The spin and orbital angular momentum (OAM) of optical fields in a silicon channel waveguide are investigated. A vortex beam carrying OAM can be generated by a superposition of two quasi-TE modes. The longitudinal OAM of the superposed vortex beam is intrinsic and mediated by the superposition coefficient. Due to high transverse confinement of the silicon waveguide, the polarization and OAM are inevitably coupled. Their hybridization degree is well described by joint average transverse wave vectors. Further, the OAM part can be separated using the topological Pancharatnam charge and Stokes parameters. Combining polarization and OAM indices, we find that the whole space of structure parameters of the waveguide can be divided into three regimes. Our result offers insight into the relationship between angular momentum and mode confinement, which is beneficial for potential applications of vector beams in photonic integrated circuits.

Topological field theories emerge at low energy in strongly correlated condensed matter systems and appear in the context of planar gravity. In particular, the study of Chern-Simons terms gives rise to the concept of flux attachment when the gauge field is coupled to matter, yielding flux-charge composites. We investigate the generation of flux attachment in a Bose-Einstein condensate in the presence of nonlinear synthetic gauge potentials. In doing so, we identify the $U\left(1\right)$ Chern-Simons gauge field as a singular density-dependent gauge potential, which in turn can be expressed as a Berry connection. We envisage a proof-of-concept scheme where the artificial gauge field is perturbatively induced by an effective light-matter detuning created by interparticle interactions. At a mean field level, we recover the action of a “charged” superfluid minimally coupled to both a background and a Chern-Simons gauge field. Remarkably, a localized density perturbation in combination with a nonlinear gauge potential gives rise to an effective composite boson model of fractional quantum Hall effect, displaying anyonic vortices.

Sensitivity and robustness appear to be contrasting concepts. However, natural proteins are robust enough to tolerate random mutations, meanwhile be susceptible enough to sense environmental signals, exhibiting both high functional sensitivity (i.e., plasticity) and mutational robustness. Uncovering how these two aspects are compatible is a fundamental question in the protein dynamics and genotype-phenotype relation. In this work, a general framework is established to analyze the dynamics of protein systems under both external and internal perturbations. We introduce fluctuation entropy for the functional sensitivity and the spectrum entropy for the mutational robustness. The compatibility of sensitivity and robustness is analyzed by the optimization of two entropies, which leads to the power-law vibration spectrum of proteins. These power-law behaviors are confirmed extensively by protein data, as a hallmark of criticality. Moreover, the dependence of functional sensitivity and mutational robustness on the protein size suggests a general evolutionary constraint for proteins with different chain lengths. This framework can also establish a general link of the criticality with robustness-plasticity compatibility, both of which are ubiquitous features in biological systems.

We show that both the flux and the cutoff energy of protons accelerated by ultraintense lasers can be simultaneously increased when using targets consisting of thin layers of bundled nanochannels. Particle-in-cell simulations suggest that the propagation of an electromagnetic field in the subwavelength channels occurs via excitation of surface plasmon polaritons that travel in the channels down to the end of the target, sustaining continuous and efficient electron acceleration and boosting acceleration of protons via enhancement of the target normal sheath acceleration mechanism.

Experiments suggest that the cerebral cortex gains several functional advantages by operating in a dynamical regime near the critical point of a phase transition. However, a long-standing criticism of this hypothesis is that critical dynamics are rather noisy, which might be detrimental to aspects of brain function that require precision. If the cortex does operate near criticality, how might it mitigate the noisy fluctuations? One possibility is that other parts of the brain may act to control the fluctuations and reduce cortical noise. To better understand basic aspects of controlling neural activity fluctuations, here we numerically and analytically study a network of binary neurons. We determine how the efficacy of controlling the population firing rate depends on proximity to criticality as well as different structural properties of the network. We find that control is most effective—errors are minimal for the widest range of target firing rates—near criticality. Optimal control is slightly away from criticality for networks with heterogeneous degree distributions. Thus, while criticality is the noisiest dynamical regime, it is also the regime that is easiest to control, which may offer a way to mitigate the noise.

Modern technologies could soon make it possible to investigate the operation cycles of quantum heat engines by counting the photons that are emitted and absorbed by their working systems. Using the quantum jump approach to open-system dynamics, we show that such experiments would give access to a set of observables that determine the trade-off between power and efficiency in finite-time engine cycles. By analyzing the single-jump statistics of thermodynamic fluxes such as heat and entropy production, we obtain a family of general bounds on the power of microscopic heat engines. Our new bounds unify two earlier results and admit a transparent physical interpretation in terms of single-photon measurements. In addition, these bounds confirm that driving-induced coherence leads to an increase in dissipation that suppresses the efficiency of slowly driven quantum engines in the weak-coupling regime. A nanoscale heat engine based on a superconducting qubit serves as an experimentally relevant example and a guiding paradigm for the development of our theory.

