Motivated by the importance of understanding various competing mechanisms to the current-induced spin-orbit torque on magnetization in complex magnets, we develop a theory of current-induced spin-orbital coupled dynamics in magnetic heterostructures. The theory describes angular momentum transfer between different degrees of freedom in solids, e.g., the electron orbital and spin, the crystal lattice, and the magnetic order parameter. Based on the continuity equations for the spin and orbital angular momenta, we derive equations of motion that relate spin and orbital current fluxes and torques describing the transfer of angular momentum between different degrees of freedom, achieved in a steady state under an applied external electric field. We then propose a classification scheme for the mechanisms of the current-induced torque in magnetic bilayers. We evaluate the sources of torque using density functional theory, effectively capturing the impact of the electronic structure on these quantities. We apply our formalism to two different magnetic bilayers, Fe/W(110) and Ni/W(110), which are chosen such that the orbital and spin Hall effects in W have opposite sign and the resulting spin- and orbital-mediated torques can compete with each other. We find that while the spin torque arising from the spin Hall effect of W is the dominant mechanism of the current-induced torque in Fe/W(110), the dominant mechanism in Ni/W(110) is the orbital torque originating in the orbital Hall effect of the nonmagnetic substrate. Thus, the effective spin Hall angles for the total torque are negative and positive in the two systems. Our prediction can be experimentally identified in moderately clean samples, where intrinsic contributions dominate. This clearly demonstrates that our formalism is ideal for studying the angular momentum transfer dynamics in spin-orbit coupled systems as it goes beyond the “spin current picture” by naturally incorporating the spin and orbital degrees of freedom on an equal footing. Our calculations reveal that, in addition to the spin and orbital torque, other contributions such as the interfacial torque and self-induced anomalous torque within the ferromagnet are not negligible in both material systems.

Certification of quantum systems and operations is a central task in quantum information processing. Most current schemes rely on a tomography with fully characterized devices, while this may not be met in real experiments. Device characterizations can be removed with device-independent tests, but it is technically challenging at the moment. In this paper, we investigate the problem of certifying entangled states and measurements via semiquantum games, a type of nonlocal quantum games with well characterized quantum inputs, balancing practicality and device independence. We first design a specific bounded-dimensional semiquantum game, with which any pure entangled state and Bell state measurement operators can be simultaneously certified. Afterward via a duality treatment of state and measurement, we interpret the dual form of this game as a source-independent bounded-dimensional entanglement swapping protocol and show the whole process, including any entangled projector and Bell states, can be certified with this protocol. In particular, our results do not require a complete Bell state measurement, which is beneficial for experiments and practical use.

Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is required. A decoder based on machine learning is considered one of the most viable solutions for this purpose since its prediction is fast once training has been done, and it is applicable to any quantum error-correcting code and any noise model. So far, various formulations of the decoding problem as the task of machine learning have been proposed. Here we discuss general constructions of machine-learning-based decoders. We find several conditions to achieve near-optimal performance and propose a criterion which should be optimized when the size of a training data set is limited. We also discuss preferable constructions of neural networks and propose a decoder using spatial structures of topological codes using a convolutional neural network. We numerically show that our method can improve the performance of machine-learning-based decoders in various topological codes and noise models.

Using a perturbative approach, we investigate the parametric down-conversion process without the semiclassical approximation. A Wigner functional formalism, which incorporates both the spatiotemproal degrees of freedom and the particle-number degrees of freedom is used to perform the analysis. First, we derive an evolution equation for the down-conversion process in the nonlinear medium. Then we use the perturbative approach to solve the equation. The leading order contribution is equivalent to the semiclassical solution. The next-to-leading order contribution provides a solution that includes the evolution of the pump field as a quantum field.

We propose a general scheme to construct a Hamiltonian $H_{\text{root}}$ describing a square root of an original Hamiltonian $H_{\text{original}}$ based on the graph theory. The square-root Hamiltonian is defined on the subdivided graph of the original graph of $H_{\text{original}}$, where the subdivided graph is obtained by putting one vertex on each link in the original graph. When $H_{\text{original}}$ describes a topological system, there emerge in-gap edge states at nonzero energy in the spectrum of $H_{\text{root}}$, which are the inherence of the topological edge states at zero energy in $H_{\text{original}}$. In this case, $H_{\text{root}}$ describes a square-root topological insulator or superconductor. Typical examples are square roots of the Su-Schrieffer-Heeger (SSH) model, the Kitaev topological superconductor model, and the Haldane model. Our scheme is also applicable to non-Hermitian topological systems, where we study an example of a nonreciprocal non-Hermitian SSH model.

