arXiv subjects

Yunhui He

Publications and source records attributed to Yunhui He.

At least 37 records · Page 2Linked to original sources

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

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↗

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

Continuous broadband Rydberg receiver using AC Stark shifts and Floquet States

We demonstrate the continuous broadband microwave receivers based on AC Stark shifts and Floquet States of Rydberg levels in a cesium atomic vapor cell. The resonant transition frequency of two adjacent Rydberg states 78$S_{1/2}$ and 78$P_{1/2}$ is tuned based on AC Stark effect of 70~MHz Radio frequency (RF) field that is applied outside the vapor cell. Meanwhile, the Rydberg states also exhibit Floquet even-order sidebands that are used to extend the bandwidths further. We achieve microwave electric field measurements over 1.172~GHz of continuous frequency range. The sensitivity of the Rydberg receiver with heterodyne technique in the absence of RF field is 280.2~nVcm$^{-1}$Hz$^{-1/2}$, while it is dramatically decreased with tuning the resonant transition frequency in the presence of RF field. Surprisingly, the sensitivity can be greatly improved if the microwave field couples the Floquet sideband transition. The achieving of continuous frequency and high sensitivity microwave detection will promote the application of Rydberg receiver in the radar technique and wireless communication.

physics.atom-ph↗

arXiv2023

Improvement of response bandwidth and sensitivity of Rydberg Receiver using multi-channel excitations

We investigate the response bandwidth of a superheterodyne Rydberg receiver at a room-temperature vapor cell, and present an architecture of multi-channel lasers excitation to increase the response bandwidth and keep sensitivity, simultaneously. Two microwave fields, denoted as a local oscillator (LO) $E_{LO}$ and a signal field $E_{Sig}$, couple two Rydberg states transition of $|52D_{5/2}\rangle\to |53P_{3/2}\rangle$. In the presence of the LO field, the frequency difference between two fields can be read out as an intermediate frequency (IF) signal using Rydberg electromagnetically induced transparency (EIT) spectroscopy. The bandwidth of the Rydberg receiver is obtained by measuring the output power of IF signal versus the frequency difference between two fields. The bandwidth dependence on the Rabi frequency of excitation lasers is presented, which shows the bandwidth decrease with the probe Rabi frequency, while it is quadratic dependence on the coupling Rabi frequency. Meanwhile, we investigate the effect of probe laser waist on the bandwidth, showing that the bandwidth is inversely proportional to the laser waist. We achieve a maximum response bandwidth of the receiver about 6.8~MHz. Finally, we design an architecture of multi-channel lasers excitation for increasing the response and keeping the sensitivity, simultaneously. Our work has the potential to extend the applications of Rydberg atoms in communications.

physics.atom-ph↗

arXiv2023

Block Preconditioners for the Marker-and-Cell Discretization of the Stokes-Darcy Equations

We consider the problem of iteratively solving large and sparse double saddle-point systems arising from the stationary Stokes-Darcy equations in two dimensions, discretized by the Marker-and-Cell (MAC) finite difference method. We analyze the eigenvalue distribution of a few ideal block preconditioners. We then derive practical preconditioners that are based on approximations of Schur complements that arise in a block decomposition of the double saddle-point matrix. We show that including the interface conditions in the preconditioners is key in the pursuit of scalability. Numerical results show good convergence behavior of our preconditioned GMRES solver and demonstrate robustness of the proposed preconditioner with respect to the physical parameters of the problem.

math.NA↗

arXiv2023

Anderson Acceleration as a Krylov Method with Application to Asymptotic Convergence Analysis

Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \in \mathbb{R}^n$, but little is known about how to quantify the convergence acceleration provided by AA. As a roadway towards gaining more understanding of convergence acceleration by AA, we study AA($m$), i.e., Anderson acceleration with finite window size $m$, applied to the case of linear fixed-point iterations $x_{k+1}=M x_{k}+b$. We write AA($m$) as a Krylov method with polynomial residual update formulas, and derive recurrence relations for the AA($m$) polynomials. Writing AA($m$) as a Krylov method immediately implies that $k$ iterations of AA($m$) cannot produce a smaller residual than $k$ iterations of GMRES without restart (but without implying anything about the relative convergence speed of (windowed) AA($m$) versus restarted GMRES($m$)). We find that the AA($m$) residual polynomials observe a periodic memory effect where increasing powers of the error iteration matrix $M$ act on the initial residual as the iteration number increases. We derive several further results based on these polynomial residual update formulas, including orthogonality relations, a lower bound on the AA(1) acceleration coefficient $β_k$, and explicit nonlinear recursions for the AA(1) residuals and residual polynomials that do not include the acceleration coefficient $β_k$. Using these recurrence relations we also derive new residual convergence bounds for AA(1) in the linear case, demonstrating how the per-iteration residual reduction $||r_{k+1}||/||r_{k}||$ depends strongly on the residual reduction in the previous iteration and on the angle between the prior residual vectors $r_k$ and $r_{k-1}$. We apply these results to study the influence of the initial guess on the asymptotic convergence factor of AA(1), and to study AA(1) residual convergence patterns.

math.NA↗

arXiv2023

Local Fourier Analysis of P-Multigrid for High-Order Finite Element Operators

Multigrid methods are popular for solving linear systems derived from discretizing PDEs. Local Fourier Analysis (LFA) is a technique for investigating and tuning multigrid methods. P-multigrid is popular for high-order or spectral finite element methods, especially on unstructured meshes. In this paper, we introduce LFAToolkit.jl, a new Julia package for LFA of high-order finite element methods. LFAToolkit.jl analyzes preconditioning techniques for arbitrary systems of second order PDEs and supports mixed finite element methods. Specifically, we develop LFA of p-multigrid with arbitrary second-order PDEs using high-order finite element discretizations and examine the performance of Jacobi and Chebyshev smoothing for two-grid schemes with aggressive p-coarsening. A natural extension of this LFA framework is the analysis of h-multigrid for finite element discretizations or finite difference discretizations that can be represented in the language of finite elements. With this extension, we can replicate previous work on the LFA of h-multigrid for arbitrary order discretizations using a convenient and extensible abstraction. Examples in one, two, and three dimensions are presented to validate our LFA of p-multigrid for the Laplacian and linear elasticity.

math.NA↗

arXiv2023

Superradiance-induced multistability in driven Rydberg lattice gases

We study steady state phases of a one-dimensional array of Rydberg atoms coupled by a microwave (MW) field where the higher energy Rydberg state decays to the lower energy one via single-body and collective (superradiant) decay. Using mean-field approaches, we examine the interplay among the MW coupling, intra-state van der Waals (vdW) interaction, and single-body and collective dissipation between Rydberg states. A linear stability analysis reveals that a series of phases, including uniform, antiferromagnetic, oscillatory, and bistable and multistable phases can be obtained. Without the vdW interaction, only uniform phases are found. In the presence of the vdW interaction, multistable solutions are enhanced when increasing the strength of the superradiant decay rate. Our numerical simulations show that the bistable and multistable phases are stabilized by superradiance in a long chain. The critical point between the uniform and multistable phases and its scaling with the atom number is obtained. Through numerically solving the master equation of a finite chain, we show that the mean-field multistable phase could be characterized by expectation values of Rydberg populations and two-body correlations between Rydberg atoms in different sites.

quant-ph↗

arXiv2022

Optimized sparse approximate inverse smoothers for solving Laplacian linear systems

In this paper we propose and analyze new efficient sparse approximate inverse (SPAI) smoothers for solving the two-dimensional (2D) and three-dimensional (3D) Laplacian linear system with geometric multigrid methods. Local Fourier analysis shows that our proposed SPAI smoother for 2D achieves a much smaller smoothing factor than the state-of-the-art SPAI smoother studied in [Bolten, M., Huckle, T.K. and Kravvaritis, C.D., 2016. Sparse matrix approximations for multigrid methods. Linear Algebra and its Applications, 502, pp.58-76.]. The proposed SPAI smoother for 3D cases provides smaller optimal smoothing factor than that of weighted Jacobi smoother. Numerical results validate our theoretical conclusions and illustrate the high-efficiency and high-effectiveness of our proposed SPAI smoothers. Such SPAI smoothers have the advantage of inherent parallelism. The MATLAB codes for implementing our proposed algorithms are publicly available online at http://github.com/junliu2050/SPAI-MG-Laplacian .

