We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz–Kaup–Newell–Segur matrix eigenvalue problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding reflectionless Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and formulate their soliton solutions via those reflectionless Riemann–Hilbert problems. Soliton solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.

Topology played an important role in physics research during the last few decades. In particular, the quantum geometric tensor that provides local information about topological properties has attracted much attention. It will reveal interesting topological properties but have not been measured in non-Abelian systems. Here, we use a four-qubit quantum system in superconducting circuits to construct a degenerate Hamiltonian with parametric modulation. By manipulating the Hamiltonian with periodic drivings, we simulate the Bernevig–Hughes–Zhang model and obtain the quantum geometric tensor from interference oscillation. In addition, we reveal its topological feature by extracting the topological invariant, demonstrating an effective protocol for quantum simulation of a non-Abelian system.

Given an image of a white shoe drawn on a blackboard, how are the white pixels deemed (say by human minds) to be informative for recognizing the shoe without any labeling information on the pixels? Here we investigate such a “white shoe” recognition problem from the perspective of tensor network (TN) machine learning and quantum entanglement. Utilizing a generative TN that captures the probability distribution of the features as quantum amplitudes, we propose an unsupervised recognition scheme of informative features with variations of entanglement entropy (EE) caused by designed measurements. In this way, a given sample, where the values of its features are statistically meaningless, is mapped to the variations of EE that statistically characterize the gain of information. We show that the EE variations identify the features that are critical to recognize this specific sample, and the EE itself reveals the information distribution of the probabilities represented by the TN model. The signs of the variations further reveal the entanglement structures among the features. We test the validity of our scheme on a toy dataset of strip images, the MNIST dataset of hand-drawn digits, the fashion-MNIST dataset of the pictures of fashion articles, and the images of nerve cord. Our scheme opens the avenue to the quantum-inspired and interpreted unsupervised learning, which can be applied to, e.g., image segmentation and object detection.

The theory of knots and links focuses on the embedding mode of one or several closed curves in three-dimensional Euclidean space. In an electromagnetic field system, all-optical knots or links composed of phase or polarization singularities have been verified theoretically and experimentally. Recent studies have shown that robust topological all-optical coding can be achieved by using optical knots and links. However, in the current design of optical knots and links based on phase or polarization singularities, the amplitude of light between adjacent singularities is relatively weak. This brings great pressure to detection of optical knots and links and limits their applications. Here, we propose a new optimization method in theory. Compared with the existing design methods, our design method improves the relative intensity distribution of light between adjacent singularities. We verify the feasibility of our design results in experiments. Our study reduces the detection difficulty of optical knots and links, and has a positive significance for promotion of applications of optical knots and links.

We present a design and development of a high-performance light-emitting diode (LED)-side-pumped Nd:YAG rod laser with strong pulse energy, high efficiency, and consistency, very good beam quality, and high uniform pumping intensity in the active area which reduces the effects of thermal gradient significantly. A five-dimensional 810 nm LED array with a full width of 30 nm at half maximum was intended to achieve high coupling efficiency by putting the LED array as close as possible to the side of the Nd:YAG laser rod for overcoming the large pumped divergence. Under 2.25 J pump energy, maximum single pulse energy of 35.86 mJ with duration of 1.24 µs at 1063.68 nm was obtained, equivalent to optical efficiency of 1.59% and a slope efficiency of 2.53%. The laser was set to repeat at a rate of 10 Hz with a beam quality factor of $M_{x}^{2} = 2.94$ and $M_{y}^{2} = 3.35$, as well as with the output power stability of $ < $ 4.1% (root mean square) and $ < $ 7.3% (peak to peak). To the best of our ability, this is the highest performance for an LED-side-pumped Nd:YAG rod laser oscillator with a 10-mJ-level output ever reported.

A branch of high-frequency Alfvénic modes is observed on the HL-2A tokamak. The electromagnetic mode can be driven unstably in the plasma with an off-axis neutral beam heating. Its mode frequency keeps almost unchanged or presents a slow-sweeping behavior, depending on the detail current evolution. The poloidal and toroidal mode numbers are $m/n=1/1$. The mode has a quite short duration ($\leq$20 ms) and usually appears 5–10 ms after the neutral beam being injected into the plasma. Hybrid simulations based on M3D-K have also been carried out. The result suggests that co-passing energetic particles are responsible for the mode excitation. The simulated mode structures are localized nearby location of minimum safety factor ($q_{\rm min}$) and agree with the structures obtained through tomography of soft x-ray arrays. Further, the modes are localized in the continuum gap and their frequencies increase with variation of $q_{\rm min}$ in a wide range. Last but not least, the characteristic of unchanged frequency on experiment is also reproduced by the nonlinear simulation with a fixed safety factor. All those evidences indicate that the $n=1$ high-frequency mode may belong to a reversed shear Alfvén eigenmode.

