We investigate and compare two particle number-conserving protocols for the preparation of a topologically nontrivial state. The first is derived from thermally coupling the system to a cold bath, while the second is based on engineered dissipation. We numerically study the time required to reach the target state as well as its robustness against physically important perturbations. Crucially, in both protocols, the cooling capability is limited by dissipatively induced diffusion processes. The resulting quadratic scaling of the cooling time with system size is also corroborated analytically using mean-field approximations and a purely classical random-walk model. Furthermore, we find that the engineered protocol admits a unique and stable dark state, which contributes to an ongoing discussion regarding the applicability of dissipative state preparation to many-body systems.

Topological wave phenomena in continuous media are fundamentally challenged by unbounded spectra and the absence of a compact Brillouin zone, which obstruct conventional bulk-interface formulations. We develop a unified phase-space framework for screened magnetized plasma based on a pseudo-Hermitian formulation with a positive-definite metric, enabling a generalized Schrödinger description and a Weyl-symbol analysis of the bulk generator. We show that the bulk Weyl symbol hosts isolated band degeneracies acting as Berry-Chern monopoles, including a higher-order spin-1 degeneracy with topological charge $+2$ that generically splits into two spin-$\frac{1}{2}$ Weyl points for finite $k_z$. To characterize topology in this noncompact setting, we introduce a strip-gap Chern number associated with finite real-frequency strips of the spectrum of the phase-space symbol, extending band Chern topology to continuum systems. This invariant governs the spectral flow of interface modes induced by spatial variations of the magnetic field and establishes a bulk-interface correspondence at the level of phase-space symbols. By solving the interface eigenvalue problem, we demonstrate that the net spectral flow across the strip gap is determined by the enclosed monopole charge. We further show that this correspondence persists under weak collisional damping as long as the complex spectrum retains a finite real-part strip gap. Our results provide a systematic phase-space framework for topological wave transport in continuous media beyond compact-band and idealized Hermitian settings.

Physics of ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ having higher Curie temperature $\left(T_C\right)$ than ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ is explored theoretically in the framework of magnetic exchange interactions. ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ and ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$ are isostructural, with ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ having one less valence electron and smaller nearest-neighbor exchange coefficients $(J_1 \text{and} J_2)$, challenging the conventional notion that larger $J_1$ or $J_2$ leads to a higher $T_C$. Based on the hybridization exchange, we show that higher-order exchange coefficients ($J_3$ or higher) are positive for ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ but negative for ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, due to a one-electron difference. As a consequence, total sum of all possible exchange coefficients in ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$ are larger than that for ${\mathrm{Fe}}_3{\mathrm{GeTe}}_2$, which accounts for higher $T_C$. To validate these findings, $T_C$ values are computed using both mean-field theory and Monte Carlo simulation. Indeed, higher-order exchange interactions, when properly accounting for the number of neighbors, confirm the higher $T_C$ of ${\mathrm{Fe}}_3{\mathrm{GaTe}}_2$.

This study investigates the emergence of cluster synchronization in a biologically inspired neuronal network composed of 59 coupled chaotic electronic oscillators that is modeled after a dissociated rat cortical culture. A recently introduced spectral block method is employed to predict the formation and sequence of synchronization clusters based solely on the network's structural connectivity, although the exact transition points depend on the values at which the master stability function changes sign. The analysis is conducted through numerical simulations of Rössler oscillators, which allow for a controlled numerical investigation, followed by a second part devoted to the experimental study of a circuit board composed of single-transistor chaotic oscillators. In both cases, the results confirm the expected hierarchical dynamical transition from incoherence to global synchronization via an intermediate cluster state. Furthermore, the analysis of the network of single-transistor chaotic units provides the first experimental validation of the spectral block method and demonstrates that cluster synchronization arises naturally in networks without intentionally designed symmetries. The experimental platform, which features a scalable and reconfigurable electronic network, thus bridges theoretical predictions and real-world observations, highlighting the robustness of cluster synchronization in the presence of nonidealities, noise, and parameter variations, while also emphasizing the practical considerations required when applying the method to real experiments, such as robust cluster identification and calibration of the critical points of the master stability function. These findings advance our understanding of self-organized synchronization in complex systems and have important implications for neuroscience, adaptive computing, and network engineering.

