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Quantum Monte Carlo study of magnetism and chiral ${\mathrm{d}}+{\mathrm{id}} $-wave superconducivity in twisted bilayer graphene
FANG Shichao, LIAO Xinyi
2025, 74 (12): 120201.
Abstract +
We employ a large-scale, unbiased constrained-path quantum Monte Carlo method to systematically simulate the effective two-orbital Hubbard model for twisted bilayer graphene in order to gain deeper insight into the relationship between correlated states and the superconducting pairing mechanism in twisted bilayer graphene, as well as the influence of the twist angle on superconductivity. Initially, we investigate the modulation of superconductivity by nearest-neighbor attractive Coulomb interactions, demonstrating that electron-phonon coupling plays a significant role in the system. Our numerical results reveal that the superconducting state is dominated by chiral NN-${\mathrm{d}}+{\mathrm{id}} $ superconducting electron pairing symmetry, and that such nearest-neighbor attractive Coulomb interactions significantly enhance the effective long-range pairing correlation function of chiral NN-${\mathrm{d}}+{\mathrm{id}} $ wave. From this perspective, it is evident that the electron-phonon coupling positively contributes to the superconductivity of the system.Then, we explore how the twist angle affects the superconducting state. The flat-band structure caused by hopping anisotropy reflects the different twist angles of the system. Our results show that as the twist angle deviates downward from 1.08°, the effective pairing correlation function of the chiral NN-${\mathrm{d}}+{\mathrm{id}} $ wave increases substantially. Conversely, as the twist angle exceeds 1.08°, the effective correlation function of the chiral NN-${\mathrm{d}}+{\mathrm{id}} $ wave exhibits a tendency of decline. These results suggest that further reduction of the twist angle may lead to higher superconducting transition temperature in twisted bilayer graphene system.Finally, we analyze how nearest-neighbor attractive Coulomb interactions and flat-band structures influence superconductivity from the standpoint of magnetic properties. The observed enhancement of the spin structure factor near the Γ point in the Brillouin zone indicates that enhanced antiferromagnetic correlations are essential for enhancing the superconducting transition temperature and for stabilizing chiral NN-${\mathrm{d}}+{\mathrm{id}} $ wave. Through these investigations, our numerical findings not only contribute to a more comprehensive understanding of strongly correlated systems such as twisted bilayer graphene, but also provide guidance for identifying twist-angle systems with potentially higher superconducting transition temperatures.
Research progress of artificial intelligence empowered quantum communication and quantum sensing systems
XU Jiaxin, XU Lechen, LIU Jingyang, DING Huajian, WANG Qin
2025, 74 (12): 120301.
Abstract +
Quantum communication and quantum sensing, which leverage the unique characteristics of quantum systems, enable information-theoretically secure communication and high-precision measurement of physical quantities. They have attracted significant attention in recent research. However, they both face numerous challenges on the path to practical application. For instance, device imperfections may lead to security vulnerability, and environmental noise may significantly reduce measurement accuracy. Traditional solutions often involve high computational complexity, long processing time, and substantial hardware resource requirements, posing major obstacles to the large-scale deployment of quantum communication and quantum sensing networks. Artificial intelligence (AI), as a major technological advancement in current scientific landscape, offers powerful data processing and analytical capabilities, providing new ideas and methods for optimizing and enhancing quantum communication and sensing systems.Significant progresses have been made in applying AI to quantum communication and sensing, thus injecting new vitality into these cutting-edge technologies. In quantum communication, AI techniques have greatly improved the performance and security of quantum key distribution, quantum memory, and quantum networks through parameter optimization, real-time feedback control, and attack detection. In quantum sensing, quantum sensing technology enables ultra-high sensitivity detection of physical quantities such as time and magnetic fields. The introduction of AI has opened up new avenues for achieving high-precision and high-sensitivity quantum measurements. With AI, sensor performance is optimized, and measurement accuracy is further enhanced through data analysis.This paper also analyzes the current challenges in using AI to empower quantum communication and sensing systems, such as implementing efficient algorithm deployment and system feedback control under limited computational resources, and addressing complex task environments, dynamically changing scenarios, and multi-task coordination requirements. Finally, this paper discusses and envisions future development prospects in this field.
