Properties of spin and orbital angular momenta of light

2021 ◽  
Vol 36 (26) ◽  
Author(s):  
Arvind ◽  
S. Chaturvedi ◽  
N. Mukunda
Keyword(s):  
Angular Momentum ◽  
Physical Properties ◽  
Degree Of Freedom ◽  
Polarization Degree ◽  
Quantum Mechanical ◽  
Light Fields ◽  
Spin Part ◽  
Full Account ◽  
Angular Momenta ◽  
Definition Of

This paper analyses the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre–Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.

TRANSFORMATION AMPLITUDES FOR VECTOR ADDITION OF ANGULAR MOMENTUM; (j3mm′|j3JM)

1952 ◽  
Vol 30 (3) ◽  
pp. 253-256 ◽  
Author(s):  
G. S. Colladay ◽  
R. E. Sells ◽  
D. L. Falkoff
Keyword(s):  
Angular Momentum ◽  
Quantum Mechanical ◽  
Angular Momenta ◽  
Vector Addition

The transformation amplitudes for the quantum-mechanical vector addition of angular momenta, [Formula: see text] are given.

scholarly journals Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics

2021 ◽  
Vol 57 (5) ◽  
Author(s):  
Enrico Speranza ◽  
Nora Weickgenannt
Keyword(s):  
Angular Momentum ◽  
Invariant Operator ◽  
Spin Tensor ◽  
Spin Part ◽  
Gauge Transformations ◽  
Nuclear Collisions ◽  
Relativistic Treatment ◽  
Relativistic Nuclear Collisions ◽  
Definition Of ◽  
Cartan Theory

AbstractThe relativistic treatment of spin is a fundamental subject which has an old history. In various physical contexts it is necessary to separate the relativistic total angular momentum into an orbital and spin contribution. However, such decomposition is affected by ambiguities since one can always redefine the orbital and spin part through the so-called pseudo-gauge transformations. We analyze this problem in detail by discussing the most common choices of energy-momentum and spin tensors with an emphasis on their physical implications, and study the spin vector which is a pseudo-gauge invariant operator. We review the angular momentum decomposition as a crucial ingredient for the formulation of relativistic spin hydrodynamics and quantum kinetic theory with a focus on relativistic nuclear collisions, where spin physics has recently attracted significant attention. Furthermore, we point out the connection between pseudo-gauge transformations and the different definitions of the relativistic center of inertia. Finally, we consider the Einstein–Cartan theory, an extension of conventional general relativity, which allows for a natural definition of the spin tensor.

scholarly journals Experimental demonstration of efficient high-dimensional quantum gates with orbital angular momentum

2021 ◽  
Author(s):  
Yunlong Wang ◽  
Shihao Ru ◽  
Feiran Wang ◽  
Pei Zhang ◽  
Fu-Li Li
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Degree Of Freedom ◽  
Quantum Gates ◽  
Polarization Degree ◽  
High Dimensional ◽  
Single Photons ◽  
Two Level Systems

Abstract Quantum gates are essential for the realization of quantum computer and have been implemented in various types of two-level systems. However, high-dimensional quantum gates are rarely investigated both theoretically and experimentally even that high-dimensional quantum systems exhibit remarkable advantages over two-level systems for some quantum information and quantum computing tasks. Here we experimentally demonstrate the four-dimensional X gate and its unique higher orders with the average conversion efficiency 93\%. All these gates are based on orbital-angular-momentum degree of freedom of single photons. Besides, a set of controlled quantum gates is implemented by use of polarization degree of freedom. Our work is an important step towards the goal of achieving arbitrary high-dimensional quantum circuit and paves a way for the implementation of high-dimensional quantum communication and computation.

Electron Spin and General Angular Momenta

2020 ◽  
pp. 356-376
Author(s):  
Jochen Autschbach
Keyword(s):  
Angular Momentum ◽  
Electron Spin ◽  
Open Shell ◽  
Historical Background ◽  
Ladder Operators ◽  
Spin Orbital ◽  
Angular Momenta ◽  
Pauli Matrices ◽  
Spin Singlet ◽  
Definition Of

The historical background of the discovery of the electron spin is provided. The Stern-Gerlach and Einstein-de Haas experiments are discussed. The operators for a single electron spin are defined, along with the formulation in terms of the 2x2 Pauli matrices. The discussion then moves on to the definition of the spin for many-electron systems and explains how the famous Hund rule (or Hund’s first rule) arises from considering the energy of an open-shell spin singlet vs. triplet state. Next, the generalized angular momentum, ladder operators, and spherical vector operators are defined, and the rules for the addition of angular momenta are derived. The chapter concludes with a discussion of the total spin, orbital, and total angular momentum for open-shell atoms, term symbols, and Hund’s second and third rule.

scholarly journals Generation of concentric perfect Poincaré beams

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Zhongzheng Gu ◽  
Da Yin ◽  
Fengyan Gu ◽  
Yanran Zhang ◽  
Shouping Nie ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Optical Communication ◽  
High Order ◽  
Degree Of Freedom ◽  
Phase Mask ◽  
Polarization Degree ◽  
Poincaré Sphere ◽  
Ring Radius ◽  
Poincare Sphere

