We present a theoretical framework connecting the pseudo-Chern number in momentum space to the spectral flow index in phase space for continuous media, with specific applications to topological Langmuir-cyclotron waves (TLCWs) in magnetized plasmas at uniform finite temperatures. By deriving a rigorous correspondence between these two topological invariants, we provide a solid justification for previous studies that applied this relationship heuristically across various continuous media. For magnetized plasmas with finite-temperature effects, we confirm the existence of TLCWs through numerical computation of bulk Chern number differences and analytical calculation of the spectral flow index. These findings advance the understanding of topological phenomena in continuous media.

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly used deep-learning approaches suffer from a lack of interpretability of the trained models. Here, we present an interpretable machine learning framework for analyzing the nonlinear evolution dynamics of optical wave packets in complex wave media. We use sparse regression to reduce microscopic discrete lattice models to simpler effective continuum models, which can accurately describe the dynamics of the wave packet envelope. We apply our approach to valley-Hall domain walls in honeycomb photonic lattices of laser-written waveguides with Kerr-type nonlinearity and different boundary shapes. The reconstructed equations accurately reproduce the linear dispersion and nonlinear effects, including self-steepening and self-focusing. This scheme is proven free of the a priori limitations imposed by the underlying hierarchy of scales traditionally employed in asymptotic analytical methods. It represents a powerful interpretable machine learning technique of interest for advancing design capabilities in photonics and framing the complex interaction-driven dynamics in various topological materials.

Time-dependent Wannier functions were initially proposed as a means for calculating the polarization current in crystals driven by external fields. In this work, we present a simple gauge where Wannier states are defined based on the maximally localized functions at the initial time, and are propagated using the time-dependent Bloch states obtained from established first-principles calculations, avoiding the costly Wannierization at each time step. We show that this basis efficiently describes the time-dependent polarization of the laser-driven system through the analysis of the motion of Wannier centers. We use this technique to analyze highly nonlinear and nonperturbative responses such as high-harmonic generation in solids, using hexagonal boron nitride as an illustrative example, and we show how it provides an intuitive picture for the physical mechanisms.

We provide a theory, algorithms, and simulations of nonequilibrium quantum systems using a one-dimensional (1D) completely positive (CP), matrix-product (MP) density-operator ($\rho$) representation. By generalizing the matrix product state's orthogonality center, to additionally store positive classical mixture correlations, the $\mathrm{MP}\rho$ factorization naturally emerges. In this setting, we analytically and numerically examine the virtual gauge freedoms associated with the representation of quantum density operators. Based on this perspective, we simplify algorithms in certain limits to speed up the integration of the canonical-form master-equation dynamics. This enables us to quickly evolve under the dynamics of two-body quantum channels without resorting to optimization-based methods. In addition to this technical advance, we also scale up numerical examples and discuss implications for accurately modeling hardware architectures and predicting their performance in the near term. This includes an example of the quantum to classical transition of informationally leaky, i.e., decohering, qubits. In this setting, because of loss from environmental interactions, nonlocal complex coherence correlations are converted into global incoherent classical statistical mixture correlations. Lastly, the representation of both global and local correlations is discussed. We expect this work to have applications in additional nonequilibrium settings, beyond qubit engineering.

We consider one-dimensional, interacting spinless bosons on a tight-binding lattice described by the Bose-Hubbard model. Besides attractive onsite two-body interactions, we include a three-body repulsive term such that the competition between these two forces allows the formation of self-bound liquid states. We investigate the properties of this system using the Gutzwiller approximation, showing that, indeed, this mean-field approach also supports liquid states. We find that for densities lower than the equilibrium density, the Gutzwiller method and other mean-field approaches—such as the Gross-Pitaevskii theory—feature a sharp transition to the vacuum state. This, however, is avoided by considering local minima of the functional in the standard manner. We also study the excitation spectrum, and calculate the speed of sound, in full agreement with the usual expression obtained from the thermodynamic equation of state. We study their corresponding quantum droplets variationally and find that the results behave in accordance with the one-dimensional liquid-drop model.

We report on the spectroscopic imaging of tin vapors laser generated from thin liquid tin targets using laser intensities around the threshold of plasma formation. Specifically, we study tin vapor using an extinction imaging method in the UV regime (230–400 nm) to obtain $40\text{−}$µm spatial-resolution images with $10\text{−}{\mathrm{cm}}^{-1}$-resolution spectra $100\mathrm{ns}$ after vaporization. The vapor is created by irradiating a nonoxidized free-flying thin film with a nanosecond laser pulse, the intensity of which is varied between $1\text{and}130\times {10}^7\mathrm{W}/{\mathrm{cm}}^2$, from below to above the threshold of producing plasma. Vapors created with laser intensities below $40\times {10}^7\mathrm{W}/{\mathrm{cm}}^2$ exhibit a spatially homogeneous neutral atomic component, with a temperature around 3000 K, as well as a broadband component due to nanoparticles. The morphology and composition of the vapor change as the plasma forms during vaporization at higher intensities, with the temperature of the vapor rising to $8000\mathrm{K}$ at the highest intensity. At these intensities, the broadband component disappears, indicating that it is a vapor composed only of free atoms.

