Berry's Phase in the Coherent Excitation of Atoms

Abstract

The adiabatic variation of a Hamiltonian can cause the wavefunction, governed by the Hamiltonian, to acquire an unexpected phase. The existence of this phase (Berry's phase) is an additional element in the well-known quantum adiabatic theorem. Berry's phase is observable in the interference between two identically prepared systems only one of which is adiabatically varied. We show that a single quantum system prepared in a superposition of the eigenstates of its Hamiltonian leads to observable Berry phase effects at all times. We examine this principle within the context of two-level optical resonance.     

The pancharatnam and the berry phases in three-level photonic systems

Abstract

A theoretical analysis of Pancharatnam and Berry phases is made for biphoton three-level systems, which are produced via frequency degenerate collinear spontaneous parametric down conversion (SPDC). The general theory of Pancharatnam phases is discussed with a special emphasis on geodesic ‘curves' in Hilbert space. Explicit expressions for Pancharatnam, dynamic and geometric phases are derived for the transformations produced by linear phase converters. The problem of gauge invariance is treated in this article.     

Pulse-shape Effects in Intense-field Laser Excitation of Atoms

A time-development operator technique is used to describe the intense-field excitation of three-level atomic systems by laser pulses of arbitrary shape. The pulses are divided into small elements for which the time-development is described using the first term in the Magnus expansion. The effects of pulse shapes, detunings, atomic decays and Doppler widths can be included in the analysis. We demonstrate the sensitivity of the dressed three-level atom state populations, Rabi oscillations, population trapping and Autler-Townes splittings on laser pulse shapes.     

Prediction of Young's modulus of particulate two phase composites

Abstract

A new approach for predicting the Young's modulus of two phase composites has been proposed based on a topological transformation and the mean field theory. The new approach has been applied to Co/WC_p,Al/SiC_p, and glass filled epoxy composites. It is shown that the new theoretical predictions are well within the Hashin and Shtrikman lower and upper bounds (the HS bounds) and are in closer agreement with the experimental results for the corresponding composite systems than both the HS bounds and the predictions of the mean field theory. An advantage of the present approach over other continuum approaches is that it can predict not only the effect of volume fraction of the reinforcing phase, but also the effects of microstructural parameters such as grain shape and phase distribution on the stiffness of composites. It is also shown that the classical linear law of mixtures is a specific case (where the reinforcing phase is continuous and perfectly aligned) of the present approach. In contrast to the classical linear law of mixtures, the present approach can be applied to a two phase composite having any volume fraction, grain shape, and phase distribution. It is shown that in a particulate composite having a given volume fraction of reinforcement, the Young's modulus of the composite increases with increasing contiguity of the constituent phases and this increment is dependent on the stiffness ratio of the constituent phases. Furthermore, the present approach can provide a simple and effective solution to the problem of interaction between particles of the same phase.

MST/1587     

考虑泊松效应的材料/结构一体化设计方法

为实现含有不同泊松比组分复合材料的优化设计,并考虑宏观结构及复杂的边界条件,提出了考虑泊松效应的材料/结构一体化设计方法,其显著特征在于不同组分材料中引入了泊松比插值,假设宏观结构由周期性排列的复合材料组成,复合材料含两种各向同性且泊松比不同的组分材料,以静态问题中柔顺度最小化或动态问题中特征值最大化为目标以及宏微观体积比为约束建立了拓扑优化模型。采用均匀化理论预测了复合材料等效性能,推导了目标函数对宏微观密度变量的敏度表达式。分别采用密度过滤和敏度过滤来消除宏微观拓扑优化中的不稳定性现象。采用优化准则法分别更新宏观、微观密度变量,考察了微观体积比和组分材料泊松比参数对优化结果的影响。三维数值算例结果表明所提出的一体化方法具有可行性和优越性。     

Criteria for Realizing Room-Temperature Electrical Transport Applications of Topological Materials

The unusual electronic states found in topological materials can enable a new generation of devices and technologies, yet a long-standing challenge has been finding materials without deleterious parallel bulk conduction. This can arise either from defects or thermally activated carriers. Here, the criteria that materials need to meet to realize transport properties dominated by the topological states, a necessity for a topological device, are clarified. This is demonstrated for 3D topological insulators, 3D Dirac materials, and 1D quantum anomalous Hall insulators, though this can be applied to similar systems. The key parameters are electronic bandgap, dielectric constant, and carrier effective mass, which dictate under what circumstances (defect density, temperature, etc.) the unwanted bulk state will conduct in parallel to the topological states. As these are fundamentally determined by the basic atomic properties, simple chemical arguments can be used to navigate the phase space to ultimately find improved materials. This will enable rapid identification of new systems with improved properties, which is crucial to designing new material systems and push a new generation of topological technologies.     

