Determination of the tunneling electron’s quantum state at the tunnel exit is a fundamental issue in the strong-field ionization. Recent experimental and theoretical investigations on atomic systems have established that the tunneling electron may populate highly excited states in the vicinity of the tunnel exit. Here, we address this tunneling-state problem for molecules by analyzing below-threshold harmonics (BTHs) emitted from the prototypical molecular system {\mathrm{H}}_2^{+} induced by the near-circularly polarized laser fields. The BTHs spectrum exhibits a double-plateau structure analogous to the atomic case. However, the cutoff energy of the first plateau displays a pronounced dependence not only on laser intensity but also on the internuclear distance R. These phenomena can be quantitatively described by a semiclassical strong-field model incorporating an analytical treatment of the near-nucleus Coulomb interaction, and attributing the first cutoff energy to the average energy of the excited bound state during tunneling. We further demonstrate that the R-dependent molecular Coulomb potential near the nucleus differs markedly from its atomic counterpart, yielding a significantly lower average energy for the molecular excited state. Our work provides critical evidence of tunneling-electron excitation before ionization in molecules, and sheds a light on the comprehensive understanding of tunneling phenomenon in strong field physics.

Ultrafast electron microscopy (UEM), also referred to as four-dimensional electron microscopy (4D-EM), has emerged as a transformative tool capable of recording atomic-scale dynamics with high spatiotemporal resolution. While the stroboscopic pump–probe mode has been extensively applied to reversible processes, many important phenomena are intrinsically irreversible and demand single-shot imaging. This review focuses on the principles and recent progress of single-shot 4D-EM for capturing non-repeatable events in space and time. We describe the two main single-shot modalities — single-frame and movie-mode (multi-frame) imaging — which rely on intense, ultrashort electron pulses to capture a transient following a single pump excitation. Representative applications are systematically surveyed, including laser-induced melting and rapid solidification, phase transitions, nanoparticle jumping and coalescence, redox and eutectic reaction dynamics, and liquid-phase behaviors. Key challenges, including the conflict between electron number and pulse duration imposed by space-charge effects, beam coherence, and detector limitations, are discussed, where correspondingly future perspectives and strategies are offered. The progress establishes single-shot 4D-EM as an indispensable platform for unraveling irreversible and stochastic processes across materials science, chemistry, physics, and biology.

Variational quantum algorithms (VQAs) have established themselves as a central computational paradigm in the Noisy Intermediate-Scale Quantum (NISQ) era. By coupling parameterized quantum circuits with classical optimization, they operate effectively under strict hardware limitations. However, as quantum architectures transition toward early fault-tolerant (EFT) and ultimate fault-tolerant (FT) regimes, the foundational principles and long-term viability of VQAs require systematic reassessment. This review offers a comprehensive analysis of VQAs and their progression toward the FT regime. We deconstruct the core algorithmic framework by examining ansatz design and classical optimization strategies, including cost function formulation, gradient computation, and optimizer selection. Concurrently, we evaluate critical training bottlenecks, notably barren plateaus (BPs), alongside established mitigation strategies. The discussion then explores the EFT phase, detailing how the integration of quantum error mitigation (QEM) and partial error correction can sustain algorithmic performance. Addressing the FT phase, we analyze the inherent challenges confronting current hybrid VQA models. Furthermore, we synthesize recent VQA applications across diverse domains, including many-body physics, quantum chemistry, machine learning, and mathematical optimization. Ultimately, this review outlines a theoretical roadmap for adapting quantum algorithms to future hardware generations, elucidating how variational principles can be systematically refined to maintain their relevance and efficiency within an error-corrected computational environment.

The nonlinear magnon−phonon coupling enables magnetic materials promising platforms for fabricating phonon combs that are powerful tools for sensing, imaging, and quantum information applications. However, magnetocrystalline anisotropy, crucial for stabilizing two-dimensional (2D) magnetic materials, has been largely overlooked in magnon−phonon coupling studies. In this work, we incorporate magnetocrystalline anisotropy to evaluate the strength of magnon−phonon coupling in monolayer CrI₃. We find that the {\mathrm{A}}_{1\mathrm{u}} mode at \sim 157.75{\mathrm{c}\mathrm{m}}^{-1} exhibits the strongest magnon−phonon coupling (\sim 2.6{\mathrm{c}\mathrm{m}}^{-1}) arising from the large parallel movements along the out-of-plane direction (z-axis) of two magnetic {\mathrm{C}\mathrm{r}}^{3+} ions. This mode corresponds to a large frequency shift of \sim 86.23{\mathrm{c}\mathrm{m}}^{-1} between the nonmagnetic and ferromagnetic phases. More interestingly, magnetocrystalline anisotropy exhibits mode-dependent effects on magnon−phonon coupling. Specifically, it enhances the coupling strength of the A_1u mode by 22.02%, while suppressing that of {\text{A}}_{\text{1g}}^2, {\text{A}}_{\text{2g}}^2 and {\text{E}}_{\text{g}}^2 modes by 69.68%, 55.9%, and 19.17%, respectively. These results identify magnetocrystalline anisotropy as a previously unexplored, symmetry-selective control knob for magnon−phonon coupling in 2D magnets.

Non-Hermitian physics provides a powerful route for controlling wave propagation in open systems, yet its role in spatially inhomogeneous topological structures remains insufficiently clarified. Here, we experimentally demonstrate a spatially inhomogeneous non-Hermitian topological metasurface on a microwave microstrip platform. A continuous geometric modulation introduces a position-dependent Dirac mass and forms a mass-domain-wall interface, while lumped resistive loading provides a controllable imaginary potential. This design transforms the conventional Hermitian degeneracy into a real-part degenerate region near the Γ point, accompanied by an imaginary-frequency bifurcation and mode-dependent attenuation. Tight-binding calculations, full-wave simulations, and microwave near-field measurements are used to characterize the complex bulk dispersion and lossy edge-state transport. We further show that the edge modes exhibit pseudospin-momentum-locked directional excitation, with non-Hermiticity providing an additional degree of freedom for attenuation and mode selectivity. These results clarify the distinct roles of geometric mass gradients and engineered dissipation, establishing a tunable microwave platform for loss-engineered topological wave transport.

High mobility is crucial for optoelectronic response and thermoelectric performance, while low thermal conductivity enhances the thermoelectric figure of merit (ZT) and reduces heat loss. PtTe₂, a novel two-dimension (2D) Dirac semimetal, is a promising optoelectronic and thermoelectric material. Here, we characterize 2D PtTe₂ films using transient thermal grating (TTG) and terahertz time-domain spectroscopy (THz-TDS). TTG reveals an extremely low thermal diffusion coefficient (~6.4 × 10⁻⁶ m²/s), much lower than most semiconductors and metals, likely from strong phonon−phonon scattering or phonon boundary scattering, with a corresponding thermal conductivity of ~10.4 W·m⁻¹·K⁻¹. THz-TDS shows excellent electrical transport: room-temperature conductivity reaches 4.7 × 10⁵ S/m and carrier mobility is 1870 cm²·V⁻¹·s⁻¹, attributed to its highly ordered crystal and Dirac band structure. The ZT is 0.002 at room temperature, comparable to reported values for 2D thermoelectric materials. Combining low thermal conductivity and high mobility, 2D PtTe₂ offers new opportunities for high-performance electronics and possible application in thermoelectrics.