The strong imposition of Dirichlet boundary conditions remains a fundamental challenge in embedded isogeometric analysis, while its extension to shell structures is still relatively underexplored. To address these limitations, this work proposes a three-dimensional embedded isogeometric method based on B++ splines for shell analysis. Within the Reissner-Mindlin shell assumptions, the shell kinematics are described by a three-dimensional displacement field defined over a structured background domain using high-order spline basis functions. The shell midsurface, represented by trimmed B-Rep geometry, is embedded into the background mesh, avoiding boundary-fitted surface discretizations and explicit coupling between multiple surface patches. To enforce essential boundary conditions within the embedded-domain framework, collocation points are introduced along the geometric boundary. By exploiting the Kronecker-delta property of the B++ spline basis, translational and rotational Dirichlet boundary conditions can be imposed strongly and straightforwardly for complex trimmed shell geometries. This strategy provides a robust treatment of shell supports and constraints while maintaining the simplicity of the background discretization. Two collocation strategies are considered, including full collocation and boundary collocation. Their performance is systematically investigated in terms of accuracy and convergence behavior. The proposed formulation naturally accommodates arbitrarily trimmed and multi-patch geometries while preserving the exact CAD description of the shell midsurface. A series of standard shell benchmark problems and two complex automotive examples are presented to assess the convergence properties and computational efficiency of the method. The results demonstrate that the proposed approach achieves accuracy comparable to or better than conventional finite element methods with significantly fewer degrees of freedom, particularly for industrial examples involving complex trimmed surface geometries.

Neutral atom arrays have emerged as a powerful platform for quantum computation, simulation, and metrology. Among them, alkaline-earth-like atoms exhibit distinct advantages, including long coherence time, high-fidelity Rydberg gates, and erasure correction for efficient quantum error correction. However, their scalability has lagged behind that of the alkali atoms. Here, we report 2400 ytterbium-174 atoms trapped in an optical tweezer array with enhanced loading efficiency of 83.5(1)% via blue-detuned light-assisted collisions. We develop a quantitative model of the collision dynamics and find good agreement between the calculated inelastic collision rates and the experimentally measured loading efficiencies. Notably, the loading efficiency is largely maintained for array sizes ranging from dozens to thousands, exhibiting excellent scalability. We further demonstrate that the enhancement exists robustly across a range of interatomic potentials, suggesting its utility for other atomic species. To establish the capability of the ^{174}Yb arrays toward universal quantum computation, we propose to encode the qubit in the ground-clock state manifold and estimate a 99.9% two-qubit gate fidelity with experimentally feasible parameters. Our work advances the prospects for realizing large-scale quantum computers using alkaline-earth-like atoms.

The coherent-state initial-value representation (IVR) for the semi-classical real-time propagator of a quantum system, developed by Herman and Kluk (HK), is widely used in computational studies of chemical dynamics. On the other hand, the Boltzmann operator e-Ĥ/(kBT), with Ĥ, kB, and T representing the Hamiltonian, Boltzmann constant, and temperature, respectively, plays a crucial role in chemical physics and other branches of quantum physics. One might naturally assume that a semi-classical IVR for the matrix element of this operator in the coordinate representation (i.e., ⟨x̃|e-Ĥ/(kBT)|x⟩, or the imaginary-time propagator) could be derived via a straightforward "real-time → imaginary-time transformation" from the HK IVR of the real-time propagator. However, this is not the case, as such a transformation results in a divergence in the high-temperature limit (T → ∞). In this work, we solve this problem and develop a reasonable HK-like semi-classical IVR for ⟨x̃|e-Ĥ/(kBT)|x⟩, specifically for systems where either the gradient of the potential energy (i.e., the force intensity) has a finite upper bound or the potential becomes harmonic in the long-range limit. The integrand in this IVR is a real Gaussian function of the positions x and x̃, which facilitates its application to realistic problems. Our HK-like IVR is exact for free particles and harmonic oscillators, and its effectiveness for other systems is demonstrated through numerical examples.