Quantum discrimination and estimation are pivotal for many quantum technologies, and their performance depends on the optimal choice of probe state and measurement. Here we show that their performance can be further improved by suitably tailoring the pulses that make up the interferometer. Developing an optimal control framework and applying it to the discrimination and estimation of a magnetic field in the presence of noise, we find an increase in the overall achievable state distinguishability. Moreover, the maximum distinguishability can be stabilized for times that are more than an order of magnitude longer than the decoherence time.

We use frequency-comb-based optical two-way time-frequency transfer (O-TWTFT) to measure the optical frequency ratio of state-of-the-art ytterbium and strontium optical atomic clocks separated by a 1.5-km open-air link. Our free-space measurement is compared to a simultaneous measurement acquired via a noise-cancelled fiber link. Despite nonstationary, ps-level time-of-flight variations in the free-space link, ratio measurements obtained from the two links, averaged over 30.5 hours across six days, agree to $6\times {10}^{-19}$, showing that O-TWTFT can support free-space atomic clock comparisons below the ${10}^{-18}$ level.

Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints due to finite measurement resolution. We derive a tight bound on the optimal precision scaling with temperature, as the temperature approaches zero. The bound demonstrates that under finite resolution, the variance in any temperature estimate must decrease slower than linearly. This scaling can be saturated by monitoring the nonequilibrium dynamics of a single-qubit probe. We support this finding by numerical simulations of a spin-boson model. In particular, this shows that thermometry with a vanishing absolute error at low temperature is possible with finite resolution, answering an interesting question left open by previous work. Our results are relevant both fundamentally, as they illuminate the ultimate limits to quantum thermometry, and practically, in guiding the development of sensitive thermometric techniques applicable at ultracold temperatures.

Neural codes have been postulated to build efficient representations of the external world. The hippocampus, an encoding system, employs neuronal firing rates and spike phases to encode external space. Although the biophysical origin of such codes is at a single neuronal level, the role of neural components in efficient coding is not understood. The complexity of this problem lies in the dimensionality of the parametric space encompassing neural components, and is amplified by the enormous biological heterogeneity observed in each parameter. A central question that spans encoding systems therefore is how neurons arrive at efficient codes in the face of widespread biological heterogeneities. To answer this, we developed a conductance-based spiking model for phase precession, a phase code of external space exhibited by hippocampal place cells. Our model accounted for several experimental observations on place cell firing and electrophysiology: the emergence of phase precession from exact spike timings of conductance-based models with neuron-specific ion channels and receptors; biological heterogeneities in neural components and excitability; the emergence of subthreshold voltage ramp, increased firing rate, enhanced theta power within the place field; a signature reduction in extracellular theta frequency compared to its intracellular counterpart; and experience-dependent asymmetry in firing-rate profile. We formulated phase-coding efficiency, using Shannon's information theory, as an information maximization problem with spike phase as the response and external space within a single place field as the stimulus. We employed an unbiased stochastic search spanning an 11-dimensional neural space, involving thousands of iterations that accounted for the biophysical richness and neuron-to-neuron heterogeneities. We found a small subset of models that exhibited efficient spatial information transfer through the phase code, and investigated the distinguishing features of this subpopulation at the parametric and functional scales. At the parametric scale, which spans the molecular components that defined the neuron, several nonunique parametric combinations with weak pairwise correlations yielded models with similar high phase-coding efficiency. Importantly, placing additional constraints on these models in terms of matching other aspects of hippocampal neural responses did not hamper parametric degeneracy. We provide quantitative evidence demonstrating this parametric degeneracy to be a consequence of a many-to-one relationship between the different parameters and phase-coding efficiency. At the functional scale, involving the cellular-scale neural properties, our analyses revealed an important higher-order constraint that was exclusive to models exhibiting efficient phase coding. Specifically, we found a counterbalancing negative correlation between neuronal gain and the strength of external synaptic inputs as a critical functional constraint for the emergence of efficient phase coding. These observations implicate intrinsic neural properties as important contributors in effectuating such counterbalance, which can be achieved by recruiting nonunique parametric combinations. Finally, we show that a change in afferent statistics, manifesting as input asymmetry onto these neuronal models, induced an adaptive shift in the phase code that preserved its efficiency. Together, our analyses unveil parametric degeneracy as a mechanism to harness widespread neuron-to-neuron heterogeneity towards accomplishing stable and efficient encoding, provided specific higher-order functional constraints on the relationship of neural gain to external inputs are satisfied.