We theoretically explore protocols for measuring the spin polarization of an ensemble of solid-state spins, with precision at or below the standard quantum limit. Such measurements in the solid state are challenging, as standard approaches based on optical fluorescence are often limited by poor readout fidelity. Indirect microwave-resonator-mediated measurements provide an attractive alternative, though a full analysis of relevant sources of measurement noise is lacking. In this work, we study dispersive readout of an inhomogeneously broadened spin ensemble via coupling to a driven resonator measured via homodyne detection. We derive generic analytic conditions for when the homodyne measurement can be limited by the fundamental spin-projection noise, as opposed to microwave-drive shot noise or resonator phase noise. By studying fluctuations of the measurement record in detail, we also propose an experimental protocol for directly detecting spin squeezing, i.e., a reduction of the spin ensemble’s intrinsic projection noise from entanglement. Our protocol provides a method for benchmarking entangled states for quantum-enhanced metrology.

Moiré patterns of twisted and scaled bilayers have recently emerged as a fertile source of quasiperiodic order in two-dimensional materials. Inspired by these systems, we introduce the near-coincidence method for generating quasiperiodic tilings of the plane. The method is intuitive—admitting pairs of nearly coincident points from superimposed layers—yet rigorous, as it maps naturally to the well-established cut-and-project formalism. It reproduces classical tilings, including the Ammann-Beenker, the Niizeki-Gähler, and the square and hexagonal Fibonacci tilings, and also reveals new tilings that are unlikely to arise from conventional constructions. The near-coincidence method is algorithmically simple and already realized in a web-based application that generates tilings from specified layer parameters and coincidence conditions. Future extensions include trilayer systems, where preliminary results yield dodecagonal order with square layers, and very small twist angles, where the method may capture the giant moiré patterns of bilayer and trilayer graphene.

The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic Schrödinger equations for quantum reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. We show that the reverse processes generalize the forward dynamics by combining the noise effects of the forward processes with an additional stochastic drift that dynamically steers a quantum state back to its initial configuration. Consequently, the exact reverse stochastic Schrödinger equations admit closed-form solutions that can be implemented in real time without the need for variational techniques. Our findings establish an analytical framework for quantum state recovery, noise-resilient quantum gates, quantum generative modeling, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.

We present a symmetry-resolved classification of two-dimensional spin-flip small-angle neutron scattering (SANS) patterns arising from dilute ensembles of spherical nanoparticles hosting magnetic vortex states. Based on a linear vortex ansatz with an axially symmetric distribution of vortex axes and the corresponding analytical expression for the orientationally averaged spin-flip SANS cross section, we show that the angular scattering patterns organize into four distinct symmetry regimes: a fourfold anisotropy corresponding to coherent field-aligned magnetization, vertical and horizontal twofold anisotropies associated with aligned and isotropically distributed vortex ensembles, and an isotropic ringlike condition separating the two twofold regimes. The corresponding symmetry boundaries are obtained analytically and define a compact symmetry landscape in the parameter space of vortex amplitude and vortex-axis distribution width. Comparison with a nonlinear vortex profile shows that these symmetry regions are robust with respect to the detailed radial structure of the vortex core. The angular anisotropies are therefore governed primarily by rotational symmetry and by the statistical distribution of vortex axes, providing a compact and model-transparent classification framework of experimental polarized SANS data.