Topological mechanical metamaterials: A brief review

Topological mechanical metamaterials have emerged with the development of topological phases and topological phase transitions in modern condensed matter physics. Their attractive topological properties provide promising applications that are hard to achieve with traditional mechanical metamaterials, such as waveguiding without backscattering loss, vibration isolation, and free motion of structures. In this review, we briefly retrospectively examine the most flourishing works on topological mechanical metamaterials and identify the mechanisms underlying these topological mechanical phases, such as analogs to quantum Hall effects and Weyl semimetals. Topological mechanical phases are classified into two categories of t depending on their behavior when working in different frequency domains, as finite frequency properties (ω ≠ 0) are related to elastic wave propagation and zero frequency properties (ω = 0) are related to quasi-static free motion. We conclude by outlining future challenges and opportunities for the topological mechanism, and the design/fabrication and application of topological mechanical metamaterials.     

Time Evolution for a Three-level Atom in Interaction with Two Modes

Abstract

The problem of a three-level atom and two modes is treated quantum mechanically and constants of motion are obtained. The evolution operator is calculated for the case of exact two-photon resonance. The probability distribution functions are calculated for the atom in one of its states. Some statistical quantities of the fields and the atomic systems are given. The interaction with squeezed light is investigated.     

A simple demonstration of the Pancharatnam phase as a geometric phase

Abstract

To demonstrate the Pancharatnam phase as a geometric (Berry's) phase, each polarization state must be obtained by projecting the previous state on it. We describe a simple interferometric arrangement for such a demonstration which only uses a single rotation linear analyser to introduce a continuously variable phase difference between the two beams.     

Topological characterization of the Bi-Ge-Te phase diagram

The available phase-diagram data for the Bi-Ge-Te, Ge-Te, Bi-Te, and Ge-Bi systems are critically evaluated. A topological image of the Bi-Ge-Te phase diagram is constructed in the form of a graph, with the nodes representing distinct phases and edges representing two-phase mixtures, ordered with respect to temperature. The proposed topological approach is used to construct isothermal sections, the liquidus surface of the ternary system, andT-x sections.     

The dynamics of three-mode coupling in a trapped Bose gas

ABSTRACT

Multiple mode couplings in topological coherent modes of Bose–Einstein condensate are considered, by introducing an external alternating (resonating) field in the system. This analysis is based on the analytical solutions of nonlinear Gross–Pitaevskii equation for a trapped Bose gas at nearly absolute zero temperature. The dynamics of fractional populations of the generated coherent modes are analysed, particularly for a three-level system in the limit of small to large detuning of the intermediate state. These coupled topological modes, though nonlinear, are analogous to a resonant atom and exhibit a variety of significant non-trivial phenomena (effects), like: dynamic phase transitions, interference patterns, critical phenomena, mode-locking and chaotic motion.     

A short guide to topological terms in the effective theories of condensed matter

Abstract

This article is meant as a gentle introduction to the topological terms that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples, mainly from the area of quantum magnetism and superfluids/superconductors. We then briefly discuss how these ideas are now finding incarnations in the studies of symmetry-protected topological phases, which are in a sense a generalization of the concept of topological insulators to a wider range of materials, including magnets and cold atoms.     

基于地域文化符号的列车涂装设计研究

目的 探究基于地域文化符号的列车涂装设计方法与理论。方法 对列车涂装设计概念,列车涂装设计与地域文化的关联、地域文化符号的构成、罗兰.巴特文化符码理论、杨裕富设计文化符码说进行了分析和探讨;提出了列车涂装设计三层次结构模型、设计文化符码转换及应用思路;设计实验了基于地域文化符号的宁波市域列车涂装设计方案。结果 验证了设计文化符码三层次模型、设计文化符码转换及应用思路对地域文化符号在列车涂装设计中的应用有效性和可行性。结论 地域文化符号融入列车涂装设计中,可以体现地域文化特色,传达地域文化内涵、塑造地域文化意象;通过设计文化符码三层次结构模型能够为列车涂装设计提供分析工具和设计方法,实现列车涂装的创意定位、意义传达和设计表现。     

Mechanical Analogue of a Majorana Bound State

The discovery of topologically nontrivial electronic systems has opened a new age in condensed matter research. From topological insulators to topological superconductors and Weyl semimetals, it is now understood that some of the most remarkable and robust phases in electronic systems (e.g., quantum Hall or anomalous quantum Hall) are the result of topological protection. These powerful ideas have recently begun to be explored also in bosonic systems. Topologically protected acoustic, mechanical, and optical edge states have been demonstrated in a number of systems that recreate the requisite topological conditions. Such states that propagate without backscattering could find important applications in communications and energy technologies. Here, a topologically bound mechanical state, a different class of nonpropagating protected state that cannot be destroyed by local perturbations, is demonstrated. It is in particular a mechanical analogue of the well‐known Majorana bound states (MBSs) of electronic topological superconductor systems. The topological binding is implemented by creating a Kekulé distortion vortex on a 2D mechanical honeycomb superlattice that can be mapped to a magnetic flux vortex in a topological superconductor.     