Uncertainty analysis of detonation based on probability learning on manifold
LIANG Xiao, WANG Yanjin, WANG Ruili
2025, 74 (12): 120501.
Abstract +
Detonation test is affected by small experimental datasets due to high risk of implementation and the huge cost of sample production and measurement. The major challenges of limited data consist in constructing the probability distribution of physical quantities and application of machine learning. Probability learning on manifold (PLoM) can generate a large number of implementations that are consistent with practical common knowledge, while preserving potential physical mechanism these generated samples. So PLoM is viewed as an efficient tool of tackling small samples. To begin with, experimental data are assumed to be concentrated on an unknown subset of Euclidean space and can be treated as the sampling of random vector to be determined. Meanwhile, experimental problem is solved in the framework of matrix and the scaling transformation is conducted on the datasets of PBX9502 with multi-physics attributes. Then the principal component analysis is utilized to normalize the scaling matrix, and the normalization matrix is labeled as training sets. Moreover, the altered multi-dimensional Gaussian kernel density estimation is utilized for estimating the probability distribution of training set. Furthermore, diffusion map is used to discover and characterize the geometry and structure of dataset. In other words, nonlinear manifold based on the training set is constructed through diffusion map. Specifically, the first eigenvalue and corresponding eigenvector is related to the construction of diffusion basis and diffusion maps. Further, Itô-MCMC sampler is associated with dissipative Hamilton system driven by Wiener process, for which the initial condition is set to be training set, and prior probability is conceived as invariant measure. Störmer-Verlet scheme is used for solving the stochastic dissipative Hamilton equations. Finally, additional realizations of learning dataset are fulfilled through the inversion transformation. The result shows that random number generated from PLoM satisfies the requirements of industrial and high fidelity simulation. The 95% confidence interval of density is included in the range calibrated by Los Alamos National Laboratory. And the value of detonation velocity calibrated by Prof. Chengwei Sun [Sun C W, Wei Y Z, Zhou Z K 2000 Applied Detonation Physics (Beijing: National Defense Industry Press) p224] also falls into 95% confidence interval of detonation velocity generated by PLoM. It is also deduced from the learning set that density and detonation velocity satisfies the affine transformation. Furthermore, detonation pressure has nonlinear relationship with density. Tiny variation of density can lead to magnificent fluctuation of detonation pressure and detonation velocity. Detonation pressure has the largest discreetness in all the physical quantities through the comparison of variation coefficients of learning set, which coincides with the existing research results. The method used is universal enough and can be extended to other detonation systems.
Imaging simulation of light scattering signals in atmospheric disturbance density fields
WANG Yuyao, SUN Xiaobing, CUI Wenyu, HU Yuan, YU Changping, SONG Bo, XU Lingling, YU Haixiao, WEI Yichen, WANG Yuxuan, YAO Shun
2025, 74 (12): 120701.
Abstract +
During flight operations, aircraft induces atmospheric disturbances in the surrounding environment through aerodynamic interactions between its geometric configuration and ambient air medium, resulting in spatially distinct density distribution characteristics that are significantly different from natural background scenario. Considering the positive correlation between atmospheric medium density and light scattering intensity, theoretical analysis shows that detecting the light scattering intensity signals in disturbed regions can map density distributions, thereby extracting the features of aircraft-induced atmospheric disturbance density fields. Based on the concept of long-range aircraft detection through atmospheric disturbance density field characterization, a novel remote sensing method for aircraft detection is proposed in this work. Specifically, a three-dimensional tomographic imaging detection mode for scattered light in an atmospheric disturbance region is designed, and a comprehensive simulation framework covering the entire process of disturbance optical signal generation, transmission, and response is constructed. The study accomplishes the following tasks: 1) the critical challenges in estimating the imaging modulation transfer function under short-exposure conditions subjected to laser pulse secondary scattering effects are resolved, and a photon scattering echo imaging simulation model for aircraft-induced disturbance density fields is established; 2) the scattering echo signal images from active light sources in disturbed density fields and the differential images obtained under disturbed background and non-disturbed background are simulated, with simulation results under varying system parameters analyzed systematically. The research demonstrates that this simulation model can be used to optimize detection system parameters, develop signal processing methods, and assess long-range detection capabilities, thus providing both theoretical foundations and technical support for advancing aircraft detection technologies based on density disturbance characteristics.