A field theoretical framework is developed for the Hawkes self-excited point process with arbitrary memory kernels by embedding the original non-Markovian one-dimensional dynamics onto a Markovian infinite-dimensional one. The corresponding Langevin dynamics of the field variables is given by stochastic partial differential equations that are Markovian. This is in contrast to the Hawkes process, which is non-Markovian (in general) by construction as a result of its (long) memory kernel. We derive the exact solutions of the Lagrange-Charpit equations for the hyperbolic master equations in the Laplace representation in the steady state, close to the critical point of the Hawkes process. The critical condition of the original Hawkes process is found to correspond to a transcritical bifurcation in the Lagrange-Charpit equations. We predict a power law scaling of the probability density function (PDF) of the intensities in an intermediate asymptotic regime, which crosses over to an asymptotic exponential function beyond a characteristic intensity that diverges as the critical condition is approached. We also discuss the formal relationship between quantum field theories and our formulation. Our field theoretical framework provides a way to tackle complex generalization of the Hawkes process, such as nonlinear Hawkes processes previously proposed to describe the multifractal properties of earthquake seismicity and of financial volatility.

We study analytically an underdamped current-biased topological Josephson junction. First, we consider a simplified model at zero temperature, where the parity of the nonlocal fermionic state formed by Majorana bound states (MBSs) localized on the junction is fixed, and show that a transition from insulating to conducting state in this case is governed by single-quasiparticle tunneling rather than by Cooper pair tunneling, in contrast to a nontopological Josephson junction. This results in a significantly lower critical current for the transition from insulating to conducting state. We propose that if the length of the system is finite, the transition from insulating to conducting state occurs at exponentially higher bias current due to hybridization of the states with different parities as a result of the overlap of MBSs localized on the junction and at the edges of the topological nanowire forming the junction. Finally, we discuss how the appearance of MBSs can be established experimentally by measuring the critical current for an insulating regime at different values of the applied magnetic field.

The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-$Z$ (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of $0.9\pm 0.03$ and $1.3\pm 0.4\%$ for the CZ and the iSWAP gate, respectively. We argue that spurious $ZZ$-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quantum approximate optimization algorithm (QAOA). We reformulate the QAOA variational minimization as a learning task, where an RL agent chooses the control parameters for the unitaries, given partial information on the system. Such an RL scheme finds a policy converging to the optimal adiabatic solution of the quantum Ising chain that can also be successfully transferred between systems with different sizes, even in the presence of disorder. This allows for immediate experimental verification of our proposal on more complicated models: the RL agent is trained on a small control system, simulated on classical hardware, and then tested on a larger physical sample.

The discovery that ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_2$, with the $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2$ infinite-layer structure, superconducts up to 15 K around the hole-doping level $x=0.2$ raises the crucial question of its fundamental electronic and magnetic processes. The unexplained basic feature that we address is that, for $x=0$ and as opposed to strongly antiferromagnetic (AFM) $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2, {\mathrm{NdNiO}}_2$ with the same structure and formal $d^9$ configuration does not undergo AFM order. We study this issue not in the conventional manner, as energetically unfavored or as frustrated magnetic order, but as an instability of the AFM phase itself. We are able to obtain the static AFM ordered state, but find that a flat band, one-dimensional-like van Hove singularity (vHs) is pinned to the Fermi level. This situation is unusual in a non-half-filled, effectively two-band system. The vHs makes the AFM phase unstable to spin-density disproportionation, breathing, and half-breathing lattice distortions, and (innate or parasitic) charge-density disproportionation. These flat band instabilities, distant relatives of single-band cuprate models, thereby inhibit but do not eliminate incipient AFM tendencies at low temperature. The primary feature is that a pair of active bands ($d_{x^2-y^2}, d_{z^2})$ eliminate half-filled physics and, due to instabilities, preclude the AFM phase seen in $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_2$. This strongly AFM correlated, conducting spin-liquid phase with strong participation of the Ni $d_{z^2}$ orbital forms the platform for superconductivity in ${\mathrm{NdNiO}}_2$.