Local environmental geometry of atoms in the Lennard-Jones systems

The distributions of topological and metrical characteristics of the Voronoi polyhedra have been obtained for the Lennard-Jones systems of atoms modelling a crystal, a liquid and a fluid. The distributions of the number of faces, the number of edges per face, the number of pentagonal faces, the histograms of topological types, the radial distributions of the Voronoi polyhedron neighbours, the distribution of edge lengths, face areas and the sphericity factor have been investigated for the Voronoi polyhedra. The local atomic structure is discussed for various phase states and various temperatures and densities. The importance is noted of a simultaneous analysis of topological and metrical characteristics of the Voronoi polyhedra.     

Quantifying Gains Using the Capabilities‐Based Test and Evaluation Method

Today's military operating environments are more operationally diverse and technically challenging. Fielding relevant weapons systems to meet the demands of this environment is increasingly difficult, prompting policy shifts that mandate a focus on systems capable of combating a wide threat range. The capabilities‐based test and evaluation construct is the Department of the Navy's effort to concentrate on integrated system design with the objective of satisfying a particular operational response (capability) under a robust range of operating conditions. One aspect of capabilities‐based test and evaluation is the increased employment of advanced mathematical and statistical techniques in the test and evaluation (T&E) process. This case study illustrates advantages of incorporating these invaluable techniques, like design of experiments and modeling and simulation, within the T&E process. We found through statistical analysis that the application of design of experiment concepts to the System Under Test throughout three primary phases of T&E quantifiably improved the accomplishment of the selected response variable of interest. Copyright © 2012 John Wiley & Sons, Ltd.     

A multi-phase model for product part change problems

The parts of a product may be changed over the product life cycle for the purpose of enhancing profits, that is to say, product part change has a direct impact on production efficiency and customer satisfaction. The analysis of product part change can provide producers with related components/part suppliers by analysing the product's configuration. Before performing the physical assembly of a specific product, selected part suppliers are connected and have to verify their ability to assemble. This paper proposes an assessment model consisting of three major phases: (1) analysis of the assembly relationship among the parts; (2) preliminary selection of the appropriate parts and their suppliers; and (3) solution selection for supplier association. The proposed model solves the product part change problem for a given related quality level, operation and cost data. The liaison graph, fuzzy theory and value engineering approaches are employed in phases 1 and 2 to analyse the product's configuration and assembly relationships, to deal with production data and to carry out the preliminary analysis. To solve the solution selection model of phase 3, a genetic algorithm based heuristic approach was developed. Finally, the configuration of the stand module of TFT-LCD is used as an example to demonstrate the application and working of the proposed approach. The results of the illustrated example are used to demonstrate its efficiency and effectiveness in solving the part change problem.     

Structure and tribological property of B2-based approximants

The present paper is concerned with a special group of approximants with B2 superstructures. In the first part, recent work on structural features of the B2 superstructure approximants is summarized. Experimental results obtained in Al-Cu-Mn and Al-Cu systems are presented, where a series of B2-based approximants are observed. These phases all have similar valence electron concentrations, in full support of thee/a-constant definition of approximants. Special emphasis is laid on the chemical twinning modes of the B2 basic structure in relation to the Al-Cu approximants. It is revealed that the B2 twinning mode responsible for the formation of local pentagonal atomic arrangements is of 180°/[111] type. This is also the origin of 5-fold twinning of the B2 phase on quasicrystal surfaces. Crystallographic features of phases B2, τ2, τ3,γ, and other newly discovered phases are also discussed. In all these phases, local pentagonal configurations are revealed. In the second part, dry tribological properties of some AlCuFe samples containing the B2-type phases are presented. The results indicated that the B2 phase having their valence ratio near that of the quasicrystal possesses low friction coefficient under various loads, comparable with the annealed quasicrystalline ingot. Such a result indicates that the B2-type phase withe/a near that of quasicrystal is indeed an approximant, which is in full support of the valence electron criterion for approximants.     

Alloying Behaviour and Atomic Size Effect in Palladium-rich Pd-RE Systems

The alloying behaviour, including solid solubilities of rare-earths as well as the formation and stability of various intermediate phases in palladium-rich Pd-RE systems were studied by means of the atomic size factor and the reduced transition temperatures. A strong analogy is observed in the plots of the reduced transition temperatures of various intermediate phases against the atomic numbers of rare-earths, and the law proposed by Hume-Rothery and Raynor for dependence of liquidus temperature on atomic radius in simple alloy systems has been extended to more complicated alloy systems.