The intrinsic rotation of electron vortex beams, governed by their phase structure, has been experimentally observed in magnetic fields by breaking the beam's cylindrical symmetry. However, conventional Landau states, which predict three fixed angular frequencies, cannot fully account for the existing experimental observations. To address this limitation, we introduce and derive the generalized Gouy rotation angle, which links the Gouy phase of an extended Landau state—featuring a periodically oscillating beam width—to the experimentally observed angular variation. In particular, this framework predicts a broader spectrum of angular frequencies and captures the reversal of rotation direction observed in electron vortex beams with negative topological charge. Calculations based on experimental parameters show good agreement with previously published data and are further validated here by numerical simulations using the Chebyshev method. Our results are, in principle, applicable to any system involving electron vortex beams in uniform magnetic fields, and provide a foundation for exploring vortex electrons in Glaser and other nonuniform magnetic fields.

We propose an approach to solving constrained combinatorial optimization problems based on embedding the concept of Lagrangian duality into the framework of adiabatic quantum computation. Within the setting of circuit-model fault-tolerant quantum computation, we demonstrate that this approach achieves a quadratic improvement in circuit depth and maintains a constraint-independent circuit width in contrast with the prevalent approach of solving constrained problems via reformulations based on the quadratic unconstrained binary optimization (QUBO) framework. In this study, we include a detailed review of the limitations encountered when using QUBO for constrained optimization. We show that the proposed method overcomes these limitations by encoding the optimal solution at an energetically elevated level of a simpler problem Hamiltonian, which results in substantially more resource-efficient quantum circuits. We consolidate our strategy with a detailed analysis on how the concepts of Lagrangian duality such as duality gap and complementary slackness relate to the success probability of sampling the optimal solution. Our findings are illustrated by benchmarking the Lagrangian dual approach against the QUBO approach using the NP-complete binary knapsack problem.

Electrons solvated in polar liquids are a prototypical many-body system, in which electric interactions on different length scales have a strong impact on quantum states and elementary excitations. Impulsively excited polarons in liquid water and alcohols display coupled coherent motions of electrons and their solvation shells at terahertz (THz) frequencies, affecting both the longitudinal and transverse dielectric function. To address the barely characterized connection between the longitudinal and transverse dielectric response in experiment, an ultrafast pump-probe scheme is employed. Two femtosecond near-infrared pump pulses in sequence generate solvated electrons by ionization of isopropanol solvent molecules. The resulting changes of the dielectric function are mapped in time-resolved measurements by a broadband THz probe pulse, which is detected in a phase-resolved way. Longitudinal polaron oscillations modulate both the longitudinal and transverse dielectric function with a frequency set by the partial electron concentration generated in the separate excitation steps. On top, the transverse response includes steplike components, which are governed by the total electron concentration and well described by Clausius-Mossotti theory. The different longitudinal and transverse response is caused by the different character and spatial range of the underlying electric interactions.

Quantum correlations are essential to the emergent behaviors of quantum systems, supporting key phenomena such as localization or delocalization of particles, quantum avalanches in many-body localized systems, and quantum information transfer. In open atom-nanophotonic systems characterized by long-range spin-exchange interactions, we examine the influence of clean system size on high-order quantum correlations among a clean-disordered atomic array with multiple atomic excitations. By initializing the system far from equilibrium, we observe a suppression of quantum correlations for localized atomic excitations in the disordered zone as the clean system size increases, showcasing the delocalization behavior in the high-order spin-exchange processes. The calculation of the entanglement entropy at the interface further substantiates this thermalizing effect. Our results manifest distinct quantum correlations enabled by long-range interactions mediated by the waveguide, enhance the theoretical comprehension of clean-disordered systems, and provide insights to nonequilibrium quantum dynamics in an atom-nanophotonic platform.

We demonstrate an efficient optical binary-switch effect in nanoslit arrays achieved via the temperature-induced phase transition of ${\mathrm{VO}}_2$. Experimental measurements reveal a polarization-dependent 60% reduction in reflectivity during the insulator-to-metal transition. Tuning a single parameter of the slit enables control over the “optical-valve” effect. Full numerical simulations support these findings, predicting a reflectivity reduction up to 90%. The nearly one-to-null transition in reflectivity mimics the operation of a digital switch, with the high-reflectivity and the low-reflectivity states providing a binary response much like digital electronics.

Geometrically local quantum codes, which are error-correction codes embedded in ${\mathbb{R}}^D$ with checks acting only on qubits within a fixed spatial distance, have garnered significant interest. Recently, it has been demonstrated how to achieve geometrically local codes that maximize both the dimension and the distance, as well as the energy barrier of the code. In this work, we focus on the constructions involving subdivision, and we show that they have an almost linear time decoder, obtained by combining the decoder of the outer good qLDPC code and a generalized version of the Union-Find decoder. This provides the first decoder for an optimal geometrically local three-dimensional code. We demonstrate the existence of a finite threshold error rate under the code capacity noise model using a minimum weight perfect matching decoder. Furthermore, we argue that this threshold is also applicable to the decoder based on the generalized Union-Find algorithm.