Recent x-ray absorption experiments have demonstrated the possibility to accurately monitor the magnetism of metallic heterostructures controlled via a time-independent perturbation caused, for example, by a static electric field. Using a first-principles, nonequilibrium Green's function scheme, we show how the measured dichroic signal for the corresponding steady-state situation can be related to the underlying electronic structure and its response to the external stimulus. The suggested approach works from the infinitesimal limit of linear response to the regime of strong electric field effects, which is realized in present experimental high-sensitivity investigations.

In a series of recent papers, anomalous Hall and Nernst effects have been theoretically discussed in the nonlinear regime and have seen some early success in experiments. In this paper, by utilizing the role of Berry curvature dipole, we derive the fundamental mathematical relations between the anomalous electric and thermoelectric transport coefficients in the nonlinear regime. The formulas we derive replace the celebrated Wiedemann-Franz law and Mott relation of anomalous thermoelectric transport coefficients defined in the linear response regime. In addition to fundamental and testable new formulas, an important by-product of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments.

We investigate the impact of the QCD vacuum at nonzero $\theta$ on the properties of light nuclei, Big Bang nucleosynthesis, and stellar nucleosynthesis. Our analysis starts with a calculation of the $\theta$-dependence of the neutron-proton mass difference and neutron decay using chiral perturbation theory. We then discuss the $\theta$-dependence of the nucleon-nucleon interaction using a one-boson-exchange model and compute the properties of the two-nucleon system. Using the universal properties of four-component fermions at large scattering length, we then deduce the binding energies of the three-nucleon and four-nucleon systems. Based on these results, we discuss the implications for primordial abundances of light nuclei, the production of nuclei in stellar environments, and implications for an anthropic view of the universe.

Spectra of bulk or edges in topological insulators are often made complex by non-Hermiticity. Here, we show that symmetry protection enables entirely real spectra for both bulk and edges even in non-Hermitian topological insulators. In particular, we demonstrate the entirely real spectra without non-Hermitian skin effects due to a combination of pseudo-Hermiticity and Kramers degeneracy. This protection relies on nonspatial fundamental symmetry and has stability against disorder. As an illustrative example, we investigate a non-Hermitian extension of the Bernevig-Hughes-Zhang model. The helical edge states exhibit oscillatory dynamics due to their nonorthogonality as a unique non-Hermitian feature.

We consider 2+1-dimensional conformal gauge theories coupled to additional degrees of freedom which induce a spatially local but long-range in time $1/{(\tau -{\tau }^{\prime })}^2$ interaction between gauge-neutral local operators. Such theories have been argued to describe the hole-doped cuprates near optimal doping. We focus on a SU(2) gauge theory with $N_h$ flavors of adjoint Higgs fields undergoing a quantum transition between Higgs and confining phases: the $1/{(\tau -{\tau }^{\prime })}^2$ interaction arises from a spectator large Fermi surface of electrons. The large $N_h$ expansion leads to an effective action containing fields which are bilocal in time but local in space. We find a strongly coupled fixed point at order $1/N_h$, with dynamic critical exponent $z>1$. We show that the entropy preserves hyperscaling but nevertheless leads to a linear in temperature specific heat with a coefficient which has a finite enhancement near the quantum critical point.