Abstract We theoretically propose and experimentally verify a method to generate new polycyclic beams, namely concentric perfect Poincaré beams (CPPBs), by using an encoded annular phase mask. The proposed beams consisting of multiple polarization structured fields can be simultaneously generated in one concentric mode, which are respectively mapped by fundamental Poincaré sphere (PS), high-order Poincaré sphere (HOPS), and hybrid-order Poincaré sphere (HyPS). Moreover, the ring radius, numbers and polarization orders of the CPPBs at arbitrary positions on arbitrary PS are independently controlled. This work enriches the mode distributions of perfect vortex and introduces a new polarization degree of freedom, which has the potential to implement more information beyond the orbital angular momentum multiplexing in optical communication.

scholarly journals Potential linear and angular momentum in the scalar diquark model

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
David Arturo Amor-Quiroz ◽  
Matthias Burkardt ◽  
William Focillon ◽  
Cédric Lorcé
Keyword(s):  
Angular Momentum ◽  
Transverse Momentum ◽  
Direct Calculation ◽  
Final State ◽  
Diquark Model ◽  
Scalar Diquark ◽  
Angular Momenta ◽  
The Difference ◽  
Definition Of ◽  
Quark Transverse Momentum

AbstractWe present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.

Transmission electron microscopy of composite materials

1988 ◽  
Vol 46 ◽  
pp. 1012-1015
Author(s):  
K.P.D. Lagerlof
Keyword(s):  
Composite Materials ◽  
Physical Properties ◽  
Structural Defects ◽  
Structural Composites ◽  
Multiphase Materials ◽  
Structural Reinforcement ◽  
Transmission Electron ◽  
Reinforced Fiber ◽  
Particulate Reinforced Composites ◽  
Definition Of

Although most materials contain more than one phase, and thus are multiphase materials, the definition of composite materials is commonly used to describe those materials containing more than one phase deliberately added to obtain certain desired physical properties. Composite materials are often classified according to their application, i.e. structural composites and electronic composites, but may also be classified according to the type of compounds making up the composite, i.e. metal/ceramic, ceramic/ceramie and metal/semiconductor composites. For structural composites it is also common to refer to the type of structural reinforcement; whisker-reinforced, fiber-reinforced, or particulate reinforced composites [1-4].For all types of composite materials, it is of fundamental importance to understand the relationship between the microstructure and the observed physical properties, and it is therefore vital to properly characterize the microstructure. The interfaces separating the different phases comprising the composite are of particular interest to understand. In structural composites the interface is often the weakest part, where fracture will nucleate, and in electronic composites structural defects at or near the interface will affect the critical electronic properties.

scholarly journals Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Yinghui Guo ◽  
Shicong Zhang ◽  
Mingbo Pu ◽  
Qiong He ◽  
Jinjin Jin ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Simultaneous Detection ◽  
Single Element ◽  
Single Shot ◽  
Single Spin ◽  
Dual Functional ◽  
Angular Momenta ◽  
Quadratic Phase ◽  
Mode Space ◽  
Optical Configuration

AbstractWith inherent orthogonality, both the spin angular momentum (SAM) and orbital angular momentum (OAM) of photons have been utilized to expand the dimensions of quantum information, optical communications, and information processing, wherein simultaneous detection of SAMs and OAMs with a single element and a single-shot measurement is highly anticipated. Here, a single azimuthal-quadratic phase metasurface-based photonic momentum transformation (PMT) is illustrated and utilized for vortex recognition. Since different vortices are converted into focusing patterns with distinct azimuthal coordinates on a transverse plane through PMT, OAMs within a large mode space can be determined through a single-shot measurement. Moreover, spin-controlled dual-functional PMTs are proposed for simultaneous SAM and OAM sorting, which is implemented by a single spin-decoupled metasurface that merges both the geometric phase and dynamic phase. Interestingly, our proposed method can detect vectorial vortices with both phase and polarization singularities, as well as superimposed vortices with a certain interval step. Experimental results obtained at several wavelengths in the visible band exhibit good agreement with the numerical modeling. With the merits of ultracompact device size, simple optical configuration, and prominent vortex recognition ability, our approach may underpin the development of integrated and high-dimensional optical and quantum systems.

scholarly journals Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Liang Sun ◽  
Zhizheng Ye ◽  
Fuwei Lu ◽  
Rongjiang Cui ◽  
Chuanyu Wu
Keyword(s):  
Degree Of Freedom ◽  
Adjacent Vertex ◽  
Topological Graph ◽  
Innovative Design ◽  
Kinematic Chains ◽  
Effectiveness And Efficiency ◽  
Definition Of ◽  
Specific Definition

AbstractIsomorphism detection is fundamental to the synthesis and innovative design of kinematic chains (KCs). The detection can be performed accurately by using the similarity of KCs. However, there are very few works on isomorphism detection based on the properties of similar vertices. In this paper, an ameliorated multi-order adjacent vertex assignment sequence (AMAVS) method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs. First, the specific definition of AMAVS is described. Through the calculation of the AMAVS, the adjacent vertex value sequence reflecting the uniqueness of the topology features is established. Based on the value sequence, all possible similar vertices, corresponding relations, and isomorphism discrimination can be realized. By checking the topological graph of KCs with a different number of links, the effectiveness and efficiency of the proposed method are verified. Finally, the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-DOF(degree of freedom) planar KCs.

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