Machine learning-driven elasticity prediction in advanced inorganic materials via convolutional neural networks
LIU Yujie, WANG Zhenyu, LEI Hang, ZHANG Guoyu, XIAN Jiawei, GAO Zhibin, SUN Jun, SONG Haifeng, DING Xiangdong
2025, 74 (12): 120702.
Abstract +
Inorganic crystal materials have shown extensive application potential in many fields due to their excellent physical and chemical properties. Elastic properties, such as shear modulus and bulk modulus, play an important role in predicting the electrical conductivity, thermal conductivity and mechanical properties of materials. However, the traditional experimental measurement method has some problems such as high cost and low efficiency. With the development of computational methods, theoretical simulation has gradually become an effective alternative to experiments. In recent years, graph neural network-based machine learning methods have achieved remarkable results in predicting the elastic properties of inorganic crystal materials, especially, crystal graph convolutional neural networks (CGCNNs), which perform well in the prediction and expansion of material data.In this study, two CGCNN models are trained by using the shear modulus and bulk modulus data of 10987 materials collected in the Matbench v0.1 dataset. These models show high accuracy and good generalization ability in predicting shear modulus and bulk modulus. The mean absolute error (MAE) is less than 13 and the coefficient of determination ($ R^2$) is close to 1. Then, two datasets are screened for materials with a band gap between 0.1 and 3.0 eV and the compounds containing radioactive elements are excluded. The dataset consists of two parts: the first part is composed of 54359 crystal structures selected from the Materials Project database, which constitute the MPED dataset; the second part is the 26305 crystal structures discovered by Merchant et al. (2023 Nature 624 80) through deep learning and graph neural network methods, which constitute the NED dataset. Finally, the shear modulus and bulk modulus of 80664 inorganic crystals are predicted in this study This work enriches the existing material elastic data resources and provides more data support for material design. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00104.
Opacities of X2Σ+, A2Π, and B2Σ+ states of CO+ molecule ion
AN Siyaolitu, WANG Tong, XIAO Lidan, LIU Di, ZHANG Xia, YAN Bing
2025, 74 (12): 123101.
Abstract +
Carbon monoxide cation (CO+) plays a dominant role in some astrophysical atmosphere environments, and theoretical research on its opacity is crucial for modeling radiative transport. In this work, based on experimentally observed vibrational energy levels of the X2Σ+, A2Π, and B2Σ+ electronic states of CO+, the potential energy curves are improved and constructed using a modified Morse (MMorse) potential function, then the vibrational energy levels and spectroscopic constants are extracted. In the meantime, the internally contracted multireference configuration interaction (MRCI) method with Davison size-extensivity correction (+Q) is used to calculate the potential energy curves and transition dipole moments. The refined MMorse potential shows excellent agreement with the computed potential energy curves, while the spectroscopic constants and vibrational levels indicate strong consistency with existing theoretical and experimental data. The opacities of the CO+ molecule is computed at different temperatures under the pressure of 100 atm. The result shows that as temperature rises, the opacities of transitions in the long-wavelength range increases because of the larger population on excited electronic states at higher temperatures. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00213.00136.
Theoretical study on excited states of ICl+ molecular ion considering spin-orbit coupling
LI Rui, DOU Ronglong, GAO Ting, LI Qinan, SONG Chaoqun
2025, 74 (12): 123102.
