arXiv subjects

Jie Peng

Publications and source records attributed to Jie Peng.

At least 109 records · Page 6Linked to original sources

arXiv2022

Optical force and torque on small particles induced by polarization singularities

Optical forces in the near fields have important applications in on-chip optical manipulations of small particles and molecules. Here, we report a study of optical force and torque on small particles induced by the optical polarization singularities of a gold cylinder. We show that the scattering of the cylinder generates both electric and magnetic C lines (i.e., lines of polarization singularities) in the near fields, and the C lines can induce complex force and torque on a dielectric/magnetic particle. The force and torque manifest dramatic spatial variations with interesting symmetry properties, providing rich degrees of freedom for near-field optical manipulations. The study, for the first time to our knowledge, uncovers the effect of optical polarization singularities on light-induced force and torque on small particles. The results contribute to the understanding of chiral light-matter interactions and can find applications in on-chip optical manipulations and optical sensing.

physics.optics↗

arXiv2022

Topological near fields generated by topological structures

The central idea of metamaterials and metaoptics is that, besides their base materials, the geometry of structures offers a broad extra dimension to explore for exotic functionalities. Here, we discover that the topology of structures fundamentally dictates the topological properties of optical near fields and offers a new dimension to exploit for optical functionalities that are irrelevant to specific material constituents or structural geometries. We find that the nontrivial topology of metal structures ensures the birth of polarization singularities (PSs) in the near field with rich morphologies and intriguing spatial evolutions including merging, bifurcation, and topological transition. By mapping the PSs to non-Hermitian exceptional points and employing homotopy theory, we extract the core invariant that governs the topological classification of the PSs and the conservation law that regulates their spatial evolutions. The results have effectively bridged three vibrant fields of singular optics, topological photonics, and non-Hermitian physics, with potential applications in chiral sensing, chiral quantum optics, and beyond photonics in other wave systems.

physics.optics↗

arXiv2022

Chiral discrimination by polarization singularities of a metal sphere

The practical applications of chiral discrimination are usually limited by the weak chiral response of enantiomers and the high complexity of detection methods. Here, we propose to use the C lines (i.e., lines of polarization singularities) emerged in light scattering by a metal sphere to detect small chiral particles. Using full-wave numerical simulations and analytical multipole expansions, we determined the absorption dissymmetry of deep-subwavelength helices (i.e., chiral particles) at different positions on the C lines. We find that the absorption dissymmetry can be much larger than that induced by circularly polarized plane wave excitation, and it can be attributed to the asymmetric absorption of the induced electric and magnetic dipoles. We also show that the absorption dissymmetry strongly depends on the anisotropy of the helices. The results may find applications in optical manipulations, optical sensing, and chiral quantum optics.

physics.optics↗

arXiv2021

Unified generation and fast emission of arbitrary single-photon multimode $W$ states

We propose a unified and deterministic scheme to generate arbitrary single-photon multimode $W$ states in circuit QED. A three-level system (qutrit) is driven by a pump-laser pulse and coupled to $N$ spatially separated resonators. The coupling strength for each spatial mode $g_i$ totally decide the generated single-photon N-mode $W$ state $\vert W_N \rangle=\frac{1}{A}\sum_{i=1}^N g_i|0_1 0_2 \cdots 1_i 0_{i+1}\cdots 0_N\rangle$, so arbitrary $\vert W_N \rangle$ can be generated just by tuning $g_i$. We could not only generate $W$ states inside resonators but also release them into transmission lines on demand. The time and fidelity for generating (or emitting) $\vert W_N \rangle$ can both be the same for arbitrary $N$. Remarkably, $\vert W_N\rangle$ can be emitted with probability reaching $98.9\%$ in $20-50$ ns depending on parameters, comparable to the recently reported fastest two-qubit gate ($30-45$ ns). Finally, the time evolution process is convenient to control since only the pump pulse is time-dependent.

quant-ph↗

arXiv2021

Byzantine-Robust Variance-Reduced Federated Learning over Distributed Non-i.i.d. Data

We consider the federated learning problem where data on workers are not independent and identically distributed (i.i.d.). During the learning process, an unknown number of Byzantine workers may send malicious messages to the central node, leading to remarkable learning error. Most of the Byzantine-robust methods address this issue by using robust aggregation rules to aggregate the received messages, but rely on the assumption that all the regular workers have i.i.d. data, which is not the case in many federated learning applications. In light of the significance of reducing stochastic gradient noise for mitigating the effect of Byzantine attacks, we use a resampling strategy to reduce the impact of both inner variation (that describes the sample heterogeneity on every regular worker) and outer variation (that describes the sample heterogeneity among the regular workers), along with a stochastic average gradient algorithm to gradually eliminate the inner variation. The variance-reduced messages are then aggregated with a robust geometric median operator. We prove that the proposed method reaches a neighborhood of the optimal solution at a linear convergence rate and the learning error is determined by the number of Byzantine workers. Numerical experiments corroborate the theoretical results and show that the proposed method outperforms the state-of-the-arts in the non-i.i.d. setting.

