, humidity, and temperature conditions, including cation diffusion via a Zr vacancy mechanism [with −4 charge, $V_{\mathrm{Zr}}\left(-4\right)$], through an $H$-substituted Zr defect mechanism [via $\mathrm{an}H$ substituted Zr defect with −3 charge, $H_{\mathrm{Zr}}\left(-3\right)$], and via formation of fully or partially bound Schottky defect complexes ($V_{\mathrm{Zr}}\text{−}{V}_{\mathrm{O}}$ and $V_{\mathrm{O}}\text{−}{V}_{\mathrm{Zr}}\text{−}{V}_{\mathrm{O}}$). At low temperatures $(T<500{}^{\circ }\mathrm{C})$ and humidity condition of 3%, the modeling results show a 0.5–0.7-eV reduction in the apparent formation free energy of $H_{\mathrm{Zr}}\left(-3\right)$ versus that of $V_{\mathrm{Zr}}\left(-4\right)$ due to the attractive interaction between interstitial hydrogen and the Zr vacancy, leading to a concentration of the $H_{\mathrm{Zr}}\left(-3\right)$ defect species that is higher than $V_{\mathrm{Zr}}\left(-4\right)$ specie. The migration barriers of the $H_{\mathrm{Zr}}\left(-3\right)$ versus $V_{\mathrm{Zr}}\left(-4\right)$ are found to be comparable, i.e., 2.7 eV versus 2.4 eV for the out-of-$ab$-plane migration and 3.1 eV versus 3.0 eV for the in-$ab$-plane migration, respectively. The calculated diffusion coefficients reveal that cation diffusion in tetragonal bulk $\mathrm{Zr}{\mathrm{O}}_2$ will transit from the $V_{\mathrm{Zr}}\left(-4\right)$ mechanism at high temperatures to the $H_{\mathrm{Zr}}\left(-3\right)$ mechanism upon lowering the operating temperature and/or increasing the humidity content. The defect thermodynamic modeling results indicate that most of the stable hydrogen defect species in tetragonal bulk $\mathrm{Zr}{\mathrm{O}}_2$ is $H_{\mathrm{Zr}}\left(-3\right)$, and its concentration is 4–6 orders of magnitude higher than that of $H$ interstitial ($H_{\mathrm{int}}$). Nonetheless, the most active hydrogen transport occurs via $H_{\mathrm{int}}\left(+1\right)$ with migration barriers 0.2–0.4 eV rather than through the stable $H_{\mathrm{Zr}}\left(-3\right)$ defect which has a larger migration barrier of 1.6 eV. At temperatures higher than 1173 K, the protonic transport rate in bulk tetragonal $\mathrm{Zr}{\mathrm{O}}_2$ is predicted to be several orders of magnitude higher than the bulk cation transport rate. Above 1573 K, the modeling results further predict another transition in the bulk cation transport mechanisms, $V_{\mathrm{Zr}}$ → fully or partially bound Schottky defects, attributed to enhanced entropic stabilization associated with oxygen vacancy formation (in the defect cluster) in equilibrium with ${\mathrm{O}}_2$ or ${\mathrm{H}}_2\mathrm{O}$ gas phase at the respective temperature. Overall, the results obtained highlight the importance of the coupling of the bulk cation transport kinetics with the dissolved $H$ defect species at lower temperature and respectively, with the cation-anion vacancy clusters at higher temperature, and predict several temperature dependent mechanistic transitions for the cation transport in tetragonal bulk zirconia.

This paper explores the benefit of added noise in increasing the computational complexity of digital recurrent neural networks (RNNs). The physically accepted model of the universe imposes rational number, stochastic limits on all calculations. An analog RNN with those limits calculates at the super-Turing complexity level BPP/log*. In this paper, we demonstrate how noise aids digital RNNs in attaining super-Turing operation similar to analog RNNs. We investigate moving limited-precision systems from not being chaotic at small amounts of noise, through consistency with chaos, to overwhelming it at large amounts of noise. A Kolmogorov-complexity-based proof shows that an infinite computational class hierarchy exists between P, the Turing class, and BPP/log*. The hierarchy offers a possibility that the noise-enhanced digital RNNs could operate at a super-Turing level less complex than BPP/log*. As the uniform noise increases, the digital RNNs develop positive Lyapunov exponents intimating that chaos is mimicked. The exponents maximize to the accepted values for the logistic and Hénon maps when the noise equals eight times the least significant bit of the noisy recurrent signals for the logistic digital RNN and four times the Hénon digital RNN.

The ability to measure small deformations or strains is useful for understanding many aspects of materials. Here, an alternate analysis of speckle x-ray diffraction peaks is presented in which the systematic shifts of the speckles are analyzed allowing for strain (or flow) patterns to be inferred. This speckle tracking technique measures strain patterns with an accuracy similar to x-ray single crystal measurements but in amorphous or highly disordered materials.