Single-ion optical clocks have shown systematic frequency uncertainties below ${10}^{-18}$, but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically induced transparency of an ${\text{Al}}^{+}$ clock ion via a cotrapped ${\text{Ca}}^{+}$ ion during clock interrogation suppresses the heating of the ions. ${\text{Al}}^{+}$ can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time-dilation shift of $(-1.69\pm 0.20)\times {10}^{-18}$. The ${\text{Ca}}^{+}$ cooling light introduces an additional light shift on the ${\text{Al}}^{+}$ clock transition of $(-9.3\pm 1.1)\times {10}^{-18}$. We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with ${10}^{-19}$ motional and cooling laser-induced uncertainties for ${\text{Al}}^{+}$ and can be employed in other ion clocks as well.

High-harmonic generation (HHG) driven by intense quantum light has recently emerged as a new frontier in strong-field physics. Yet, the mechanism underlying HHG with nonclassical fields such as bright squeezed vacuum (BSV) light—characterized by a vanishing mean electric field—remains elusive. In this work, we develop a fully quantum theory for HHG under arbitrary quantum driving fields. We show that the fluctuation component of the dipole correlation operator plays a central role in HHG with quantum light and is essential for BSV-driven HHG. Furthermore, our framework reveals the photon statistics distribution within individual harmonics and across different harmonics, demonstrating that the statistics inherit the statistical properties of the driving field. This theory overcomes key limitations of existing approaches and uncovers new quantum features of HHG in the presence of nonclassical light.

Variational quantum algorithms (VQAs) are promising candidates for near-term quantum computing, yet they face scalability challenges due to barren plateaus, where gradients vanish exponentially in the system size. Recent conjectures suggest that avoiding barren plateaus might inherently lead to classical simulability, thus limiting the opportunities for quantum advantage. In this work, we advance the theoretical understanding of the relationship between gradient scalability at initialization and computational complexity of VQAs. We first present the Taylor surrogate, a classical simulation technique matching Pauli path runtime guarantees on near-Clifford regions, with run-time advantages in specific regimes. Leveraging the Taylor surrogate, we prove that beyond the previously established classically simulable regions the computational complexity is at least superpolynomial. Next, we introduce the linear Clifford encoder (LCE), a classically efficient ansatz modifier that ensures constant-scaling gradients within landscape regions close to Clifford circuits. Finally, numerical experiments on LCE-modified landscapes provide preliminary empirical evidence of a transition zone where the constant-scaling gradients may start to decay polynomially in superpolynomially complex regions rather than exponentially. These findings suggest speculative instances where nonvanishing gradients and superpolynomial complexity could potentially coexist, vindicating the need for future formal proofs.

Macroscopically, the population density function of random walk models can satisfy self-contained dynamics and exhibit unexpected order. Here, we show how a two-species random walk model that includes diffusion, probabilistic absorption of walkers mediated by a potential function, cross-species annihilation, and normalization of the population density can be implemented semianalytically (by propagating the population density directly instead of simulating individual walkers) to yield steady states that precisely match eigenstates of the Hamiltonian with the corresponding potential function. Key parameters of the random walk model, namely, the absorption coefficient and the diffusion displacement variance, are constrained by establishing an explicit correspondence between the model and imaginary-time propagation of the Schrödinger equation for small time steps. To enforce convergence toward a targeted excited state—rather than merely the ground state—we implement a sparse and periodic orthogonalization where components of the population density proportional to lower-energy eigenstates are removed. This adjustment is sufficient to ensure that the population density propagates within the subspace orthogonal to the span of the lower-energy states, while still converging toward the target state. The model is tested in one- and two-dimensional cases, for different potential functions and different energy levels. The model converges to steady states whose energy uncertainty extrapolates to zero in the limit of vanishing time step, and comparison with theoretical eigenfunctions yields error norms ranging from ${10}^{-3}$ to ${10}^{-11}$. Beyond the application to Hamiltonian eigenvalue problems, this work gives insight into the emergence of nontrivial macroscopic observables based on microscopic, stochastic dynamics.