Abstract +
The electronic structure of the ICl+ molecular ion is investigated by using high-level multireference configuration interaction (MRCI) method. To improve computational accuracy, Davidson corrections, spin-orbit coupling (SOC), and core-valence electron correlations effects are incorporated into the calculations. The potential energy curves (PECs) of 21 Λ-S states associated with the two lowest dissociation limits I+(1Dg)+Cl(2Pu) and I+(3Pg)+Cl(2Pu) are obtained. The dipole moments (DMs) of the 21 Λ-S states of ICl+ are systematically studied, and the variations of DMs of the identical symmetry state (22Σ+/32Σ+ and 22Π/32Π) in the avoided crossing regions are elucidated by analyzing the dominant electronic configuration. When considering the SOC effect, the Λ-S states with the same Ω components may form new avoided crossing point, making the PECs more complex. With the help of calculated SOC matrix element, the interaction between crossing states can be elucidated. Spin-orbit coupling matrix elements involving the 22Π, 32Π, 12Δ and 22Δ states are calculated. By analyzing potential energy curves of these states and the nearby electronic states, the possible predissociation channels for 22Π, 32Π, 12Δ and 22Δ states are provided. Based on the computed PECs, the spectroscopic constants of bound Λ-S and Ω states are determined. The comparison of the spectroscopic constants between Λ-S and Ω states indicates that the SOC effect has an obvious correction to the spectroscopic properties of low-lying states. Finally, the transition properties between excited states and the ground state are studied. Based on the computed transition dipole moments and Franck-Condon factors, radiative lifetimes for the low-lying vibrational levels of excited states are evaluated. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j 00213.00140.
Application of spherical vector wave function to electromagnetic scattering from a buried gyrotropic anisotropic sphere
JIA Yongbing, GENG Youlin
2025, 74 (12): 124101.
Abstract +
The electromagnetic scattering of buried gyrotropic anisotropic media is crucial for resource exploration and environmental monitoring. However, the existing analytical solutions for electromagnetic scattering of a gyrotropic anisotropic sphere are primarily limited to free-space cases due to computational complexity. To address this limitation, an analytical solution that combines spherical vector wave functions (SVWFs), the T-matrix method, the image method, and the addition theorem of SVWFs is proposed in this work. The proposed method is detailed as follows. The transmitted field of a vertically incident plane wave transmitting through the ground serves as the first incident field on the gyrotropic anisotropic sphere, which can be expanded in terms of SVWFs. Using the analytical solution for a gyrotropic anisotropic sphere in free space, expressions for the internal electromagnetic field are derived. Based on the orthogonality of the SVWFs in the surface of the buried gyrotropic anisotropic sphere, the first scattered field is obtained. This scattered field then acts as the incident field on the ground, and its reflection is calculated using the image method. The reflected field can then serve as the secondary incident field for the dielectric sphere, and this process is repeated iteratively until the field components on the ground converge.Unlike the existing methods of computing the field at a fixed point for buried homogeneous cylinder or isotropic sphere, the proposed method computes the electric field distribution along a line L on the ground, which is parallel to both the Y-axis and the sphere’s central axis. The comparison of the results from the proposed method with FEKO simulation results shows their excellent agreement with each other, with an average relative error below 0.1%, thereby validating the correctness of the proposed analytical solution. Moreover, compared with FEKO simulation method, the proposed analytical method indicates a significant advantage in computational efficiency. Using the analytical model established in this work, the influence of incident wave frequency, buried depth and other parameters on the distribution of electric field along the Y-axis is also analyzed in detail. These findings provide practical value for enhancing the accuracy of geological exploration and the reliability of environmental monitoring.
Spatial coherence analysis of intense ultra-flat white laser
YANG Lan, LIU Junming, HONG Lihong, LIU Liqiang, LI Zhiyuan
2025, 74 (12): 124201.