We investigate the effective interaction and synthetic mutual gauge field between two polar molecules subject to a combination of a static electric field (E-field) and a blue-detuned circularly polarized microwave. We consider all rotational states strongly coupled by the static E-field (up to J = 9) and demonstrate that the effective inter-molecular potential exhibits three distinct behaviors as the E-field strength increases. Specifically, two critical field strengths, denoted as ( ) E-c((1)) and E-c((2)) (E-c((1))< E-c((2))), mark the transitions. When the static E-field strength E-z is below E-c((1)), the effective interaction is characterized by an anti-dipolar potential with a shortrange repulsive barrier. For E-c((1))< E-z < E-c((2)), the long-range potential becomes dipolar, but it still features a short-range repulsive barrier. However, when E-z exceeds E-c((2)), the effective potential becomes attractive along the field axis, signaling the breakdown of three-dimensional shielding. Additionally, the synthetic magnetic flux outside the shielding core is widely tunable, ranging from nearly zero to values approaching 2 pi, offering a mechanism for engineering the adiabatic gauge effects arising from microwave shielding.

Dense asymmetric ceramic membranes are key components in solid oxide cells (SOCs) and gas separation technologies. In particular, proton‐conducting SOCs efficiently generate power and hydrogen at low temperatures. However, high‐temperature sintering of these membranes causes elemental volatilization, segregation, and migration, significantly reducing the protonic conductivity of the electrolyte layer (e.g., BaCe 0.7 Zr 0.1 Y 0.2 O 3‐δ (BCZY712)) and limiting cell performance. Here we report a self‐compressive stress strategy to promote densification of a BCZY712 proton‐conducting electrolyte layer. By precisely regulating the pore former content and the pre‐sintering temperature of the anode substrate which shrinks more than the electrolyte layer, a compressive stress is applied to the electrolyte layer. Under the compressive stress, the densification temperature decreased by ∼150 °C, achieving a relative density of ∼99%. The reduced co‐sintering temperature effectively suppresses barium evaporation, Y 2 O 3 impurity segregation, and Ni migration from the anode substrate to the electrolyte. Consequently, the electrolyte exhibits a markedly 151%‐higher conductivity and the cell delivers an 89%‐improved peak power density compared to a cell co‐sintered at conventional high‐temperature.

Husimi function (Q-function) of a quantum state is the distribution function of the density operator in the coherent state representation. It is widely used in theoretical research, such as in quantum optics. The Wehrl entropy is the Shannon entropy of the Husimi function, and is non-zero even for pure states. This entropy has been extensively studied in mathematical physics. Recent research also suggests a significant connection between the Wehrl entropy and many-body quantum entanglement in spin systems. We investigate the statistical interpretation of the Husimi function and the Wehrl entropy, taking the system of N spin-1/2 particles as an example. Due to the completeness of coherent states, the Husimi function and Wehrl entropy can be explained via the positive operator-valued measurement (POVM) theory, although the coherent states are not a set of orthonormal basis. Here, with the help of the Bayes' theorem, we provide an alternative probabilistic interpretation for the Husimi function and the Wehrl entropy. This interpretation is based on direct measurements of the system, and thus does not require the introduction of an ancillary system as in POVM theory. Moreover, under this interpretation the classical correspondences of the Husimi function and Wehrl entropy are just phase-space probability distribution function of N classical tops, and its associated entropy, respectively. Therefore, this explanation contributes to a better understanding of the relationship between the Husimi function, Wehrl entropy, and classical-quantum correspondence. The generalization of this statistical interpretation to continuous-variable systems is also discussed.

Quantum entanglement is key to understanding correlations and emergent phenomena in quantum many-body systems. For N qubits (distinguishable spin-1/2 particles) in a pure quantum state, many-body entanglement can be characterized by the purity of the reduced density matrix of a subsystem, defined as the trace of the square of this reduced density matrix. Nevertheless, this approach depends on the choice of subsystem. In this letter, we establish an exact relation between the Wehrl-Rényi entropy (WRE) S_W^(2), which is the 2nd Rényi entropy of the Husimi function of the entire system, and the purities of all possible subsystems. Specifically, we prove the relation e^-S_W^(2) = (6π)^-N∑_A Tr(ρ̂_A^2), where A denotes a subsystem with reduced density matrix ρ̂_A, and the summation runs over all 2^N possible subsystems. Furthermore, we show that the WRE can be experimentally measured via a concrete scheme. Therefore, the WRE is a subsystem-independent and experimentally measurable characterization of the overall entanglement in pure states of N qubits. It can be applied to the study of strongly correlated spin systems, particularly those with all-to-all couplings that do not have a natural subsystem division, such as systems realized with natural atoms in optical tweezer arrays or superconducting quantum circuits. We also analytically derive the WRE for several representative many-body states, including Haar-random states, the Greenberger-Horne-Zeilinger (GHZ) state, and the W state.

