arXiv subjects

Yunhui He

Publications and source records attributed to Yunhui He.

At least 19 recordsLinked to original sources

arXiv2026

Doppler-enhanced superheterodyne Rydberg microwave receiver

We report the enhanced sensitivity of the Rydberg microwave (MW) receiver by exploiting the Doppler effect in a vapor cell. A two-photon Rydberg ladder scheme is implemented via the co-propagation of probe and coupling lasers, which enhances the Doppler effect. When an MW field is applied, microwave dressing modifies the velocity-dependent resonance condition, enabling stronger contributions from atoms with non-zero velocities and leading to an enhancement of the EIT transmission. Based on this mechanism, we achieve a sensitivity of $35.1\ \mathrm{nV\ cm^{-1}\ Hz^{-1/2}}$ using the heterodyne technique, which is 1.5 times better than that obtained in the counter-propagating configuration. Meanwhile, the required local oscillator (LO) field is reduced by a factor of 17.6 compared with the counter-propagating configuration, which is advantageous for applications requiring minimal radiation and low power consumption. Moreover, the co-propagating configuration is more amenable to integration or portable sensing platforms because multiple laser fields can be delivered through a single optical fiber.

physics.atom-ph↗

arXiv2026

On a blended Anderson / NGMRES acceleration for the Navier-Stokes Picard iteration: convergence analysis and adaptive depth selection

Anderson acceleration (AA) and nonlinear GMRES (NGMRES) have been successfully applied to improve the efficiency and robustness of many nonlinear solvers, with each being shown to have certain advantages over the other. There are two differences between the AA and NGMRES algorithms: the extrapolations are different, and AA uses fixed point residuals in the optimization problem while NGMRES uses true nonlinear residuals. Motivated by recent AA and NGMRES analyses and numerical testing, we consider a blend of AA and NGMRES that uses the AA extrapolation and the true nonlinear residuals for the optimization problem. To focus our study, we consider the blended method applied to the Picard iteration for the Navier-Stokes equations, but many of the ideas developed herein are extendable to a wide variety of nonlinear systems and solvers. We provide a convergence analysis and proof of acceleration of the blended method, provide a detailed numerical comparison of AA, NMGRES and the blended method for several benchmark tests, and develop an effective adaptive depth strategy.

math.NA↗

arXiv2026

Convergence analysis and proof of acceleration for NGMRES applied to the Picard iteration for Navier-Stokes equations

We consider nonlinear GMRES (NGMRES) as an acceleration technique for the Navier-Stokes Picard iteration, a direction that has not previously been explored. We identify the optimal norm for the least squares optimization problem arising in the NGMRES algorithm, and establish a convergence analysis for NGMRES with general depth that proves NGMRES scales the Picard Lipschitz constant by the gain of the optimization problem. To our knowledge, this is the first convergence proof for NGMRES that identifies the mechanism responsible for convergence acceleration. Numerical experiments demonstrate that the convergence estimates are remarkably sharp. In addition, NGMRES greatly improves the performance of the Picard iteration, even in cases where the unaccelerated iteration diverges.

math.NA↗

arXiv2026

Properties of Nonlinear GMRES Applied to the Preconditioned Richardson Iteration

In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply these new approaches to accelerate the preconditioned Richardson iteration. We establish connections between the proposed variants and both left- and right-preconditioned GMRES. In particular, we show that full NGMRES applied to the preconditioned Richardson iteration is equivalent to right-preconditioned GMRES, while full NGMRES equipped with the new least-squares formulation is equivalent to left-preconditioned GMRES. Furthermore, under certain conditions on the preconditioned coefficient matrix, an equivalence between windowed NGMRES with any depth and preconditioned GMRES. These theoretical results deepen our understanding of NGMRES for solving linear systems and clarify its relationship to classical preconditioned GMRES. Finally, we establish conditions for monotonicity of the various variants. Numerical results are presented to validate our theoretical findings.

math.NA↗

arXiv2025

Vanka-smoothed shifted Laplacian multigrid preconditioners for the Helmholtz equations

We present an improved multigrid preconditioner for the acoustic Helmholtz equation with enhanced scalability. Standard multigrid fails to converge for the Helmholtz equation, and the well-known complex shifted Laplacian method overcomes it by adding a complex shift and using the shifted system as a preconditioner. However, the added complex shift grows with the frequency and interferes with the preconditioner's scalability. In this work, we present an additive Vanka smoother that requires a much lower shift than point-wise smoothers, and thereby enhances the scalability. By carefully designing different ingredients of the multigrid cycle, the presented method enables deep V-cycles with a small and bounded shift, even when many levels are used. We validate our method theoretically by local Fourier analysis, and hold numerical experiments for homogeneous and heterogeneous media. We show that our method outperforms plain shifted Laplacian in terms of runtimes and performs well on challenging geophysical media in 2D and 3D.

