Dark-soliton collisions exhibit two distinct regimes, fusion and non-fusion, characterized by different density profiles at the collision instant. For symmetric soliton pairs on a homogeneous background, the two regimes are separated by the critical velocity v_c=c_s/2. In a harmonically trapped Bose–Einstein condensate, however, both the background density and the soliton velocities vary along the trajectories, making the incoming local conditions position dependent. Combining the exact homogeneous two-soliton solution with a local-density description of the trapped background, we obtain {\rho }_{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}=n(x_c^{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}})[2A_{\mathrm{a}\mathrm{v}\mathrm{g},\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l}}(x_c^{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}})-1{]}^2, where x_c^{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}} is the encounter position predicted from the isolated-soliton trajectories and A_{\mathrm{a}\mathrm{v}\mathrm{g},\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l}}=|v_1-v_2|/(2c_s) is the normalized local relative speed evaluated at that position. The expression predicts the minimum density of the merged dip in the fusion regime and the height of the central bump in the non-fusion regime, with the local threshold at A_{\mathrm{a}\mathrm{v}\mathrm{g},\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l}}=1/2. Gross–Pitaevskii simulations of symmetric and asymmetric soliton pairs in both head-on and catch-up geometries provide a direct determination of the collision outcome and of the collision-center density {\rho }_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{s}}. After normalization by n(x_c^{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}), the measured densities collapse onto the curve (2A_{\mathrm{a}\mathrm{v}\mathrm{g},\mathrm{l}\mathrm{o}\mathrm{c}\mathrm{a}\mathrm{l}}-1{)}^2 over both collision regimes.

We propose a physical scheme to realize a parity-time (\mathcal{P}\mathcal{T})-symmetric triple-well potential in a coherent atomic gas and investigate the emergence of higher-order exceptional points (EPs). Through careful parameter tuning, we successfully identify a third-order EP (EP3), observing its characteristic cube-root response to perturbations—a key signature distinguishing it from second-order EPs (EP2). Notably, EP3 exhibits significantly enhanced sensitivity, underscoring its potential for advancing quantum information technologies. Furthermore, we show that the imaginary part of the nonlinear \mathcal{P}\mathcal{T} potential critically governs \mathcal{P}\mathcal{T} phase transitions and dynamically reshapes the phase diagram. Our system also supports stable optical solitons, whose properties can be precisely controlled by tuning the interplay between linear and nonlinear \mathcal{P}\mathcal{T} potentials. When these potentials act as defects, soliton scattering displays strongly asymmetric behavior, directly adjustable via the potentials’ imaginary components. These findings open new avenues for applications in optical switch, optical sensing, and high-precision information transmission.

Quantum entanglement is a crucial resource in quantum information processing, yet its efficient, scalable and robust classification in multipartite systems remains theoretically challenging. Although supervised machine-learning has been applied to this task, most existing methods still suffer from high measurement costs, computational consumption, and weak noise robustness. In this work, by incorporating multipartite uncertainty relations as prior guidance, we propose a neural network approach to classify distinct Stochastic Local Operations and Classical Communication (SLOCC) multipartite entanglement classes based on states sampled from their local unitary (LU) orbits. Compared with traditional techniques, our method reduces experimental measurement-resource requirements and computational overhead, showing high adaptability to large-scale systems. The classification accuracy of our method reaches 99.5% in 20-qubit systems. The numerical validation is performed on states generated by random LU transformations, which preserve the SLOCC class. Within this setting, the proposed method offers strong effectiveness, scalability, and robustness for multipartite entanglement classification.

We study self-bound quantum droplets in the regime dominated by microwave-induced non-axisymmetric dipole−dipole interactions, using the extended Gross−Pitaevskii equation with the Lee−Huang−Yang corrections. We identify the existence region through numerical simulations and employ an anisotropic Gaussian−super-Gaussian variational ansätz to capture the characteristic density profile of the droplets, with a Gaussian profile along the narrow x direction and super-Gaussian profiles in the extended (y, z) plane. Within this variational framework, we characterize the self-binding, spatial localization, and density-compression properties of the droplets and find good agreement between the variational predictions and the numerical results. Collisions between droplets moving along different directions reveal a strong directional dependence, with outcomes ranging from quasi-elastic rebound and merger to fragmentation. In addition, we explore the rotational dynamics of a single self-bound droplet about all three Cartesian axes, revealing rich and controllable three-dimensional rotational dynamics. Together, these results demonstrate how non-axisymmetric dipolar interactions provide versatile means for controlling the translational, collisional, and rotational dynamics of self-bound quantum droplets.

Variational quantum algorithms (VQAs) constitute a prominent paradigm for exploring the capabilities of near-term quantum computers. As the effectiveness of VQAs depends heavily on the design of variational quantum circuits, Quantum Architecture Search (QAS) has emerged as a critical research area to automate the discovery of high-performing circuit structures. This paper reviews key advancements in current research on QAS, including its core concepts, representative methodologies, applications, and emerging trends. The content is structured to ensure broad accessibility for a diverse audience of researchers while preserving the core principles of complex methodologies. In addition, we discuss remaining challenges and suggest potential research directions to offer perspectives on future exploration in this rapidly evolving field.