Abstract +
White light is typically considered incoherent; however, the recently popular supercontinuum laser, also known as white laser, spans the visible spectrum and features high laser intensity and good coherence, challenging this traditional limitation. The white laser has a wide range of applications, including multi-channel confocal microscopy, color holography, and white light interferometric surface topography. Although white lasers have been proposed and developed extensively in terms of technology, specific analyses of their optical wave properties—especially spatial coherence—are still lacking. Since many applications impose certain requirements on the spatial coherence of white light, the lack of research into the spatial coherence of white lasers has, to some extent, limited their practical use.This paper presents a detailed experimental study and analysis of the wavefront intensity, polarization characteristics, and spatial coherence of the high-intensity ultra-flat spectrum white laser that was independently developed by our research group in 2023. The laser is generated by broadening the spectrum of a high-intensity Ti:sapphire femtosecond laser through second- and third-order nonlinear effects.A bandpass filter is used to extract eight components from the white laser, with a central wavelength range from 405 nm to 700 nm and a bandwidth of 10 nm for each component. By measuring the performance of these eight quasi-monochromatic lasers, the characteristics of the white laser of the entire visible spectrum can be evaluated.The CCD imaging of the collimated quasi-monochromatic laser spots reveals that their wavefront intensities exhibit a quasi-Gaussian distribution with uniform beam profiles. Polarization measurements by using polarizers at various angles show that the white laser is linearly polarized. A Young’s double-slit interferometer is used to measure the interference fringe contrast of the eight quasi-monochromatic beams to assess their spatial coherence. The experimental results show that the average interference fringe contrast of the entire visible spectrum is 0.77, and the difference between different wavelengths is very small.This indicates that the white laser has excellent spatial coherence in the visible range.The eight quasi-monochromatic lasers in the visible spectrum all exhibit quasi-Gaussian wavefront intensity distributions, linear polarization, and high spatial coherence. This indicates that the white laser inherits the excellent properties of the Ti:sapphire laser. All of these data provide valuable guidance for the application of white lasers in color holography, white light interferometric surface tomography, microscopic imaging, and other fields that require white light with a certain degree of coherence.
Real-time entropy source evaluated dual-parallel continuous variable quantum random number generator
GUO Xiaomin, WANG Qiqi, LUO Yue, SONG Zhijie, LI Zhengya, QU Yikun, GUO Yanqiang, XIAO Liantuan
2025, 74 (12): 124202.
Abstract +
Continuous-variable quantum random number generator (cv-QRNG) has attracted much attention due to its convenient state preparation and high measurement bandwidth. Chip-size integration of this type of QRNG is expectable because all components involved have been integrated on a single chip recently. Most of the existing schemes, including all existing commercial schemes, usually use a once-and-for-all approach to evaluate quantum entropy. In this work, we propose a double-level parallel cv-QRNG scheme that integrates real-time phase-space monitoring and entropy evaluation. By using dynamic threshold monitoring and self-adapting scaling of Toeplitz matrix, the security and generation rate of QRNG can be enhanced simultaneously.Experimentally, a parallel extraction system of vacuum state double quadratures and multiple sideband modes is constructed based on heterodyne, providing sufficient raw data for high-precision and high-speed tomography reconstruction of quantum entropy source and parallel extraction of QRNG. Based on the statistical analysis of data under long-term stable operation of the system, dynamic KLD-sensitive security threshold for statistical distribution of Husimi-Q function of the entropy source is established. When a weak chaotic field is injected to simulate a thermal state attack, the KLD value jumps and quickly deviates from the steady state baseline, manifesting a sensitive identification of the attack. It is worth pointing out that the threshold parameter can be dynamically optimized according to the security requirements of actual application scenarios. An FPGA-based real-time feedback Toeplitz-hash extractor employs a maximum matrix bit-width truncation method to dynamically adjust Toeplitz matrix parameters. This optimization reduces the maximum extraction ratio interval from 6% to 1.8%, with all intervals below 1% for extraction ratios ≤76%, significantly mitigating entropy losses caused by discrete adjustment of the Toeplitz matrix, and achieving a minimum extraction ratio of 16.9%. This flexibility enables the system to accurately control the response sensitivity of abnormal signals while maintaining the real-time generation of quantum random bits. Finally, real-time generation rate of 17.512 Gbit/s is attained with security parameters at the level of 10–50 and the generated random numbers passed NIST SP 800-22, Diehard, and TestU01 standard tests.This research provides a technical path for real-time assessment of entropy source security in QRNG. The proposed scheme has good integrability and scalability, presenting a feasible solution for QRNG to enter the application stage.
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