arXiv subjects

Yan Jiang

Publications and source records attributed to Yan Jiang.

124 records · Page 7Linked to original sources

arXiv2018

Dispersion Analysis of Finite Difference and Discontinuous Galerkin Schemes for Maxwell's Equations in Linear Lorentz Media

In this paper, we consider Maxwell's equations in linear dispersive media described by a single-pole Lorentz model for electronic polarization. We study two classes of commonly used spatial discretizations: finite difference methods (FD) with arbitrary even order accuracy in space and high spatial order discontinuous Galerkin (DG) finite element methods. Both types of spatial discretizations are coupled with second order semi-implicit leap-frog and implicit trapezoidal temporal schemes studied in our previous research [5,6]. By performing detailed dispersion analysis for the semi-discrete and fully discrete schemes, we obtain rigorous quantification of the dispersion error for Lorentz dispersive dielectrics. In particular, comparisons of dispersion error can be made taking into account the model parameters, and mesh sizes in the design of the two types of schemes. The results for the numerical dispersion analysis can guide us in the optimal choice of discretization parameters for the more complicated and nonlinear models. The numerical dispersion analysis of the fully discrete FD and DG schemes, for the dispersive Maxwell model considered in this paper, clearly indicate the dependence of the numerical dispersion errors on spatial and temporal discretizations, their order of accuracy, mesh discretization parameters and model parameters. The results obtained here cannot be arrived at by considering discretizations of Maxwell's equations in free space. In particular, our results contrast the advantages and disadvantages of using high order FD or DG schemes and leap-frog or trapezoidal time integrators over different frequency ranges using a variety of measures of numerical dispersion errors. Finally, we highlight the limitations of the second order accurate temporal discretizations considered.

math.NA↗

arXiv2018

Hybrid entanglement of three quantum memories with three photons

Quantum network has significant applications both practically and fundamentally. A hybrid architecture with photons and stationary nodes is highly promising. So far, experimental realizations are limited to two nodes with two photons. Going beyond state of the art by entangling many photons with many quantum nodes is highly appreciated. Here, we report an experiment realizing hybrid entanglement between three photons and three atomic-ensemble quantum memories. We make use of three similar setups, in each of which one pair of photon-memory entanglement with high overall efficiency is created via cavity enhancement. Through three-photon interference, the three quantum memories get entangled with the three photons. Via measuring the photons and applying feedforward, we heraldedly entangle the three memories. Our work demonstrates the largest size of hybrid memory-photon entanglement, which may be employed as a build block to construct larger and complex quantum network.

quant-ph↗

arXiv2018

A high-order finite difference WENO scheme for ideal magnetohydrodynamics on curvilinear meshes

A high-order finite difference numerical scheme is developed for the ideal magnetohydrodynamic equations based on an alternative flux formulation of the weighted essentially non-oscillatory (WENO) scheme. It computes a high-order numerical flux by a Taylor expansion in space, with the lowest-order term solved from a Riemann solver and the higher-order terms constructed from physical fluxes by limited central differences. The scheme coupled with several Riemann solvers, including a Lax-Friedrichs solver and HLL-type solvers, is developed on general curvilinear meshes in two dimensions and verified on a number of benchmark problems. In particular, a HLLD solver on Cartesian meshes is extended to curvilinear meshes with proper modifications. A numerical boundary condition for the perfect electrical conductor (PEC) boundary is derived for general geometry and verified through a bow shock flow. Numerical results also confirm the advantages of using low dissipative Riemann solvers in the current framework.

math.NA↗

arXiv2018

A Kernel Based High Order "Explicit" Unconditionally Stable Scheme for Time Dependent Hamilton-Jacobi Equations

In this paper, a class of high order numerical schemes is proposed for solving Hamilton-Jacobi (H-J) equations. This work is regarded as an extension of our previous work for nonlinear degenerate parabolic equations, see Christlieb et al. \emph{arXiv preprint arXiv:1707.09294},, which relies on a special kernel-based formulation of the solutions and successive convolution. When applied to the H-J equations, the newly proposed scheme attains genuinely high order accuracy in both space and time, and more importantly, it is unconditionally stable, hence allowing for much larger time step evolution compared with other explicit schemes and saving computational cost. A high order weighted essentially non-oscillatory methodology and a novel nonlinear filter are further incorporated to capture the correct viscosity solution. Furthermore, by coupling the recently proposed inverse Lax-Wendroff boundary treatment technique, this method is very flexible in handing complex geometry as well as general boundary conditions. We perform numerical experiments on a collection of numerical examples, including H-J equations with linear, nonlinear, convex or non-convex Hamiltonians. The efficacy and efficiency of the proposed scheme in approximating the viscosity solution of general H-J equations is verified.

math.NA↗

arXiv2018

Kernel Based High Order "Explicit" Unconditionally-Stable Scheme for Nonlinear Degenerate Advection-Diffusion Equations

