Electrical Detection of Magnetization Dynamics via Spin Rectification Effects

The purpose of this article is to review the current status of a frontier in dynamic spintronics and contemporary magnetism, in which much progress has been made in the past decade, based on the creation of a variety of micro- and nano-structured devices that enable electrical detection of magnetization dynamics. The primary focus is on the physics of spin rectification effects, which are well suited for studying magnetization dynamics and spin transport in a variety of magnetic materials and spintronic devices. Intended to be intelligible to a broad audience, the paper begins with a pedagogical introduction, comparing the methods of electrical detection of charge and spin dynamics in semiconductors and magnetic materials respectively. After that it provides a comprehensive account of the theoretical study of both the angular dependence and line shape of electrically detected ferromagnetic resonance (FMR), which is summarized in a handbook formate easy to be used for analyzing experimental data. We then review and examine the similarity and differences of various spin rectification effects found in ferromagnetic films, magnetic bilayers and magnetic tunnel junctions, including a discussion of how to properly distinguish spin rectification from the spin pumping/inverse spin Hall effect generated voltage. After this we review the broad applications of rectification effects for studying spin waves, nonlinear dynamics, domain wall dynamics, spin current, and microwave imaging. We also discuss spin rectification in ferromagnetic semiconductors. The paper concludes with both historical and future perspectives, by summarizing and comparing three generations of FMR spectroscopy which have been developed for studying magnetization dynamics.Comment: Review article submitted to Physics Reports. 75 pages, 37 figure

Criterion of Local Unitary Equivalence for Multipartite States

We study the local unitary equivalence of arbitrary dimensional multipartite quantum mixed states. We present a necessary and sufficient criterion of the local unitary equivalence for general multipartite states based on matrix realignment. The criterion is shown to be operational even for particularly degenerated states by detailed examples. Besides, explicit expressions of the local unitary operators are constructed for locally equivalent states. In complement to the criterion, an alternative approach based on partial transposition of matrices is also given, which makes the criterion more effective in dealing with generally degenerated mixed states.Comment: 12page

Identification of three-qubit entanglement

We present a way of identifying all kinds of entanglement for three-qubit pure states in terms of the expectation values of Pauli operators. The necessary and sufficient conditions to classify the fully separable, biseparable, and genuine entangled states are explicitly given. The approach can be generalized to multipartite high-dimensional cases. For three-qubit mixed states, we propose two kinds of inequalities in terms of the expectation values of complementary observables. One inequality has advantages in entanglement detection of the quantum state with positive partial transpositions, and the other is able to detect genuine entanglement. The results give an effective method for experimental entanglement identification.Comment: 5 pages, 2 figure

Entanglement Detection and Distillation for Arbitrary Bipartite Systems

We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability.Comment: 11 page

Dependence of Intensities of Major Geomagnetic Storms (Dst ≤\le -100 nT) on Associated Solar Wind Parameters

A geomagnetic storm is the result of sustained interaction between solar wind with a southward magnetic field and the magnetosphere. To investigate the influence of various solar wind parameters on the intensity of major geomagnetic storm, 67 major geomagnetic storms that occurred between 1998 and 2006 were used to calculate the correlation coefficients (CCs) between the intensities of major geomagnetic storms and the time integrals of southward interplanetary magnetic field $B_s$, solar wind electric field ($E_y$) and injection function (Q) during the main phase of the associated geomagnetic storms. SYM-H$_{min}$ was used to indicate the intensity of the associated major geomagnetic storm, while I($B_z$), I($E_y$) and I(Q) were used to indicate the time integrals of $B_z$, $E_y$ and Q during the main phase of associated major geomagnetic storm respectively. The derived CC between I($B_z$) and SYM-H$_{min}$ is 0.33, while the CC between I($E_y$) and SYM-H$_{min}$ is 0.57 and the CC between I(Q) and SYM-H$_{min}$ is 0.86. The results provide statistical evidence that solar wind dynamic pressure or solar wind density plays a significant role in transferring solar wind energy into the magnetosphere, in addition to the southward magnetic field and solar wind speed. Solar wind that has a strong geoeffectiveness requires solar wind dynamic pressure $>$3 nPa or solar wind density $>3$ nPa$/V_{sw}^2$. Large and long duration $B_s$ alone cannot ensure a major geomagnetic storm, especially if the solar wind dynamic pressure is very low, as large and long duration Bs is not a full condition, only a necessary condition to trigger a major geomagnetic storm

Local unitary invariants for multipartite states

We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For multipartite mixed states, we propose a set of invariants in terms of the trace of coefficient matrices. For full ranked mixed states with nondegenerate eigenvalues, this set of invariants is also the necessary and sufficient conditions for the local unitary equivalence of such two states.Comment: 8 page

Sum uncertainty relations based on Wigner-Yanase skew information

We study sum uncertainty relations for arbitrary finite $N$ quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented.Comment: 12 pages, 1 figur

Estimation on geometric measure of quantum coherence

We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states -- maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.Comment: 13 pages, 1 figur

Dynamics and entanglement of a membrane-in-the-middle optomechanical system in the extremely-large-amplitude regime

The study of optomechanical systems has attracted much attention, most of which are concentrated in the physics in the small-amplitude regime. While in this article, we focus on optomechanics in the extremely-large-amplitude regime and consider both classical and quantum dynamics. Firstly, we study classical dynamics in a membrane-in-the-middle optomechanical system in which a partially reflecting and flexible membrane is suspended inside an optical cavity. We show that the membrane can present self-sustained oscillations with limit cycles in the shape of sawtooth-edged ellipses and exhibit dynamical multistability. Then, we study the dynamics of the quantum fluctuations around the classical orbits. By using the logarithmic negativity, we calculate the evolution of the quantum entanglement between the optical cavity mode and the membrane during the mechanical oscillation. We show that there is some synchronism between the classical dynamical process and the evolution of the quantum entanglement.Comment: 9 pages, 7 figures. To appear in Sci China-Phys Mech Astro

Texture Mixing by Interpolating Deep Statistics via Gaussian Models

Recently, enthusiastic studies have devoted to texture synthesis using deep neural networks, because these networks excel at handling complex patterns in images. In these models, second-order statistics, such as Gram matrix, are used to describe textures. Despite the fact that these model have achieved promising results, the structure of their parametric space is still unclear, consequently, it is difficult to use them to mix textures. This paper addresses the texture mixing problem by using a Gaussian scheme to interpolate deep statistics computed from deep neural networks. More precisely, we first reveal that the statistics used in existing deep models can be unified using a stationary Gaussian scheme. We then present a novel algorithm to mix these statistics by interpolating between Gaussian models using optimal transport. We further apply our scheme to Neural Style Transfer, where we can create mixed styles. The experiments demonstrate that our method can achieve state-of-the-art results. Because all the computations are implemented in closed forms, our mixing algorithm adds only negligible time to the original texture synthesis procedure