cs.LG↗

arXiv2021

Estimating Fiber Orientation Distribution through Blockwise Adaptive Thresholding with Application to HCP Young Adults Data

Due to recent technological advances, large brain imaging data sets can now be collected. Such data are highly complex so extraction of meaningful information from them remains challenging. Thus, there is an urgent need for statistical procedures that are computationally scalable and can provide accurate estimates that capture the neuronal structures and their functionalities. We propose a fast method for estimating the fiber orientation distribution(FOD) based on diffusion MRI data. This method models the observed dMRI signal at any voxel as a convolved and noisy version of the underlying FOD, and utilizes the spherical harmonics basis for representing the FOD, where the spherical harmonic coefficients are adaptively and nonlinearly shrunk by using a James-Stein type estimator. To further improve the estimation accuracy by enhancing the localized peaks of the FOD, as a second step a super-resolution sharpening process is then applied. The resulting estimated FODs can be fed to a fiber tracking algorithm to reconstruct the white matter fiber tracts. We illustrate the overall methodology using both synthetic data and data from the Human Connectome Project.

stat.AP↗

arXiv2021

Two-level overlapping Schwarz methods based on local generalized eigenproblems for Hermitian variational problems

The research of two-level overlapping Schwarz (TL-OS) method based on constrained energy minimizing coarse space is still in its infancy, and there exist some defects, e.g. mainly for second order elliptic problem and too heavy computational cost of coarse space construction. In this paper, by introducing appropriate assumptions, we propose more concise coarse basis functions for general Hermitian positive and definite discrete systems, and establish the algorithmic and theoretical frameworks of the corresponding TL-OS methods. Furthermore, to enhance the practicability of the algorithm, we design two economical TL-OS preconditioners and prove the condition number estimate. As the first application of the frameworks, we prove that the assumptions hold for the linear finite element discretization of second order elliptic problem with high contrast and oscillatory coefficient and the condition number of the TL-OS preconditioned system is robust with respect to the model and mesh parameters. In particular, we also prove that the condition number of the economically preconditioned system is independent of the jump range under a certain jump distribution. Experimental results show that the first kind of economical preconditioner is more efficient and stable than the existed one. Secondly, we construct TL-OS and the economical TL-OS preconditioners for the plane wave least squares discrete system of Helmholtz equation by using the frameworks. The numerical results for homogeneous and non-homogeneous cases illustrate that the PCG method based on the proposed preconditioners have good stability in terms of the angular frequency, mesh parameters and the number of degrees of freedom in each element.

math.NA↗

arXiv2021

One-photon Solutions to Multiqubit Multimode quantum Rabi model

General solutions to the quantum Rabi model involve subspaces with unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for arbitrary number of qubits and photon modes. Unlike the Juddian solution, ours exists for arbitrary single qubit-photon coupling strength with constant eigenenergy. This corresponds to a horizontal line in the spectrum, while still being a qubit-photon entangled state. As a possible application, we propose an adiabatic scheme for the fast generation of arbitrary single-photon multimode W states with nonadiabatic error less than 1%. Finally, we propose a superconducting circuit design, showing the experimental feasibility of the multimode multiqubit Rabi model.

quant-ph↗

arXiv2021

Polarization Singularities in Light Scattering by Small Particles

Using full-wave numerical simulations and analytical multipole expansions we investigated the properties of real-space polarization singularities that emerge in light scattering by subwavelength particles. We considered spherical and torus particles made of dielectric or perfect-electric-conductor material. We determined the topological indices and the trajectories of electric-field polarization singularities in both the near-field and far-field regions. In the far-field region, a total of four singularities are identified and the sum of their polarization topological indices is two, independent of the particle's geometric shape. In the near-field region, the polarization singularities strongly depend on the particle's shape and the polarization of incident light, and their index sum is not governed by the Poincaré-Hopf theorem anymore due to the non-transverse nature of the fields. From near field to far field, a flipping of sign can happen to the polarization topological indices of the C lines. The far-field properties of the singularities can be well explained by the interference of the excited multipoles, but their near-field properties can be strongly affected by the evanescent fields that are not captured by the multipole expansions. Our work uncovers the important relationship between particles' geometric properties and the polarization singularities of their scattering field. The results can be applied to manipulate polarization singularities in nanophotonic systems and could generate novel applications in optical sensing.