In this paper, we present a novel numerical scheme for solving a class of nonlinear degenerate parabolic equations with non-smooth solutions. The proposed method relies on a special kernel based formulation of the solutions found in our early work on the method of lines transpose and successive convolution. In such a framework, a high order weighted essentially non-oscillatory (WENO) methodology and a nonlinear filter are further employed to avoid spurious oscillations. High order accuracy in time is realized by using the high order explicit strong-stability-preserving (SSP) Runge-Kutta method. Moreover, theoretical investigations of the kernel based formulation combined with an explicit SSP method indicates that the combined scheme is unconditionally stable and up to third order accuracy. Evaluation of the kernel based approach is done with a fast $\mathcal{O}(N)$ summation algorithm. The new method allows for much larger time step evolution compared with other explicit schemes with the same order accuracy, leading to remarkable computational savings.

math.NA↗

arXiv2017

Performance tradeoffs of dynamically controlled grid-connected inverters in low inertia power systems

Implementing frequency response using grid-connected inverters is one of the popular proposed alternatives to mitigate the dynamic degradation experienced in low inertia power systems. However, such solution faces several challenges as inverters do not intrinsically possess the natural response to power fluctuations that synchronous generators have. Thus, to synthetically generate this response, inverters need to take frequency measurements, which are usually noisy, and subsequently make changes in the output power, which are therefore delayed. This paper explores the system-wide performance tradeoffs that arise when measurement noise, power disturbances, and delayed actions are considered in the design of dynamic controllers for grid-connected inverters. Using a recently proposed dynamic droop (iDroop) control for grid-connected inverters, which is inspired by classical first order lead-lag compensation, we show that the sets of parameters that result in highest noise attenuation, power disturbance mitigation, and delay robustness do not necessarily have a common intersection. In particular, lead compensation is desired in systems where power disturbances are the predominant source of degradation, while lag compensation is a better alternative when the system is dominated by delays or frequency noise. Our analysis further shows that iDroop can outperform the standard droop alternative in both joint noise and disturbance mitigation, and delay robustness.

eess.SY↗

arXiv2017

Energy Stable Discontinuous Galerkin Methods for Maxwell's Equations in Nonlinear Optical Media

The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on nonlinear optical media whose response is modeled by a system of first order nonlinear ordinary differential equations (ODEs), which include a single resonance linear Lorentz dispersion, and the nonlinearity comes from the instantaneous electronic Kerr response and the residual Raman molecular vibrational response. To design efficient, accurate, and stable computational methods, we apply high order discontinuous Galerkin discretizations in space to the hybrid PDE-ODE Maxwell system with several choices of numerical fluxes, and the resulting semi-discrete methods are shown to be energy stable. Under some restrictions on the strength of the nonlinearity, error estimates are also established. When we turn to fully discrete methods, the challenge to achieve provable stability lies in the temporal discretizations of the nonlinear terms. To overcome this, novel strategies are proposed to treat the nonlinearity in our model within the framework of the second-order leap-frog and implicit trapezoidal time integrators. The performance of the overall algorithms are demonstrated through numerical simulations of kink and antikink waves, and third-harmonic generation in soliton propagation.

math.NA↗

arXiv2016

Algorithms for Generalized Cluster-wise Linear Regression

Cluster-wise linear regression (CLR), a clustering problem intertwined with regression, is to find clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each entity to have more than one observation, and refer to it as generalized CLR. We propose an exact mathematical programming based approach relying on column generation, a column generation based heuristic algorithm that clusters predefined groups of entities, a metaheuristic genetic algorithm with adapted Lloyd's algorithm for K-means clustering, a two-stage approach, and a modified algorithm of Sp{ä}th \cite{Spath1979} for solving generalized CLR. We examine the performance of our algorithms on a stock keeping unit (SKU) clustering problem employed in forecasting halo and cannibalization effects in promotions using real-world retail data from a large supermarket chain. In the SKU clustering problem, the retailer needs to cluster SKUs based on their seasonal effects in response to promotions. The seasonal effects are the results of regressions with predictors being promotion mechanisms and seasonal dummies performed over clusters generated. We compare the performance of all proposed algorithms for the SKU problem with real-world and synthetic data.

stat.ML↗

arXiv2016

A WENO-based Method of Line Transpose Approach for Vlasov Simulations

In this paper, a high order implicit Method of Line Transpose (MOL$^T$ ) method based on a weighted essentially non-oscillatory (WENO) methodology is developed for one-dimensional linear transport equations and further applied to the Vlasov-Poisson (VP) simulations via dimensional splitting. In the MOL$^T$ framework, the time variable is first discretized by a diagonally implicit strong-stability-preserving Runge-Kutta method, resulting in a boundary value problem (BVP) at the discrete time levels. Then an integral formulation coupled with a high order WENO methodology is employed to solve the BVP. As a result, the proposed scheme is high order accurate in both space and time and free of oscillations even though the solution is discontinuous or has sharp gradients. Moreover, the scheme is able to take larger time step evolution compared with an explicit MOL WENO scheme with the same order of accuracy. The desired positivity-preserving (PP) property of the scheme is further attained by incorporating a newly proposed high order PP limiter. We perform numerical experiments on several benchmarks including linear advection, solid body rotation problem; and on the Landau damping, two-stream instabilities, bump-on-tail, and plasma sheath by solving the VP system. The efficacy and efficiency of the proposed scheme is numerically verified.