Square-root topological insulators can inherit edge states from an underlying topological parent system, but existing realizations are typically limited to low degeneracy and small winding numbers. Here, we introduce a general design strategy for extending square-root topological phases to an arbitrary winding number N by combining a fixed structural-subdivision framework with long-range couplings, enabling the number of inherited edge states to increase systematically without raising the root order. We reveal a parity-dependent winding-number phase diagram, where odd and even maximum winding numbers exhibit distinct phase-boundary structures and topological transition sequences. The resulting square-root lattices host N-fold degenerate topological edge states within each of two bulk band gaps, with the corresponding modes exhibiting characteristic fixed-position spatial localization. We also discuss experimentally accessible implementations in photonic waveguide arrays and topolectrical circuits. Our approach provides a scalable route to highly degenerate topological modes and multi-gap wave control in artificial lattices.

Quantum materials such as topological semimetals have gained consummate interest due to their exotic band crossings and protected surface states. In particular, Ta₃GeTe₆ has emerged as a prototypical hourglass Dirac semimetal, as confirmed by both experimental and theoretical analysis. The ARPES confirm the topological hourglass-type band dispersions and Rashba-like surface band, while Hall measurements reveal a high hole carrier concentration and nonreciprocal transport behavior. These findings are further supported by a phenomenological toy model, which predicts a nonreciprocal resistance, consistent with the observed direction-dependent magnetoresistance. Furthermore, the Raman spectroscopy uncovers two-fold and four-fold phonon symmetries drag of highly anisotropic phonons, which establishes symmetry-dependent resistance. DFT calculations reveal Dirac-like and hourglass Dirac band crossings near the Fermi level for the bulk, with Rashba-type spin splitting induced by the surface inversion-symmetry breaking, leading to spin-polarized surface states. The combined experimental and theoretical results demonstrate that Ta₃GeTe₆ hosts a non-trivial electronic topology, with the inversion-symmetry breaking at the surface as the driver of this nonreciprocal transport behavior.

We investigate spin wave (SW) spectra in two-dimensional (2D) magnonic quasicrystals (MQCs) based on Ammann−Beenker (AB) tiling using micromagnetic simulations. The AB MQC structure is realized as an antidot lattice (ADL) etched into a thin Permalloy (Py) strip, generated via projection from a four-dimensional (4D) hypercube onto a 2D plane within a selection window in perpendicular space. Our simulations reveal SW dispersion with distinct circular ring patterns in frequency slices. The centers of these rings coincide with high-intensity diffraction points predicted by the higher-dimensional projection method, and their intensity correlates with corresponding diffraction peaks, confirming origins from Bragg reflection. The spectra exhibit numerous band gaps and fractal characteristics inherent to quasiperiodicity. Crucially, band gap tuning can be achieved by scaling the perpendicular-space selection window, which modifies diffraction intensities and thereby adjusts the SW band structure. This introduces a new design degree of freedom for reconfigurable magnonic devices. Our results demonstrate the effectiveness of the higher-dimensional projection method for analyzing MQC SW dispersion and highlight the potential of quasiperiodic modulation in engineering SW spectra for low-cost, reconfigurable spintronic applications.

Multiferroic tunnel junction (MFTJ) integrating magnetic electrodes with semiconducting ferroelectrics (FEs) as central tunneling barrier holds great promise for next-generation nonvolatile memory. The emergence of room-temperature van der Waals ferromagnets (e.g., Fe₃GaTe₂) and FEs (e.g., α-In₂Se₃, CuInP₂S₆) renders the possibility of all-vdW MFTJ under ambient conditions. Here, we employ first-principles calculations combined with nonequilibrium Green’s function methods to explore spin-dependent transport in Fe₃GaTe₂/α-In₂Se₃/CuInP₂S₆/Fe₃GaTe₂ junctions. The α-In₂Se₃/CuInP₂S₆ dual FE heterojunction introduces an additional degree of freedom for band alignment and interfacial charge modulation under external electric field, dramatically enhancing tunneling electroresistance. We find that polarization reversal leads to a giant tunneling electroresistance exceeding 6.2 × 10⁴ %, far surpassing conventional tunnel junction with a single barrier. Furthermore, adjusting the relative magnetization of Fe₃GaTe₂ electrodes yields a colossal tunneling magnetoresistance up to 5.8 × 10⁶ % upon polarization reversal. These results demonstrate the feasibility of multiple resistance states in MFTJ through coupled electric and magnetic field control, establishing ferroelectric heterojunctions as a powerful route toward high-density, multifunctional memory technologies.

The well-established non-Bloch band theory predicts exponential localization of skin-mode eigenstates in one-dimensional (1D) non-Hermitian systems. Recent studies, however, have uncovered anomalous algebraic localization in higher dimensions. Here, we extend these ideas to Hermitian bosonic quadratic Hamiltonians incorporating quantum squeezing, offering a genuine quantum framework to explore non-Hermitian phenomena without external reservoirs. We construct a two-dimensional (2D) bosonic lattice model with two-mode squeezing and study the spectral properties of its bosonic excitation within the Bogoliubov–de Gennes (BdG) formalism. We demonstrate an algebraic non-Hermitian skin effect (NHSE), characterized by quasi-long-range power-law localization of complex eigenstates. The system shows ultra spectral sensitivity to perturbations involving either two infinitesimal on-site impurities or a weak long-range hopping impurity, while remaining insensitive to a single weak on-site impurity. Analytical treatment via the Green’s function reveals that this sensitivity originates from the divergence of the nonlocal Green’s function associated with the formation of nonlocal bound states. Our study establishes a framework for realizing novel higher-dimensional non-Hermitian physics in Hermitian bosonic platforms such as superconducting circuits, photonic lattices, and optomechanical arrays, with the demonstrated ultra spectral sensitivity suggesting potential applications in quantum sensing and amplification.