physics.optics↗

arXiv2021

Constructing new APN functions through relative trace functions

In 2020, Budaghyan, Helleseth and Kaleyski [IEEE TIT 66(11): 7081-7087, 2020] considered an infinite family of quadrinomials over $\mathbb{F}_{2^{n}}$ of the form $x^3+a(x^{2^s+1})^{2^k}+bx^{3\cdot 2^m}+c(x^{2^{s+m}+2^m})^{2^k}$, where $n=2m$ with $m$ odd. They proved that such kind of quadrinomials can provide new almost perfect nonlinear (APN) functions when $\gcd(3,m)=1$, $ k=0 $, and $(s,a,b,c)=(m-2,ω, ω^2,1)$ or $((m-2)^{-1}~{\rm mod}~n,ω, ω^2,1)$ in which $ω\in\mathbb{F}_4\setminus \mathbb{F}_2$. By taking $a=ω$ and $b=c=ω^2$, we observe that such kind of quadrinomials can be rewritten as $a {\rm Tr}^{n}_{m}(bx^3)+a^q{\rm Tr}^{n}_{m}(cx^{2^s+1})$, where $q=2^m$ and $ {\rm Tr}^n_{m}(x)=x+x^{2^m} $ for $ n=2m$. Inspired by the quadrinomials and our observation, in this paper we study a class of functions with the form $f(x)=a{\rm Tr}^{n}_{m}(F(x))+a^q{\rm Tr}^{n}_{m}(G(x))$ and determine the APN-ness of this new kind of functions, where $a \in \mathbb{F}_{2^n} $ such that $ a+a^q\neq 0$, and both $F$ and $G$ are quadratic functions over $\mathbb{F}_{2^n}$. We first obtain a characterization of the conditions for $f(x)$ such that $f(x) $ is an APN function. With the help of this characterization, we obtain an infinite family of APN functions for $ n=2m $ with $m$ being an odd positive integer: $ f(x)=a{\rm Tr}^{n}_{m}(bx^3)+a^q{\rm Tr}^{n}_{m}(b^3x^9) $, where $ a\in \mathbb{F}_{2^n}$ such that $ a+a^q\neq 0 $ and $ b $ is a non-cube in $ \mathbb{F}_{2^n} $.

cs.IT↗

arXiv2021

Discontinuous Galerkin methods for semilinear elliptic boundary value problem

A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretizations are established, and the corresponding existence and uniqueness theorem is proved by using Brouwer's fixed point method. Some optimal priori error estimates under both DG norm and $L^2$ norm are presented. Numerical results are also shown to confirm the efficiency of the proposed approach.

math.NA↗

arXiv2020

Byzantine-Robust Decentralized Stochastic Optimization over Static and Time-Varying Networks

In this paper, we consider the Byzantine-robust stochastic optimization problem defined over decentralized static and time-varying networks, where the agents collaboratively minimize the summation of expectations of stochastic local cost functions, but some of the agents are unreliable due to data corruptions, equipment failures or cyber-attacks. The unreliable agents, which are called as Byzantine agents thereafter, can send faulty values to their neighbors and bias the optimization process. Our key idea to handle the Byzantine attacks is to formulate a total variation (TV) norm-penalized approximation of the Byzantine-free problem, where the penalty term forces the local models of regular agents to be close, but also allows the existence of outliers from the Byzantine agents. A stochastic subgradient method is applied to solve the penalized problem. We prove that the proposed method reaches a neighborhood of the Byzantine-free optimal solution, and the size of neighborhood is determined by the number of Byzantine agents and the network topology. Numerical experiments corroborate the theoretical analysis, as well as demonstrate the robustness of the proposed method to Byzantine attacks and its superior performance comparing to existing methods.

math.OC↗

arXiv2020

Optical Forces in Coupled Chiral Particles

Structural chirality can induce counter-intuitive optical forces due to inherent symmetry properties. While optical forces on a single chiral particle in the Rayleigh regime have been well studied, optical forces in coupled chiral particles remain less explored. By using full-wave numerical simulations and analytical methods of source representation and coupled mode theory, we investigated the optical forces induced by a plane wave on two chiral particles coupling with each other via the evanescent near fields. We found that the induced electric and magnetic dipoles of the chiral particles have complicated couplings that give rise to dark and bright modes. The interaction force between the particles can be either attractive or repulsive, and its magnitude can be significantly enhanced by the resonance modes. The attractive force is much stronger if two particles are of opposite handedness compared with the case of same handedness. The electric dipole force and the magnetic dipole force have the same sign for two particles with the same handedness, while they are of different signs for two particles with opposite handedness. The results can lead to a better understanding of chirality-induced optical forces with potential applications in optical manipulations and chiral light-matter interactions.