A defining feature in the field of quantum computing is the potential of a quantum device to outperform its classical counterpart for a specific computational task. By now, several proposals exist showing that certain sampling problems can be done efficiently quantumly, but are not possible efficiently classically, assuming strongly held conjectures in complexity theory, a feature dubbed quantum speedup. However, the effect of noise on these proposals is not well understood in general, and in certain cases it is known that simple noise can destroy the quantum speedup. Here we develop a fault-tolerant version of one family of these sampling problems, based on nonadaptive measurements on regular graph states composed of $m$ qubits. We show that these sampling problems can be implemented fault tolerantly using quantum circuits of constant depth. We present two constructions, each taking $\text{poly}\left(m\right)$ physical qubits, some of which are prepared in noisy magic states. The first of our constructions is a constant depth quantum circuit composed of single- and two-qubit nearest-neighbor Clifford gates in four dimensions. This circuit has one layer of interaction with a classical computer before final measurements. Our second construction is a constant depth quantum circuit with single- and two-qubit nearest-neighbor Clifford gates in three dimensions, but with two layers of interaction with a classical computer before the final measurements. For each of these constructions, we show that there is no classical algorithm which can sample according to its output distribution in $\text{poly}\left(m\right)$ time, assuming two standard complexity theoretic conjectures hold. The noise model we assume is the so-called local stochastic quantum noise. Along the way, we introduce various concepts such as constant depth magic state distillation and constant depth output routing, which arise naturally in measurement based quantum computation, but have no constant-depth analog in the circuit model.

We compare and contrast the excitation properties of cardiac myocytes and cardiac tissue modeled by (a) a Hodgkin-Huxley-model (HHM) and (b) Markov-chain-model (MM) formalisms for the sodium (Na) ion channel. Specifically, we bring out the differences between HHM and MM formalisms, for both wild-type (WT) and mutant (MUT) models, for ion-channel kinetics, single-myocyte action potentials, and the spatiotemporal evolutions of spiral and scroll waves in different mathematical models of cardiac tissue. We show that the kinetic properties of Na ion channels are not the same for HHM and MM models; in particular, the range of values of the trans-membrane potential $V_m$, in which there is a significant window current, depends significantly on these models, so there are marked differences in the opening times of the Na ion channels, the maximal amplitude of the Na current, and the presence or absence of a late Na current. Furthermore, these changes lead to different excitation behaviors in cardiac tissue; specifically, two of the WT models show stable spiral waves, but the other one shows meandering and transiently breaking spiral waves. Our results are based on extensive direct numerical simulations of waves of electrical activation in these models, in two- and three-dimensional (2D and 3D) homogeneous simulation domains and also in domains with localized heterogeneities, either obstacles with randomly distributed inexcitable regions or mutant cells in a wild-type background. Our study brings out the sensitive dependence of spiral- and scroll-wave dynamics on these five models and the parameters that define them. We list desiderata for a good model for the Na wild-type ion channel; we use these desired properties to select one of the MM models that we study.

The pseudogap is a ubiquitous phenomenon in strongly correlated systems, such as high-$T_{\mathrm{c}}$ superconductors, ultracold atoms, and nuclear physics. Whereas pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental one-dimensional models, that is, Gaudin-Yang model. In this paper, we show how the pseudogap effect emerges in the single-particle excitation in this system using a diagrammatic approach. Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to the pseudogap state with increasing the attractive interaction and the number density at finite temperature. Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, indicating the validity of our approach even in the region where the pseudogap appears.

We study transport through strongly interacting quantum dots with $N$ energy levels that are weakly coupled to generic multichannel metallic leads. In the regime of coherent sequential tunneling, where level spacing and broadening are of the same order but small compared to temperature, we present a unified $\text{SU}\left(N\right)$-invariant form of the kinetic equation for the reduced density matrix of the dot and the tunneling current. This is achieved by introducing the concept of flavor polarization for the dot and the reservoirs and splitting the kinetic equation in terms of flavor accumulation, anisotropic flavor relaxation, and exchange-field- and detuning-induced flavor rotation. In particular, we identify the exchange field as the cause of negative differential conductance at off-resonance bias voltages appearing in generic quantum-dot models. To illustrate the notion of flavor polarization, we analyze the nonlinear current through a triple-quantum-dot device.

We propose an experimental method utilizing a strongly spin-orbit coupled metal to quantum magnet bilayer that will probe quantum magnets lacking long-range magnetic order, e.g., quantum spin liquids, via examination of the voltage noise spectrum in the metal layer. The bilayer is held in thermal and chemical equilibrium, and spin fluctuations arising across the single interface are converted into voltage fluctuations in the metal as a result of the inverse spin Hall effect. We elucidate the theoretical workings of the proposed bilayer system and provide precise predictions for the frequency characteristics of the enhancement to the ac electrical resistance measured in the metal layer for three candidate quantum spin liquid models. Application to the Heisenberg spin-$1/2$ kagomé lattice model should allow for the extraction of any spinon gap present. A quantum spin liquid consisting of fermionic spinons coupled to a U(1) gauge field should cause subdominant ${\mathrm{\Omega }}^{4/3}$ scaling of the resistance of the coupled metal. Finally, if the magnet is well-captured by the Kitaev model in the gapless spin liquid phase, then the proposed bilayer can extract the two-flux gap which arises in spite of the gapless spectrum of the fermions. We, therefore, show that spectral analysis of the ac resistance in the metal in a single interface, equilibrium bilayer can test the relevance of a quantum spin liquid model to a given candidate material.