math.NA↗

arXiv2025

A generalized alternating NGMRES method for PDE-constrained optimization problems governed by transport equations

In this work, we propose a generalized alternating nonlinear generalized minimal residual method (GA-NGMRES) to accelerate first-order optimization schemes for PDE-constrained optimization problems governed by transport equations. We apply GA-NGMRES to a preconditioned first-order optimization scheme by interpreting the update rule as a fixed-point (FP) iteration. Our approach introduces a novel periodic mixing strategy that integrates NGMRES updates with FP steps. This new scheme improves efficiency in terms of both iteration count and runtime compared to the state-of-the-art. We include a comparison to first-order preconditioned gradient descent and preconditioned, inexact Gauss--Newton--Krylov methods. Since the proposed optimization scheme only relies on first-order derivative information, its implementation is straightforward. We evaluate performance as a function of hyperparameters, the mesh size, and the regularization parameter. We consider advection, incompressible flows, and mass-preserving transport (i.e., optimal transport-type problems) as PDE models. Stipulating adequate smoothness requirements based on variational regularization of the control variable ensures that the computed transport maps are diffeomorphic. Numerical experiments on real-world and synthetic problems highlight the robustness and effectiveness of the proposed method. Our approach yields runtimes that are up to 5x faster than state-of-the-art Newton--Krylov methods, without sacrificing accuracy. Additionally, our GA-NGMRES algorithm outperforms the well-known Anderson acceleration for the models and numerical approach considered in this work.

math.OC↗

arXiv2025

Arbitrary Instantaneous Bandwidth Microwave Receiver via Scalable Rydberg Vapor Cell Array with Stark Comb

Rydberg atoms have great potential for microwave (MW) measurements due to their high sensitivity, broad carrier bandwidth, and traceability. However, the narrow instantaneous bandwidth of the MW receiver limits its applications. Improving the instantaneous bandwidth of the receiver is an ongoing challenge. Here, we report on the achievement of an arbitrary instantaneous bandwidth MW receiver via a linear array of scalable Rydberg vapor cells with Stark comb, where the Stark comb consists of an MW frequency comb (MFC) and a position-dependent Stark field. In the presence of the Stark field, the resonance MW transition frequency between two Rydberg states is position dependent, so that we can make each MFC line act as a local oscillator (LO) field to resonantly couple one Rydberg cell. Thus, each cell receives part of a broadband MW signal within its instantaneous bandwidth using atomic heterodyne detection, achieving the measurements of the broadband MW signal simultaneously. In our proof-of-principle experiment, we demonstrate the MW receiver with 210~MHz instantaneous bandwidth using an MFC field with 21 lines. Meanwhile, we achieve an overall sensitivity of 326.6~nVcm$^{-1}$Hz$^{-1/2}$. In principle, the method allows for achieving an arbitrary instantaneous bandwidth of the receiver, provided we have enough MFC lines with enough power. Our work paves the way to design and develop a scalable MW receiver for applications in radar, communication, and spectrum monitoring.

quant-ph↗

arXiv2025

Implicit-Explicit Scheme with Multiscale Vanka Two-Grid Solver for Heterogeneous Unsaturated Poroelasticity

We consider a coupled nonlinear system of equations that describe unsaturated flow in heterogeneous poroelastic media. For the numerical solution, we use a finite element approximation in space and present an efficient multiscale two-grid solver for solving the coupled system of equations. The proposed two-grid solver contains two main parts: (i) accurate coarse grid approximation based on local spectral spaces and (ii) coupled smoothing iterations based on an overlapping multiscale Vanka method. A Vanka smoother and local spectral coarse grids come with significant computational cost in the setup phase. To avoid constructing a new solver for each time step and/or nonlinear iteration, we utilize an implicit-explicit integration scheme in time, where we partition the nonlinear operator as a sum of linear and nonlinear parts. In particular, we construct an implicit linear approximation of the stiff components that remains fixed across all time, while treating the remaining nonlinear residual explicitly. This allows us to construct a robust two-grid solver offline and utilize it for fast and efficient online time integration. A linear stability analysis of the proposed novel coupled scheme is presented based on the representation of the system as a two-step scheme. We show that the careful decomposition of linear and nonlinear parts guarantees a linearly stable scheme. A numerical study is presented for a two-dimensional nonlinear coupled test problem of unsaturated flow in heterogeneous poroelastic media. We demonstrate the robustness of the two-grid solver, particularly the efficacy of block smoothing compared with simple pointwise smoothing, and illustrate the accuracy and stability of implicit-explicit time integration.