physics.optics↗

arXiv2020

Adaptive-Multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems

In this paper, we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algorithms for solving the resulting discrete system. In order to form the adaptive coarse components, the local generalized eigenvalue problems for each common face and each common edge are carefully designed. The condition number of the two-level adaptive BDDC preconditioned system is proved to be bounded above by a user-defined tolerance and a constant which is dependent on the maximum number of faces and edges per subdomain and the number of subdomains sharing a common edge. The efficiency of these algorithms is illustrated on a benchmark problem. The numerical results show the robustness of our two-level adaptive BDDC algorithms with respect to the wave number, the number of subdomains and the mesh size, and illustrate that our multi-level adaptive BDDC algorithm can reduce the scale of the coarse problem and can be used to solve large wave number problems efficiently.

math.NA↗

arXiv2019

On constructions and properties of $(n,m)$-functions with maximal number of bent components

For any positive integers $n=2k$ and $m$ such that $m\geq k$, in this paper we show the maximal number of bent components of any $(n,m)$-functions is equal to $2^{m}-2^{m-k}$, and for those attaining the equality, their algebraic degree is at most $k$. It is easily seen that all $(n,m)$-functions of the form $G(x)=(F(x),0)$ with $F(x)$ being any vectorial bent $(n,k)$-function, have the maximum number of bent components. Those simple functions $G$ are called trivial in this paper. We show that for a power $(n,n)$-function, it has such large number of bent components if and only if it is trivial under a mild condition. We also consider the $(n,n)$-function of the form $F^{i}(x)=x^{2^{i}}h({\rm Tr}^{n}_{e}(x))$, where $h: \mathbb{F}_{2^{e}} \rightarrow \mathbb{F}_{2^{e}}$, and show that $F^{i}$ has such large number if and only if $e=k$, and $h$ is a permutation over $\mathbb{F}_{2^{k}}$. It proves that all the previously known nontrivial such functions are subclasses of the functions $F^{i}$. Based on the Maiorana-McFarland class, we present constructions of large numbers of $(n,m)$-functions with maximal number of bent components for any integer $m$ in bivariate representation. We also determine the differential spectrum and Walsh spectrum of the constructed functions. It is found that our constructions can also provide new plateaued vectorial functions.

cs.IT↗

arXiv2019

Constructing vectorial bent functions via second-order derivatives

Let $n$ be an even positive integer, and $m<n$ be one of its positive divisors. In this paper, inspired by a nice work of Tang et al. on constructing large classes of bent functions from known bent functions [27, IEEE TIT, 63(10): 6149-6157, 2017], we consider the construction of vectorial bent and vectorial plateaued $(n,m)$-functions of the form $H(x)=G(x)+g(x)$, where $G(x)$ is a vectorial bent $(n,m)$-function, and $g(x)$ is a Boolean function over $\mathbb{F}_{2^{n}}$. We find an efficient generic method to construct vectorial bent and vectorial plateaued functions of this form by establishing a link between the condition on the second-order derivatives and the key condition given by [27]. This allows us to provide (at least) three new infinite families of vectorial bent functions with high algebraic degrees. New vectorial plateaued $(n,m+t)$-functions are also obtained ($t\geq 0$ depending on $n$ can be taken as a very large number), two classes of which have the maximal number of bent components.

cs.IT↗

arXiv2019

Unified Superradiant phase transitions

We prove, by means of a unified treatment, that the superradiant phase transitions of Dicke and classical oscillator limits of simple light-matter models are indeed of the same type. We show that the mean-field approximation is exact in both cases, and compute the structure and location of the transitions in parameter space. We extend this study to a fuller range of models, paying special attention to symmetry considerations. We uncover general features of the phase structure in the space of parameters of these models.

quant-ph↗

arXiv2018

Adaptive BDDC algorithms for the system arising from plane wave discretization of Helmholtz equations

Balancing domain decomposition by constraints (BDDC) algorithms with adaptive primal constraints are developed in a concise variational framework for the weighted plane wave least-squares (PWLS) discritization of Helmholtz equations with high and various wave numbers. The unknowns to be solved in this preconditioned system are defined on elements rather than vertices or edges, which are different from the well-known discritizations such as the classical finite element method. Through choosing suitable "interface" and appropriate primal constraints with complex coefficients and introducing some local techniques, we developed a two-level adaptive BDDC algorithm for the PWLS discretization, and the condition number of the preconditioned system is proved to be bounded above by a user-defined tolerance and a constant which is only dependent on the maximum number of interfaces per subdomain. A multilevel algorithm is also attempted to resolve the bottleneck in large scale coarse problem. Numerical results are carried out to confirm the theoretical results and illustrate the efficiency of the proposed algorithms.

math.NA↗