Scintillator is a key material for the development of X-ray detectors, which has a promising application in medical imaging, security inspection and industrial non-injury detection. The majority of scintillators currently used in imaging are real-time imaging scintillators, which can cause ionization radiation damage to biological subjects or detection equipment during the imaging process and require complex, highly sensitive detection systems. Therefore, exploring stable, environmentally friendly scintillator materials that can achieve delayed imaging is of significance in the field of imaging. Herein, we developed an X-ray time-lapse imaging scintillator, Sr2Al6O11:Dy3+ phosphor, which generates stable traps by X-ray irradiation, thus endowing it with excellent persistent luminescence and information storage properties (>42 d). Moreover, traps constructed by X-ray can be repeatedly refilled (>40 times) under UV light and carriers are released in the form of mechanical or thermal excitation when refilling is complete. By constructing the traps in the phosphor during X-ray excitation and using it for repetitive imaging, the detection limit is 74.78 nGy/s, and the spatial imaging resolution is as high as 16 lp/mm. This discovery provides a new idea for the development of time-delayed X-ray scintillator.

Distinguishing between enantiomers is crucial in chemistry and pharmacology. Existing optical methods rely on enantiospecific three-photon electric-dipole transitions, requiring phase locking, three-photon resonance, and precise beam control, limiting their practicality. Here, we propose an optical method that eliminates these constraints by applying a static electric field, which breaks a symmetry combining rotation and time reversal, leading to distinct two-photon selection rules for enantiomers. This enables selective excitation of a target enantiomer using two beams without phase locking or intensity control, greatly improving the feasibility of optical enantiomer differentiation.

Neutral atom arrays have emerged as a powerful platform for quantum computation, simulation, and metrology. Among them, alkaline-earth-like atoms exhibit distinct advantages, including long coherence time and high-fidelity Rydberg gates. However, their scalability has lagged behind that of the alkali atoms. Here, we report 2,400 Ytterbium-174 atoms trapped in an optical tweezer array with enhanced single-atom loading efficiency of 83.5(1)

By generalizing Bo Gao's approach [Phys. Rev. A 58, 1728 (1998)] for solving the Schrödinger equation for an isotropic van der Waals (vdW) potential to the systems with a multi-scale anisotropic long-range interaction, we derive the solutions for the Schrödinger equation for an anisotropic dipole-dipole interaction plus an isotropic attractive vdW potential, i.e., ${C_d(1-3\cos^2\theta)}/{r^3}-{C_6}/{r^6}$, which is projected to the subspace with angular momentum $l\leq l_{\rm cut}$, with $l_{\rm cut}$ being an arbitrary angular-momentum cutoff. Here $\theta$ is the polar angle of the coordinate $\boldsymbol{r}$ and $r=|\boldsymbol{r}|$. The asymptotic behaviors of these solutions for $r\rightarrow 0$ and $r\rightarrow \infty$ are obtained. These results can be used in the research of collisions and chemical reactions between ultra-cold polar molecules in a static electric field. Our approach to derive the solutions can be applied to the systems with a general long-range potential $\sum_{\lambda= 2}^{\lambda_{\rm max}} {V_\lambda(\theta,\varphi)}/{r^\lambda}$, with $\varphi$ being the azimuthal angle of $\boldsymbol{r}$, and thus can be used in various problems on molecule-molecule interaction.