math.NA↗

arXiv2025

A Generalized Alternating Anderson Acceleration Method

In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and nonlinear problems. This allows flexibility to use different combinations of fixed-point iteration and Anderson iteration. We present a convergence analysis of the proposed scheme for accelerating the Richardson iteration in the linear case, with a focus on specific parameter choices of interest. Specifically, we prove convergence of the proposed method under contractive fixed-point iteration and provide a sufficient condition for convergence when the Richardson iteration matrix is diagonalizable and noncontractive. To demonstrate the broader applicability of our proposed method, we use it to accelerate Jacobi iteration, Picard iteration, gradient descent, and the alternating direction method of multipliers in solving partial differential equations and nonlinear, nonsmooth optimization problems. The numerical results illustrate that the proposed scheme is more efficient than the existing windowed Anderson acceleration and alternating Anderson ($s=1$) in terms of iteration number and CPU time for careful choice of parameters $m, s, t$.

math.NA↗

arXiv2025

An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time

We consider a Runge--Kutta method for the numerical time integration of the nonstationary incompressible Navier--Stokes equations. This yields a sequence of nonlinear problems to be solved for the stages of the Runge--Kutta method. The resulting nonlinear system of differential equations is discretized using a finite element method. To compute a numerical approximation of the stages at each time step, we employ Newton's method, which requires the solution of a large and sparse generalized saddle-point problem at each nonlinear iteration. We devise an augmented Lagrangian preconditioner within the flexible GMRES method for solving the Newton systems at each time step. The preconditioner can be applied inexactly with the help of a multigrid routine. We present numerical evidence of the robustness and efficiency of the proposed strategy for different values of the viscosity, mesh size, time step, and number of stages of the Runge--Kutta method.

math.NA↗

arXiv2025

Convergence Analysis of An Alternating Nonlinear GMRES on Linear Systems

In this work, we develop an alternating nonlinear Generalized Minimum Residual (NGMRES) algorithm with depth $m$ and periodicity $p$, denoted by aNGMRES($m, p$), applied to linear systems. We provide a theoretical analysis to quantify by how much one-step NGMRES($m$) using Richardson iterations as initial guesses can improve the convergence speed of the underlying fixed-point iteration for diagonalizable and symmetric positive definite cases. Our theoretical analysis gives us a better understanding of which factors affect the convergence speed. Moreover, under certain conditions, we prove the periodic equivalence between the proposed aNGMRES applied to Richardson iteration and GMRES. Specifically, aNGMRES($\infty,p$) and full GMRES are identical at the iteration index $jp$. Therefore, aNGMRES($\infty,p$) can be regarded as an alternative to GMRES for solving linear systems. For finite $m$, the iterates of aNGMRES($m,m+1$) and restarted GMRES (GMRES($m+1$)) are the same at the end of each periodic interval of length $p$, i.e, at the iteration index $jp$. In Addition, we present a convergence analysis of aNGMRES when applied to accelerate Richardson iteration. The advantages of aNGMRES($m,p$) method are that there is no need to solve a least-squares problem at each iteration which can reduce the computational cost, and it can enhance the robustness against stagnations, which could occur for NGMRES($m$).

math.NA↗

arXiv2025

Reciprocal Floquet thermalization in one-dimensional Rydberg atom array

Periodically driven Floquet quantum systems hold great promise for engineering exotic quantum phases and matter, but are often limited by rapid thermalization. In this work, we propose and demonstrate a square-wave-modulated Floquet engineering protocol to steer and study the thermalization dynamics in one-dimensional Rydberg atom arrays. We identify a reciprocal Floquet thermalization mechanism, which is triggered when the combination of laser detuning and Rydberg atom interactions inversely matches the Floquet period. The level statistics show narrow peaks when the reciprocal condition is met, while thermalization is suppressed between two adjacent peaks. We extract signatures of thermalization and its suppression from the stroboscopic evolution of the atomic population. Critically, thermalization occurs in a disorder-free regime, with rapid equilibration achieved within the Rydberg lifetime and experimentally accessible initial states. Our study establishes a robust framework for exploring thermalization-to-localization transitions and designing effective Hamiltonians, and highlights the unique potential of the Rydberg atom array setting for quantum simulations.