We determine quantum precision limits for estimation of damping constants and temperature of lossy bosonic channels. A direct application would be the use of light for estimation of the absorption and the temperature of a transparent slab. Analytic lower bounds are obtained for the uncertainty in the estimation, through a purification procedure that replaces the master equation description by a unitary evolution involving the system and ad hoc environments. For zero temperature, Fock states are shown to lead to the minimal uncertainty in the estimation of damping, with boson-counting being the best measurement procedure. In both damping and temperature estimates, sequential prethermalization measurements, through a stream of single bosons, may lead to huge gain in precision.

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result—energy and charge density distribution of the ground state—is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.

We propose a nanoscale device consisting of a double quantum dot with strong intra- and interdot Coulomb repulsions. In this design, the current can only flow through the lower dot, but is triggered by the gate-controlled occupancy of the upper dot. At low temperatures, our calculations predict the double dot to pass through a narrow Kondo regime, resulting in highly sensitive switching characteristics between three well-defined states—insulating, normal conduction, and resonant conduction.

We investigate the dynamics of chiral edge states in topological polariton systems under laser driving. Using a model system comprised of topolgically trivial excitons and photons with a chiral coupling proposed by Karzig et al. [Phys. Rev. X 5, 031001 (2015)], we investigate the real-time dynamics of a lattice version of this model driven by a laser pulse. By analyzing the time- and momentum-resolved spectral function, measured by time- and angle-resolved photoluminescence in analogy with time- and angle-resolved photoemission spectroscopy in electronic systems, we find that polaritonic states in a ribbon geometry are selectively excited via their resonance with the pump laser photon frequency. This selective excitation mechanism is independent of the necessity of strong laser pumping and polariton condensation. Our work highlights the potential of time-resolved spectroscopy as a complementary tool to real-space imaging for the investigation of topological edge state engineering in devices.

We construct and study quantum trimer models and resonating $\mathrm{SU}\left(3\right)$-singlet models on the kagome lattice, which generalize quantum dimer models and the resonating valence bond wave functions to a trimer and $\mathrm{SU}\left(3\right)$ setting. We demonstrate that these models carry a ${\mathbb{Z}}_3$ symmetry which originates in the structure of trimers and the $\mathrm{SU}\left(3\right)$ representation theory, and which becomes the only symmetry under renormalization. Based on this, we construct simple and exact parent Hamiltonians for the model which exhibit a topological ninefold degenerate ground space. A combination of analytical reasoning and numerical analysis reveals that the quantum order ultimately displayed by the model depends on the relative weight assigned to different types of trimers—it can display either ${\mathbb{Z}}_3$ topological order or form a symmetry-broken trimer crystal, and in addition possesses a point with an enhanced $\mathrm{U}\left(1\right)$ symmetry and critical behavior. Our results accordingly hold for the $\mathrm{SU}\left(3\right)$ model, where the two natural choices for trimer weights give rise to either a topological spin liquid or a system with symmetry-broken order, respectively. Our work thus demonstrates the suitability of resonating trimer and $\mathrm{SU}\left(3\right)$-singlet ansatzes to model $\mathrm{SU}\left(3\right)$ topological spin liquids on the kagome lattice.

Using conceptually and procedurally consistent density functional theory (DFT) calculations with an advanced meta-generalized gradient approximation (GGA) exchange-correlation functional in ab initio Born-Oppenheimer molecular dynamics (BOMD) simulations, we determine the insulator-metal transition (IMT) of warm dense fluid hydrogen from 50 to 300 GPa to be in better agreement with experiment than previous DFT predictions. The inclusion of nuclear quantum effects via path-integral molecular dynamics (PIMD) sharpens the transition and lowers its temperature relative to the BOMD results. A rapid decrease in the molecular character of the system, as observed via the ionic pair correlation function, coincides with an abrupt conductivity increase, confirming a metallic transition due to molecular hydrogen dissociation that is coincident with abrupt band-gap closure. Comparison of the PIMD and BOMD results clearly demonstrates an isotope effect on the IMT. Exploitation of differing methodologies for using the orbital-dependent and deorbitalized versions of the meta-GGA enables us to quantify exchange-correlation approximation effects. Distinct from stochastic simulations, these results do not depend upon any clever but uncontrolled combination of ground-state and finite-T methodologies and should provide a reliable benchmark for further studies.