Distinguishing between enantiomers is crucial in the study of chiral molecules in chemistry and pharmacology. Many optical approaches rely on enantiospecific cyclic electric-dipole transitions induced by three microwave or laser beams. However, these approaches impose stringent requirements, including phase locking, three-photon resonance, and precise control over beam intensities and operation times, which enhance the complexity and restrict the applicability. In this letter, we present a novel optical method that eliminates these constraints entirely. Specifically, we demonstrate that in the presence of a static electric field, there is a selection rule for two-photon electric-dipole transitions that differs between enantiomers. This distinction arises because the static electric field breaks the symmetry associated with the combined action of a specific rotation and time-reversal transformation. Leveraging the enantiospecific two-photon selection rule, one can selectively excite a desired enantiomer using two beams, without the need for phase locking, resonance condition, and the precise control of their intensities and operation times. Our method significantly enhances the feasibility and applicability of optical approaches for enantiomer differentiation.

The recent breakthrough of realizing the Bose-Einstein condensate of polar molecules and degenerate Fermi molecules in three dimensions relies crucially on the microwave shielding technique, which strongly suppresses the collision loss between molecules. In this letter, we show that the cooperation of microwave shielding and dipolar interaction naturally leads to the emergence of a synthetic gauge field. Unlike that studied in cold atoms before, this gauge field couples to the relative motion of every two molecules instead of single-particle motion, therefore being a mutual gauge field. In this case, every molecule carrying a synthetic charge sees the other molecule as carrying the source of the magnetic field, and the spatial distribution of the magnetic field is reminiscent of a solenoid attached to the molecule. In other words, in addition to microwave-shielded interaction, another part of the interaction between two molecules behaves as a charge interacting with a solenoid, which was missed in the previous discussion. We argue that the physical manifestation of this gauge field is breaking time-reversal symmetry in the collective spatial motion of molecules. Finally, we discuss the challenges in quantitatively studying such a quantum many-body system.

The decoherence of high-dimensional orbital angular momentum (OAM) entanglement in the weak scintillation regime has been investigated. In this study, we simulate atmospheric turbulence by utilizing a multiple-phase screen imprinted with anisotropic non-Kolmogorov turbulence. The entanglement negativity and fidelity are introduced to quantify the entanglement of a high-dimensional OAM state. The numerical evaluation results indicate that entanglement negativity and fidelity last longer for a high-dimensional OAM state when the azimuthal mode has a lower value. Additionally, the evolution of higher-dimensional OAM entanglement is significantly influenced by OAM beam parameters and turbulence parameters. Compared to isotropic atmospheric turbulence, anisotropic turbulence has a lesser influence on high-dimensional OAM entanglement.

Enantiomer-specific state transfer (ESST), which involves transferring enantiomers with different handedness of a chiral molecule into different-energy internal states, is a challenging yet significant task. Previous ESST methods are based on dynamic processes and thus require the preparation of initial states and precise control of microwave operation times. We propose a novel ESST approach, called enantiomer-specific pumping (ESP), which is based on a dissipative process and thereby eliminates the need for these two technical requirements. This approach utilizes a special microwave-induced dark state that appears exclusively for the enantiomer with a specific handedness. Specifically, in ESP, the enantiomer lacking the dark state can be pumped out of the subspace of relevant internal states, while the enantiomer with the dark state maintains a finite probability within this subspace, offering high efficiency in ESST. Notably, ESP facilitates enantiodetection without the need for enantiopure samples as reference.

The eikonal approximation (EA) is widely used in various high-energy scattering problems. In this work we generalize this approximation from the scattering problems with time-independent Hamiltonian to the ones with periodical Hamiltonians, i.e., the Floquet scattering problems. We further illustrate the applicability of our generalized EA via the scattering problem with respect to a shaking spherical square-well potential, by comparing the results given by this approximation and the exact ones. The generalized EA we developed is helpful for the research of manipulation of high-energy scattering processes with external field, e.g. the manipulation of atom, molecule or nuclear collisions or reactions via strong laser fields.