quant-ph↗

arXiv2025

Convergence Properties of Nonlinear GMRES Applied to Linear Systems

The Nonlinear GMRES (NGMRES) proposed by Washio and Oosterlee [Electron. Trans. Numer. Anal, 6(271-290), 1997] is an acceleration method for fixed point iterations. It has been demonstrated to be effective, but its convergence properties have not been extensively studied in the literature so far. In this work we aim to close some of this gap, by offering a convergence analysis for NGMRES applied to linear systems. A central part of our analysis focuses on identifying equivalences between NGMRES and the classical Krylov subspace GMRES method.

math.NA↗

arXiv2025

The worst-case root-convergence factor of GMRES(1)

In this work, we analyze the asymptotic convergence factor of minimal residual iteration (MRI) (or GMRES(1)) for solving linear systems $Ax=b$ based on vector-dependent nonlinear eigenvalue problems. The worst-case root-convergence factor is derived for linear systems with $A$ being symmetric or $I-A$ being skew-symmetric. When $A$ is symmetric, the asymptotic convergence factor highly depends on the initial guess. While $M=I-A$ is skew-symmetric, GMRES(1) converges unconditionally and the worst-case root-convergence factor relies solely on the spectral radius of $M$. We also derive the q-linear convergence factor, which is the same as the worst-case root-convergence factor. Numerical experiments are presented to validate our theoretical results.

math.NA↗

arXiv2025

Convergence Analysis for Nonlinear GMRES

In this work, we revisit nonlinear generalized minimal residual method (NGMRES) applied to nonlinear problems. NGMRES is used to accelerate the convergence of fixed-point iterations, which can substantially improve the performance of the underlying fixed-point iterations. We consider NGMRES with a finite window size $m$, denoted as NGMRES($m$). However, there is no convergence analysis for NGMRES($m$) applied to nonlinear systems. We prove that for general $m>0$, the residuals of NGMRES($m$) converge r-linearly under some conditions. For $m=0$, we prove that the residuals of NGMRES(0) converge q-linearly.

math.NA↗

arXiv2024

Observation of electric field induced superradiance slowdown in ultracold Rydberg atomic gases

Atoms excited to electronically high-lying Rydberg states decay to low-energy states through spontaneous emission processes. We investigate the impact of a static electric field on the superradiant emission process between Rydberg $|60D_{5/2}\rangle$ and $|61P_{3/2}\rangle$ states in an ultracold Cesium Rydberg atom ensemble. We report experimental observations of a significant slowdown in superradiance upon applying an electric field. To understand the slowing down dynamics, we employ a discrete truncated Wigner approximation (DTWA) method to solve the corresponding master equation numerically. Our numerical simulations demonstrate that superradiance decoherence is caused by the Stark shifts of the Rydberg level. Our theoretical simulations qualitatively match the experimental observations. Our work provides new insights into controlling quantum critical behaviors, with implications for quantum many-body dynamics, and the study of quantum phase transitions.

physics.atom-ph↗

arXiv2024

Quantum Lotka-Volterra dynamics

Physical systems that display competitive non-linear dynamics have played a key role in the development of mathematical models of Nature. Important examples include predator-prey models in ecology, biology, consumer-resource models in economics, and reaction-diffusion equations in chemical reactions. However, as real world systems are embedded in complex environments, where it is difficult or even impossible to control external parameters, quantitative comparison between measurements and simple models remains challenging. This motivates the search for competitive dynamics in isolated physical systems, with precise control. An ideal candidate is laser excitation in dilute atomic ensembles. For example, atoms in highly-excited Rydberg states display rich many-body dynamics including ergodicity breaking, synchronisation and time crystals. Here, we demonstrate predator-prey dynamics by laser excitation and ionisation of Rydberg atoms in a room temperature vapour cell. Ionisation of excited atoms produce electric fields that suppress further excitation. This starves the ionisation process of resource, giving rise to predator-prey dynamics. By comparing our results to the Lotka-Volterra model, we demonstrate that as well applications in non-linear dynamics, our experiment has applications in metrology, and remote sensing of localised plasmas.

quant-ph↗

arXiv2024

A preconditioner for the grad-div stabilized equal-order finite elements discretizations of the Oseen problem

The paper considers grad-div stabilized equal-order finite elements (FE) methods for the linearized Navier-Stokes equations. A block triangular preconditioner for the resulting system of algebraic equations is proposed which is closely related to the Augmented Lagrangian (AL) preconditioner. A field-of-values analysis of a preconditioned Krylov subspace method shows convergence bounds that are independent of the mesh parameter variation. Numerical studies support the theory and demonstrate the robustness of the approach also with respect to the viscosity parameter variation, as is typical for AL preconditioners when applied to inf-sup stable FE pairs. The numerical experiments also address the accuracy of grad-div stabilized equal-order FE method for the steady state Navier-Stokes equations.

math.NA↗