We investigate the uniaxial-pressure dependence of resistivity for URu$_{2-x}$Fe$_x$Si$_2$ samples with $x = 0$ and 0.2, which host a hidden order (HO) and a large-moment antiferromagnetic (LMAFM) phase, respectively. For both samples, the elastoresistivity $\zeta$ shows a seemingly divergent behavior above the transition temperature $T_0$ and a quick decrease below it. We find that the temperature dependence of $\zeta$ for both samples can be well described by assuming the uniaxial pressure effect on the gap or certain energy scale except for $\zeta_{(110)}$ of the $x = 0$ sample, which exhibits a nonzero residual value at 0 K. We show that this provides a qualitative difference between the HO and LMAFM phases. Our results suggest that there is an in-plane anisotropic response to the uniaxial pressure that only exists in the hidden order state without necessarily breaking the rotational lattice symmetry.

We investigate the magnetic ground state of Sm$_3$BWO$_9$ with a distorted kagome lattice. A magnetic phase transition is identified at $T_{\rm N}=0.75$ K from the temperature dependence of specific heat. From $^{11}$B nuclear magnetic resonance measurements, an incommensurate magnetic order is shown by the double-horn type spectra under a $c$-axis magnetic field, and absence of line splitting is observed for field oriented within the $ab$-plane, indicating the incommensurate modulation of the internal field strictly along $c$-axis. From the spin dynamics, the critical slowing-down behavior is observed in the temperature dependence of $1/T_1$ with $\mu_0H$$\perp$$c$-axis, which is completely absent in the case with $\mu_0H||c$-axis. Based on the local symmetry of $^{11}$B sites, we analyze the hyperfine coupling tensors and propose two constraints on the possible magnetic structure. The single ion anisotropy should play an important role in determination of contrasting ground states of Sm$_3$BWO$_9$ and Pr$_3$BWO$_9$.

The structure and magnetic properties of rare-earth ions Tm$^{3+}$ Kagomé lattice Tm$_3$Sb$_3$Mg$_2$O$_{14}$ are studied by x-ray diffraction, magnetic susceptibility and muon spin relaxation (μSR) experiments. The existence of a small amount of Tm/Mg site-mixing disorder is revealed. DC magnetic susceptibility measurement shows that Tm$^{3+}$ magnetic moments are antiferromagnetically correlated with a negative Curie–Weiss temperature of $-$26.3 K. Neither long-range magnetic order nor spin-glass transition is observed by DC and AC magnetic susceptibility, and confirmed by μSR experiment down to 0.1 K. However, the emergence of short-range magnetic order is indicated by the zero-field μSR experiments, and the absence of spin dynamics at low temperatures is evidenced by the longitudinal-field μSR technique. Compared with the results of Tm$_3$Sb$_3$Zn$_2$O$_{14}$, another Tm-based Kagomé lattice with much more site-mixing disorder, the gapless spin liquid like behaviors in Tm$_3$Sb$_3$Zn$_2$O$_{14}$ can be induced by disorder effect. Samples with perfect geometrical frustration are in urgent demand to establish whether QSL exists in this kind of materials with rare-earth Kagomé lattice.

Two analytic expressions of temperature-dependent peak positions employing the localized-state ensemble (LSE) luminescence model are deduced for the cases of ${\Delta E=E_{\rm a}-E}_{0} >0$ and $ < 0$, respectively, under the first-order approximation of Taylor's expansion. Then, the deduced formulas are applied to examine the experimental variable-temperature photoluminescence data of non- and semi-polar InGaN/GaN quantum-wells (QWs) array by jointly considering the monotonic bandgap shrinking described by Pässler's empirical formula. S-shaped temperature dependence of luminescence peaks of both non- and semi-polar QWs is well reproduced with the analytic formulas. As a result, the localization depths are found to be 31.5 and 32.2 meV, respectively, for non- and semi-polar QWs.