We investigate the scattering and two-body bound states of two ultracold atoms in a quasi-two-dimensional (quasi-2D) confinement, with the confinement potential being an infinite square well (box potential) in the transverse ($z$-) direction, and the motion of the atoms in the $x$-$y$ plane being free. Specifically, we calculate the effective 2D scattering length and 2D effective range of the low-energy scattering, as well as the energy and the transverse-excited-mode probability of the bound states. Comparing these results with those obtained under a harmonic transverse confinement potential, we find that in most of the cases the 2D effective range for the box confinement is approximately 0.28 of the one for the harmonic confinement. Moreover, the transverse-excited-mode probability of the bound states for the box confinement is also much lower than the one for the harmonic confinement. These results suggest that the transverse excitation in the box confinement is notably weaker than the one in a harmonic confinement. Therefore, achieving quasi-2D ultracold gases well-described by pure-2D effective models, particularly those with 2D contact interaction, is more feasible through box confinement. Our results are helpful for the quantum simulation of 2D many-body physics with ultracold atoms, e.g., the suppression of 2D effective range may lead to an enhancement of quantum anomaly in two-dimensional Fermi Gases. Additionally, our calculation method is applicable to the two-body problems of ultracold atoms in other types of quasi-2D confinements.

In a previous paper [Phys. Rev. A 95, 060 701（R）（2017）], we demonstrated that a new type of two-body interaction, which depends on the center of mass（CoM） momentum, can be realized for ultracold atoms via laser-modulated magnetic Feshbach resonance（MFR）. Further studies（e.g. L He et al, Phys. Rev. Lett. 120, 045 302（2018）） show that various interesting phenomena, such as Fulde–Ferrell superfluids, can be induced by scattering between ultracold atoms with this interaction. In this work we investigate the shallow bound states of two ultracold atoms with this type of interaction. We show that when the magnetic field B is below the MFR point B 0 , two shallow bound states can appear in this system. Namely, a ‘two-component dimer’ or a dimer with pseudo-spin 1/2 can be formed by two atoms. Furthermore, the dispersion curve of the dimer may have either single or double minimums in the CoM momentum space. The latter case can be explained as a result from significant pseudo-spin-orbital coupling（SOC） effects. Our results show that the ultracold gases with CoM momentum dependent interaction may be a candidate for quantum simulations with ultracold two-component molecules, especially the molecule gases with SOC.

The Wehrl entropy of a quantum state is the entropy of the coherent-state distribution function (Husimi function), and is non-zero even for pure states. We investigate the Wehrl entropy for $N$ spin-1/2 particles with respect to SU(2)$^{\otimes N}$ coherent states (i.e., the direct products of spin coherent states of each particle). We focus on: (1) The statistical interpretation of this Wehrl entropy. (2) The relationship between the Wehrl entropy and quantum entanglement. For (1), despite the coherent states not forming a group of orthonormal bases, we prove that the Wehrl entropy can still be interpreted as the entropy of a probability distribution with clear physical meaning. For (2), we numerically calculate the Wehrl entropy of various entangled pure states with particle number $2\leq N\leq 20$. Our results show that for the large-$N$ ($N\gtrsim 10$) systems the Wehrl entropy of the highly chaotic entangled states are much larger than that of the regular ones (e.g., the GHZ state). These results, together with the fact that the Wehrl entropy is invariant under local unitary transformations, indicate that the Wehrl entropy can reflect the complexity of the quantum entanglement (entanglement complexity) of many-body pure states, as A. Sugita proposed directly from the definitions of the Husimi function and Wehrl entropy (Jour. Phys. A 36, 9081 (2003)). Furthermore, the Wehrl entropy per particle can serve as a quantitative description of this complexity. We further show that the many-body pure entangled states can be classified into three types, according to the behaviors of the Wehrl entropy per particle in the limit $N\rightarrow\infty$, with the states of each type having very different entanglement complexity.

We propose and demonstrate the effectual generation and control of nonparaxial self-accelerating beams by using UV-resin pendant droplets. We show that the geometrical shape of the hanging droplets formed as a result of the interplay between surface tension and gravity offers a natural curvature enabling the generation of nonparaxial self-accelerating beams. By simply adjusting the tilt angle of the surface where the droplets reside, a passing light beam is set to propagate along different curved trajectories, bending into large angles with non-diffracting features superior to a conventional Airy beam. Such self-accelerating beams are directly traced experimentally through the scattered light in yeast-cell suspensions, along with extensive ray tracing and numerical simulations. Furthermore, by modifying the shape of uncured pendant resin droplets in real time, we showcase the dynamical trajectory control of the self-accelerating beams. Our scheme and experimental method may be adopted for droplet-based shaping of other waves such as microfluidic jets and surface acoustic waves.