Chromium thiophosphate (${\mathrm{CrPS}}_4$) is a long-known material: A layered semiconducting antiferromagnet. Its recently discovered gate-tunable metamagnetic phase transitions, the remarkable positive and oscillating magnetoresistance as a tunnel barrier, and its Fano-resonance luminescence, elusive among the multitude of ${\mathrm{Cr}}^{3+}$ compounds, call for revisiting the understanding of its electronic structure, especially regarding how it relates to magnetic order. Here, we employ X-ray magnetic circular dichroism, implemented in both absorption and resonant inelastic X-ray spectroscopies, together with quantum many-body calculations, to unveil the role of metal-ligand covalency in mediating the metamagnetic transitions in ${\mathrm{CrPS}}_4$, using crystal-field and charge-transfer excitations as fingerprints of the evolving magnetic order. We reveal the role of extended superexchange paths involving P and S atoms, coupling interactions between the Cr spins across the different magnetic phases—antiferromagnetic, canted, and ferromagnetic. Our results elucidate the electronic states involved in these phases and provide prescriptions for engineering the metamagnetic phase diagram of ${\mathrm{CrPS}}_4$.

Controlled unidirectional remote plasma production in a radio-frequency (rf) plasma source is demonstrated by placing magnetic nozzle throat several tens of centimeters away from the rf antenna, where a local density peak forms near the throat. The experiment indicates that the dominant electron energization mechanism responsible for the density peak in the magnetic nozzle throat is electrostatic electron acceleration driven by a spontaneously formed ambipolar electric field, yielding an energy gain of approximately 5 eV and enhanced remote ionization. These results establish plasma sources driven by spontaneous electrostatic electron acceleration.

Extracting useful work from quantum systems is a fundamental problem in quantum thermodynamics. In scenarios where rapid protocols are desired—whether due to practical constraints or deliberate design choices—a fundamental trade-off between power and efficiency is yet to be established. Here, we investigate the problem of finite-time optimal work extraction from closed quantum systems, subject to a constraint on the magnitude of the control Hamiltonian. We first reveal the trade-off relation between power and work under a general setup, showing that these fundamental performance metrics cannot be maximized simultaneously. We then identify a solvable class of finite-time optimal work-extraction problems. This class includes nontrivial many-body models such as the Heisenberg model and the $\mathrm{SU}\left(n\right)$-Hubbard model. The key assumption is that the control Hamiltonian is optimized over a Lie algebra preserved by the uncontrolled dynamics. Within this class, the optimal work-extraction problem admits an exact reduction to a nonlinear self-consistent equation, circumventing extensive search over time-dependent control paths. The resulting optimal protocol turns out to be particularly simple: It suffices to use a time-independent control Hamiltonian in the interaction picture, determined by that equation. By exploiting the Lie-algebraic structure of the controllable terms, our approach is applicable to quantum many-body systems through efficient numerical computation. Our results highlight the necessity of rapid protocols to achieve the maximum power and provide an exact route to finite-time optimal work extraction in many-body quantum systems.

We present a framework for characterizing higher-order topological phases directly from the one-particle density matrix, without any reference to an underlying Hamiltonian. Our approach extends the mode-shell correspondence, originally formulated for single-particle Hamiltonians, to Gaussian states subject to chiral constraints. In this correspondence, the mode index counts topological boundary modes, while the shell index quantifies the bulk topology in a region surrounding the modes, providing a bulk-boundary diagnostic. In one-dimensional topological insulators, the shell index reduces to the local chiral marker, recovering the winding number in the translation-invariant limit. We apply the mode-shell correspondence to a $C_4$-symmetric higher-order topological insulator with a chiral constraint and show that a fractional shell index implies that the higher-order phase is intrinsic. The one-particle density matrix is formulated in real space, so the mode-shell correspondence also applies to models without translation invariance. By introducing structural disorder into the $C_4$-symmetric higher-order insulator, we show that the mode-shell correspondence remains a meaningful diagnostic in amorphous structures. The mode-shell correspondence generalizes to interacting states with a gapped bulk spectrum in the one-particle density matrix, providing a practical and diverse route to characterize higher-order topology from the quantum state itself.