The theoretical analysis of topological insulators (TIs) has been traditionally focused on infinite homogeneous crystals with band gap in the bulk and nontrivial topology of their wave functions, or infinite wires whose boundaries host surface or edge metallic states. Such infinite-length edge states exhibit quantized conductance which is insensitive to edge disorder, as long as it does not break the underlying symmetry or introduce energy scale larger than the bulk gap. However, experimental devices contain finite-size topological region attached to normal metal (NM) leads, which poses a question about how precise is quantization of longitudinal conductance and how electrons transition from topologically trivial NM leads into the edge states. This particularly pressing issue for recently conjectured two-dimensional (2D) Floquet TI where electrons flow from time-independent NM leads into time-dependent edge states, the very recent experimental realization [J. W. McIver et al., Nat. Phys. 16, 38 (2020)] of Floquet TI using graphene irradiated by circularly polarized light did not exhibit either quantized longitudinal or Hall conductance. Here, we employ a charge-conserving solution for Floquet-nonequilibrium Green functions of irradiated graphene nanoribbon to compute longitudinal two-terminal conductance, as well as spatial profiles of local current density as electrons propagate from NM leads into the Floquet TI. For comparison, we also compute conductance of graphene-based realization of 2D quantum Hall, quantum anomalous Hall, and quantum spin Hall insulators. Although zero-temperature conductance within the gap of these three conventional time-independent 2D TIs of finite length exhibits small oscillations due to reflections at the NM-lead/2D-TI interface, it remains very close to perfectly quantized plateau at $2e^2/h$ and completely insensitive to edge disorder. This is due to the fact that inside conventional TIs there is only edge local current density which circumvents any disorder. In contrast, in the case of Floquet TI both bulk and edge local current densities contribute equally to total current, which leads to longitudinal conductance below the expected quantized plateau that is further reduced by edge vacancies. We propose two experimental schemes to detect coexistence of bulk and edge current densities within Floquet TI: (i) drilling a nanopore in the interior of irradiated region of graphene will induce backscattering of bulk current density, thereby reducing longitudinal conductance by $\sim 28\%$; (ii) imaging of magnetic field produced by local current density using diamond nitrogen-vacancy centers.

Forces and torques exerted on dielectric disks trapped in a Gaussian standing wave are analyzed theoretically for disks of radius $2\mu \text{m}$ with indices of refraction $n=1.45$ and $n=2.0$ as well as disks of radius 200 nm with $n=1.45$. Calculations of the forces and torques were conducted both analytically and numerically using a discrete-dipole approximation method. Besides harmonic terms, third-order rotranslational coupling terms in the potential energy can be significant and a necessary consideration when describing the dynamics of disks outside of the Rayleigh limit. The coupling terms are a result of the finite extension of the disk coupling to both the Gaussian and standing-wave geometry of the beam. The resulting dynamics of the degrees of freedom most affected by the coupling terms exhibit several sidebands as evidenced in the power spectral densities. Simulations show that for Gaussian beam waists of $2–4\mu \text{m}$ the disk remains stably trapped.

Liquid-crystalline ordering in vertically vibrated granular monolayers of metallic rods confined in annuli of different sizes is examined. The annuli consist of circular cavities with a central circular obstruction. In the absence of the central obstruction, rods of low aspect ratio exhibit global tetratic order, except for the existence of four small defected regions which restore the tetratic symmetry broken by the circular confinement. However, very different configurations are observed in the annuli, with a complex structure consisting of alternating layered regions separated by tetratic domain walls. We use concepts of equilibrium elastic theory for liquid crystals and topology along with arguments based on dissipation mechanisms to qualitatively explain this behavior. The results show that selective confinement of vertically vibrated monolayers of rods could be used as a tool to study the creation and dynamics of various types of defects in ordered systems.

We report on half-integer Shapiro steps observed in a gate-tunable short ballistic InAs nanowire Josephson junction. We observed the Shapiro steps of the short ballistic InAs nanowire Josephson junction and found the half-integer steps in addition to the conventional integer steps. In this Josephson junction device the junction transmission can be varied with gate voltage. From measurements of the gate voltage and temperature dependences of the Shapiro steps, the origin of half-integer steps is assigned to the skewness of the current phase relation in the short ballistic Josephson junctions. These results will contribute to establish and control the superconductivity physics in the short ballistic semiconductor nanowires.