math.NA↗

arXiv2022

Linear Asymptotic Convergence of Anderson Acceleration: Fixed-Point Analysis

We study the asymptotic convergence of AA($m$), i.e., Anderson acceleration with window size $m$ for accelerating fixed-point methods $x_{k+1}=q(x_{k})$, $x_k \in R^n$. Convergence acceleration by AA($m$) has been widely observed but is not well understood. We consider the case where the fixed-point iteration function $q(x)$ is differentiable and the convergence of the fixed-point method itself is root-linear. We identify numerically several conspicuous properties of AA($m$) convergence: First, AA($m$) sequences $\{x_k\}$ converge root-linearly but the root-linear convergence factor depends strongly on the initial condition. Second, the AA($m$) acceleration coefficients $β^{(k)}$ do not converge but oscillate as $\{x_k\}$ converges to $x^*$. To shed light on these observations, we write the AA($m$) iteration as an augmented fixed-point iteration $z_{k+1} =Ψ(z_k)$, $z_k \in R^{n(m+1)}$ and analyze the continuity and differentiability properties of $Ψ(z)$ and $β(z)$. We find that the vector of acceleration coefficients $β(z)$ is not continuous at the fixed point $z^*$. However, we show that, despite the discontinuity of $β(z)$, the iteration function $Ψ(z)$ is Lipschitz continuous and directionally differentiable at $z^*$ for AA(1), and we generalize this to AA($m$) with $m>1$ for most cases. Furthermore, we find that $Ψ(z)$ is not differentiable at $z^*$. We then discuss how these theoretical findings relate to the observed convergence behaviour of AA($m$). The discontinuity of $β(z)$ at $z^*$ allows $β^{(k)}$ to oscillate as $\{x_k\}$ converges to $x^*$, and the non-differentiability of $Ψ(z)$ allows AA($m$) sequences to converge with root-linear convergence factors that strongly depend on the initial condition. Additional numerical results illustrate our findings.

math.OC↗

arXiv2022

Parameter-robust Braess-Sarazin-type smoothers for linear elasticity problems

In this work, we propose three Braess-Sarazin-type multigrid relaxation schemes for solving linear elasticity problems, where the marker and cell scheme, a finite difference method, is used for the discretization. The three relaxation schemes are Jacobi-Braess-Sarazin, Mass-Braess-Sarazin, and Vanka-Braess-Sarazin. A local Fourier analysis (LFA) for the block-structured relaxation schemes is presented to study multigrid convergence behavior. From LFA, we derive optimal LFA smoothing factor for each case. We obtain highly efficient smoothing factors, which are independent of Lamé constants. Vanka-Braess-Sarazin relaxation scheme leads to the most efficient one. In each relaxation, a Schur complement system needs to be solved. Due to the fact that direct solve is often expensive, an inexact version is developed, where we simply use at most three weighted Jacobi iterations on the Schur complement system. Finally, two-grid and V-cycle multigrid performances are presented to validate our theoretical results. Our numerical results show that inexact versions can achieve the same performance as that of exact versions and our methods are robust to the Lamé constants.

math.NA↗

arXiv2022

A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems

We propose a block-structured multigrid relaxation scheme for solving the Stokes-Darcy Brinkman equations discretized by the marker and cell scheme. An element-based additive Vanka smoother is used to solve the corresponding shifted Laplacian operator. Using local Fourier analysis, we present the stencil for the additive Vanka smoother and derive an optimal smoothing factor for Vanka-based Braess-Sarazin relaxation for the Stokes-Darcy Brinkman equations. Although the optimal damping parameter is dependent on meshsize and physical parameter, it is very close to one. Numerical results of two-grid and V(1,1)-cycle are presented, which show high efficiency of the proposed relaxation scheme and its robustness to physical parameters and the meshsize. Using a damping parameter equal to one gives almost the same results as these for the optimal damping parameter at a lower computational overhead.

