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 . 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 , where is the encounter position predicted from the isolated-soliton trajectories and 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 . 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 . After normalization by , the measured densities collapse onto the curve over both collision regimes.
We propose a physical scheme to realize a parity-time ()-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 potential critically governs 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 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.
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.