math.NA↗

arXiv2016

Freezing motion-induced dephasing in an atomic-ensemble quantum memory

Motion-induced dephasing is a dominant decoherence mechanism for atom-gas quantum memories. In this paper, we develop a new coherent manipulation technique which enables arbitrary engineering of the spin-wave momentum with neglectable noise. By zeroing the spin-wave momentum, motion-induced dephasing can be frozen completely. We experimentally demonstrate this scheme with laser-cooled atoms in a DLCZ configuration. By applying the freezing pulses, memory lifetime gets extended significantly to the limit of atom cloud expansion and does not depend on the detection angle anymore. The observed high cross-correlation above 20 proves that high-fidelity memory operation is well preserved after coherent manipulation.

quant-ph↗

arXiv2015

Arbitrary Rotation of a Single Spinwave Qubit in an Atomic-Ensemble Quantum Memory

We report the first experimental realization of single-qubit manipulation for single spinwaves stored in an atomic ensemble quantum memory. In order to have high-fidelity gate operations, we make use of stimulated Raman transition and controlled Lamor precession jointly. We characterize the gate performances with quantum state tomography and quantum process tomography, both of which imply that high-fidelity operations have been achieved. Our work complements the experimental toolbox of atomic-ensemble quantum memories by adding the capability of single-qubit manipulation, thus may have important applications in future scalable quantum networks.

quant-ph↗

arXiv2015

Experimental demonstration of quantum lithography beyond diffraction limit via Rabi oscillations

Diffraction of light sets the fundamental limit for optical lithography. Many quantum lithography schemes have so far been proposed to overcome this limit either by making use of highly entangled photons, multi-photon processes or multiple Lambda transitions, which are all experimentally high-demanding. Recently, Liao et al. proposed a novel quantum lithography scheme which merely employs Rabi oscillation to surpass the diffraction limit. Here we report a faithful experimental realization of this scheme. Resolution up to ninth of the Rayleigh diffraction limit has been observed. Possibility of creating an arbitrary pattern is also tested experimentally by demonstrating the peak narrowing process using several Rabi floppings together with state-selective optical depletion. Our work may have direct applications in atom pattern engineering for quantum information or quantum simulation applications, and will also possibly boost the adoption of quantum lithography into real-world applications in the near future.

quant-ph↗

arXiv2015

Operating Spin Echo in the Quantum Regime for an Atomic-Ensemble Quantum Memory

Spin echo is a powerful technique to extend atomic or nuclear coherence time by overcoming the dephasing due to inhomogeneous broadening. However, applying this technique to an ensemble-based quantum memory at single-quanta level remains challenging. In our experimental study we find that noise due to imperfection of the rephasing pulses is highly directional. By properly arranging the beam directions and optimizing the pulse fidelities, we have successfully managed to operate the spin echo technique in the quantum regime and observed nonclassical photon-photon correlations. In comparison to the case without applying the rephasing pulses, quantum memory lifetime is extended by 5 folds. Our work for the first time demonstrates the feasibility of harnessing the spin echo technique to extend lifetime of ensemble-based quantum memories at single-quanta level.

quant-ph↗

arXiv2014

Self-organized Voids Revisited: Experimental Verification of the Formation Mechanism*

In this paper, several experiments were conducted to further clarify the formation mechanism of self organized void array induced by a single laser beam, including energy-related experiments, refractive-index-contrast-related experiments, depth-related experiments and effective-numerical-aperture experiment. These experiments indicate that the interface spherical aberration is indeed responsible for the formation of void arrays.

physics.optics↗

arXiv2013

Quantum teleportation and entanglement distribution over 100-kilometre free-space channels

A long standing goal for quantum communication is to transfer a quantum state over arbitrary distances. Free-space quantum communication provides a promising solution towards this challenging goal. Here, through a 97-km free space channel, we demonstrate long distance quantum teleportation over a 35-53 dB loss one-link channel, and entanglement distribution over a 66-85 dB high-loss two-link channel. We achieve an average fidelity of {80.4(9)}% for teleporting six distinct initial states and observe the violation of the Clauser-Horne-Shimony-Holt inequality after distributing entanglement. Besides being of fundamental interest, our result represents a significant step towards a global quantum network. Moreover, the high-frequency and high-accuracy acquiring, pointing and tracking technique developed in our experiment provides an essential tool for future satellite-based quantum communication.

quant-ph↗

arXiv2012

Implementing the Deutsch's algorithm with spin-orbital angular momentum of photon without interferometer

Deutsch's algorithm is the simplest quantum algorithm which shows the acceleration of quantum computer. In this paper, we theoretically advance a scheme to implement quantum Deutsch's algorithm in spin-orbital angular momentum space. Our scheme exploits a newly developed optical device called "q-plate", which can couple and manipulate the spin-orbital angular momentum simultaneously. This experimental setup is of high stability and efficiency theoretically for there is no interferometer in it.

quant-ph↗