Fe$^{2+}$ is of considerable importance in plant growth and crop production. However, most Fe elements in nature favor existing in the trivalent state, which often causes the deficiency of Fe$^{2+}$ in plants. Here, we report the Fe valence state change from Fe$^{3+}$ to Fe$^{2+}$ by using leaves. This valence state change was confirmed by x-ray photoelectron spectroscopy in Fe-Cl@leaves. Fourier transform infrared and ultraviolet-visible spectroscopy demonstrated that aromatic ring groups were included in leaves, and cation-$\pi$ interactions between Fe cations and the components containing aromatic rings in leaves were measured. Further, density functional theory calculations revealed that the most stable adsorption site for hydrated Fe$^{3+}$ cation was the region where hydroxyl groups and aromatic rings coexist. Moreover, molecular orbital and charge decomposition analysis revealed that the aromatic rings took the major part (59%) of the whole net charge transfer between leaves and Fe cations. This work provides a high-efficiency and eco-friendly way to transform the Fe valence state from Fe$^{3+}$ to Fe$^{2+}$, and affords a new insight into the valance change between plant organisms with cations.

We report a significantly enhanced anomalous Hall effect (AHE) of Pt on antiferromagnetic insulator thin film (3-unit-cell La$_{0.7}$Sr$_{0.3}$MnO$_{3}$, abbreviated as LSMO), which is one order of magnitude larger than that of Pt on other ferromagnetic (e.g. Y$_{3}$Fe$_{5}$O$_{12}$) and antiferromagnetic (e.g. Cr$_{2}$O$_{3}$) insulator thin films. Our experiments demonstrate that the antiferromagnetic La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ with fully compensated surface suppresses the positive anomalous Hall resistivity induced by the magnetic proximity effect and facilitates the negative anomalous Hall resistivity induced by the spin Hall effect. By changing the substrate's temperature during Pt deposition, we observed that the diffusion of Mn atoms into Pt layer can further enhance the AHE. The anomalous Hall resistivity increases with increasing temperature and persists even well above the Neel temperature ($T_{\rm N}$) of LSMO. The Monte Carlo simulations manifest that the unusual rise of anomalous Hall resistivity above $T_{\rm N}$ originates from the thermal induced magnetization in the antiferromagnetic insulator.

We investigate the current-driven characteristics and applications of magnetic skyrmion strings by micromagnetic simulations. Under the spin-polarized driving current, the skyrmion string presents different moving trajectories in different layers due to the skyrmion Hall effect. Moreover, a series of skyrmion bobbers can be generated with a notch defect placed in the surface and the skyrmion bobbers will follow the skyrmion string. By varying the current density, the bobbers' characteristics such as number and velocity can be manipulated, which inspires us to propose a skyrmion string-based diode. In addition, an AND logic gate and an OR logic gate in the identical scheme based on the skyrmion string are proposed. AND logic and OR logic behaviors can be realized by varying the driving current densities. Our findings will contribute to further research of magnetic skyrmion strings for data storage, processing, and energy-efficient computing.

The SARS-CoV-2 Omicron variant has become the dominant variant in the world. Uncovering the structural basis of altered immune response and enhanced transmission of Omicron is particularly important. Here, taking twenty-five antibodies from four groups as examples, we comprehensively reveal the underlying mechanism of how mutations in Omicron induces the weak neutralization by using molecular simulations. Overall, the binding strength of 68% antibodies is weakened in Omicron, much larger than that in Delta (40%). Specifically, the percentage of the weakened antibodies vary largely in different groups. Moreover, the mutation-induced repulsion is mainly responsive for the weak neutralization in AB/CD groups but does not take effect in EF group. Significantly, we demonstrate that the disappearance of hydrophobic interaction and salt bridges due to residue deletions contributes to the decreased binding energy in NTD group. This work provides unprecedented atomistic details for the distinct neutralization of WT/Delta/Omicron, which informs prospective efforts to design antibodies/vaccines against Omicron.

Bacteria can spontaneously develop collective motions by aligning their motions in dense systems. Here we show that bacteria can also respond collectively to an alternating electrical field and form dynamic clusters oscillating at the same frequency of the field. As the dynamic clusters go beyond a critical size, they split into smaller ones spontaneously. The critical size for splitting depends on the frequency of electric field and the concentration of bacteria. We show that, instead of their biological activity, the physical properties of bacteria as charged particles are responsible for the formation of dynamic clusters. Electroconvective flows across the system play the key role in stabilizing the clusters. However, to form clusters, collective hydrodynamic cooperation between bacteria is important such that no aggregation occurs in dilute suspensions. The findings in this study illustrate that bio-systems can respond collectively to an external field, promising an effective way to control and modulate the behavior of organisms. Moreover, the controlled aggregation and condensation of bacteria offer a robust approach to improve the local concentration of bacteria for early and rapid detection, which has wide applications in clinics.