math.NA↗

arXiv2022

Smoothing analysis of two robust multigrid methods for elliptic optimal control problems

In this paper we study and compare two multigrid relaxation schemes with coarsening by two, three, and four for solving elliptic sparse optimal control problems with control constraints. First, we perform a detailed local Fourier analysis (LFA) of a well-known collective Jacobi relaxation (CJR) scheme, where the optimal smoothing factors are derived. This insightful analysis reveals that the optimal relaxation parameters depend on mesh size and regularization parameters, which was not investigated in literature. Second, we propose and analyze a new mass-based Braess-Sarazin relaxation (BSR) scheme, which is proven to provide smaller smoothing factors than the CJR scheme when $α\ge ch^4$ for a small constant $c$. Here $α$ is the regularization parameter and $h$ is the spatial mesh step size. These schemes are successfully extended to control-constrained cases through the semi-smooth Newton method. Coarsening by three or four with BSR is competitive with coarsening by two. Numerical examples are presented to validate our theoretical outcomes. The proposed inexact BSR (IBSR) scheme, where two preconditioned conjugate gradients iterations are applied to the Schur complement system, yields better computational efficiency than the CJR scheme.

math.NA↗

arXiv2022

A Vanka-type multigrid solver for complex-shifted Laplacian systems from diagonalization-based parallel-in-time algorithms

We propose and analyze a Vanka-type multigrid solver for solving a sequence of complex-shifted Laplacian systems arising in diagonalization-based parallel-in-time algorithms for evolutionary equations. Under suitable assumption, local Fourier analysis shows the proposed Vanka-type smoother achieves a uniform smoothing factor, which is verified by several numerical examples.

math.NA↗

arXiv2022

Optimal smoothing factor with coarsening by three for the MAC scheme for the Stokes equations

In this work, we propose a local Fourier analysis for multigrid methods with coarsening by a factor of three for the staggered finite-difference method applied to the Stokes equations. In [21], local Fourier analysis has been applied to a mass-based Braess-Sarazin relaxation, a mass-based $σ$-Uzawa relaxation, and a mass-based distributive relaxation, with standard coarsening on staggered grids for the Stokes equations. Here, we consider multigrid methods with coarsening by three for these relaxation schemes. We derive theoretically optimal smoothing factors for this coarsening strategy. The optimal smoothing factors of coarsening by three are nearly equal to those obtained from standard coarsening. Thus, coarsening by three is superior computationally. Moreover, coarsening by three generates a nested hierarchy of grids, which simplifies and unifies the construction of grid-transfer operators.

math.NA↗

arXiv2022

Monolithic multigrid for a reduced-quadrature discretization of poroelasticity

Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity. This paper was motivated by an attempt to develop monolithic multigrid preconditioners for the discretization developed in [48]; we show here why this is a difficult task and, as a result, we modify the discretization in [48] through the use of a reduced quadrature approximation, yielding a more "solver-friendly" discretization. Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess-Sarazin relaxation. Numerical results are presented to validate the LFA predictions and demonstrate efficiency of the algorithms. Finally, a comparison to existing block-factorization preconditioners is also given.

math.NA↗

arXiv2021

A novel multigrid method for elliptic distributed control problems

Large linear systems of saddle-point type have arisen in a wide variety of applications throughout computational science and engineering. The discretizations of distributed control problems have a saddle-point structure. The numerical solution of saddle-point problems has attracted considerable interest in recent years. In this work, we propose a novel Braess-Sarazin multigrid relaxation scheme for finite element discretizations of the distributed control problems, where we use the stiffness matrix obtained from the five-point finite difference method for the Laplacian to approximate the inverse of the mass matrix arising in the saddle-point system. We apply local Fourier analysis to examine the smoothing properties of the Braess-Sarazin multigrid relaxation. From our analysis, the optimal smoothing factor for Braess-Sarazin relaxation is derived. Numerical experiments validate our theoretical results. The relaxation scheme considered here shows its high efficiency and robustness with respect to the regularization parameter and grid size.

math.NA↗