Orbital and Field Angular Momentum in the Nucleon

The nucleon spin problem raises experimental and theoretical questions regarding the contribution of the orbital angular momentum of the quarks to the total spin of the nucleon. In this article we examine the commutation relationships of various operators that contribute to the total angular momentum of the nucleon. We find that the sum of the orbital plus gluon field angular momenta should satisfy the angular momentum commutators, at least up to the one-loop level. This, requirement on the sum of these operators imposes a non-trivial restriction on the form of the color electric and magnetic fields. This is similar to the magnetic monopole/electric charge system where it is only the sum of the orbital plus field angular momentum that satisfies the correct commutation relationships.     

Spin matrices for gravitons and the humblet decomposition of the angular momentum of gravitational radiation in the linearized theory

We develop spin matrices for a classical gravitational field in the linearized theory which satisfy angular-momentum commutation relations and are appropriate for a spin angular momentum of two. The same spin matrices come out of a decomposition of the angular momentum density of the linearized gravitational field into orbital and spin parts, similar to that carried out by Humblet for the electromagnetic field. To achieve this decomposition, we use the momentum density for the gravitational field obtained from the Landau-Lifshitz pseudo-tensor in the weak gravity limit. We note a formal connection between the spin angular momenta of gravitational and electromagnetic fields using the Kaluza-Klein idea.     

Spin-orbit interaction and evolution of optical eddies in perturbed weakly directing optical fibers

The transformation of the angular momentum of an optical eddy in a weakly directing perturbed optical fiber is analyzed within the spin-orbit operator representation. The case of fibers with anisotropy of the core and cladding materials and the case of fibers with an elliptic cross section are considered. The spectrum of polarization corrections to the scalar propagation constant is determined for fibers of two types. For both the strongly anisotropic and elliptic fibers, the spin angular momentum of the linearly polarized LV eddy is suppressed and the orbital angular momentum is characterized by simple oscillations with a beating length dependent only on the spin-orbit parameter of an unperturbed fiber. The orbital and spin angular momenta of the circularly polarized CV eddy in the anisotropic fiber interchange in the elliptic fiber. The orbital angular momentum can be completely restored in the strongly anisotropic fiber, whereas only the spin angular momentum is completely restored in the elliptic fiber.     

Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms

We report on the generation of light carrying orbital angular momentum through Bragg diffraction into an electromagnetically induced coherence grating in a degenerate two-level system of cold cesium atoms. The induced Zeeman coherence grating is shown to contain the spatial phase structure of the incident beams. The exchange of phase information between a light beam with orbital angular momentum and a long-lived atomic coherence opens up the way to process quantum information encoded in a multidimensional state space.     

Spatial mode properties of plasmon-assisted transmission

Orbital angular momentum of photons is explored to study the spatial mode properties of the plasmon-assisted transmission process. We found that photons carrying different orbital angular momenta have different transmission efficiencies, while the coherence between these spatial modes can be preserved.     

Hall effect of light

We derive the semiclassical equation of motion for the wave packet of light taking into account the Berry curvature in momentum-space. This equation naturally describes the interplay between orbital and spin angular momenta, i.e., the conservation of the total angular momentum of light. This leads to the shift of wave-packet motion perpendicular to the gradient of the dielectric constant, i.e., the polarization-dependent Hall effect of light. An enhancement of this effect in photonic crystals is also proposed.     

Spin dynamics of a vortical condensate of exciton polaritons in a GaAs microcavity

The temporal dynamics of a spinor exciton-polariton condensate in a high-quality anisotropic GaAs microcavity under pulsed resonant excitation with light possessing a nonzero orbital angular momentum is investigated. The phenomenon of spatial separation of the spin components of the polariton condensate upon pumping with a coherent superposition of two beams with opposite circular polarizations and orbital angular momenta is observed. The key factors for the observation of this effect are the lateral anisotropy of the microcavity that causes a splitting between the linear components of the polariton ground state and the occurrence of opposite orbital angular momenta for the two spin components of the condensate. The experimental results are in qualitative agreement with the theoretical model of the phenomenon developed in JETP Lett. 104, 827 (2016).     

Spin-to-orbital angular momentum conversion in spin Hall effect of light

From the viewpoint of classical electrodynamics, we identify the role of spin-to-orbital angular momentum conversion in spin Hall effect (SHE) of light. We introduce a distinct separation between spin and orbital angular momenta to clarify the spin–orbital interaction in conventional beam refraction. We demonstrate that the refractive index gradient can enhance or suppress the spin-to-orbital angular momentum conversion, and thus can control the SHE of light. We suggest that the metamaterial whose refractive index can be tailored arbitrarily may become a good candidate for amplifying or eliminating the SHE of light, and by properly facilitating the spin-to-orbital angular momentum conversion the SHE may be enhanced dramatically. The transverse spatial shifts governed by the spin-to-orbital angular momentum conversion, provide us a clear physical picture to clarify the role of refractive index gradient in the SHE of light. These findings provide a pathway for modulating the SHE of light and can be extrapolated to other physical systems.     

On the experimental value of the intrinsic angular momentum of the A-phase of superfluid helium-3

A simple relation between the equilibrium spin and orbital angular momenta of the superfluid phases of helium-3 close to T_c has been obtained. The intrinsic angular momentum of the A-phase has been found from the existing experimental data using this relation.     

Gauge-Invariant Spin and Orbital Angular Momentum of Laguerre--Gaussian Laser

We adopt a gauge-invariant definition to calculate the spin and orbital angular momenta of a so-called Ith order Laguerre-Gaussian laser. The results reveal that photons on the axis of the beam may carry an orbital angular momentum of （l - 1）h besides lh per photon. For the spin, we obtain a more reasonable expression proportional to the beam intensity instead of the gradient of the intensity as previously derived. We also discuss how to experimentally discriminate the angular momentum expressions given here and those commonly accepted in the literature.     

Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner

We use a Laguerre-Gaussian laser mode within an optical tweezers arrangement to demonstrate the transfer of the orbital angular momentum of a laser mode to a trapped particle. The particle is optically confined in three dimensions and can be made to rotate; thus the apparatus is an optical spanner. We show that the spin angular momentum of +/-?per photon associated with circularly polarized light can add to, or subtract from, the orbital angular momentum to give a total angular momentum. The observed cancellation of the spin and orbital angular momentum shows that, as predicted, a Laguerre-Gaussian mode with an azimuthal mode index l=1 has a well-defined orbital angular momentum corresponding to ? per photon.     

Origin of orbital ferromagnetism and giant magnetic anisotropy at the nanoscale

The origin of orbital magnetism recently observed in different nanostructured films and particles is discussed as a consequence of spin-orbit coupling. It is shown that contact potentials induced at the thin film surface by broken symmetries, as domain boundaries in self-assembled monolayers, lead to orbital states that in some cases are of large radius. The component of the angular momentum normal to the surface can reach very high values that decrease the total energy by decreasing spin-orbit interaction energy. Intraorbital ferromagnetic spin correlations induce orbital momenta alignment. The estimated values of the magnetic moments per atom are in good agreement with the experimental observations in thiol capped gold films and nanoparticles.     

光子的动量矩

在动量表象中光子的波函数是满足横波条件的矢量函数Ａ（ｋ），由于横波条件的限制，光子量轨道动量自旋动量矩不再具有直接的物理意义，真正有物理意义的是光子的总动量矩，动量矩具有确定值的光子态可分为两类，分别有相反的宇称。     

Orbital angular momentum and nonparaxial light beams

The simple relationship between total angular momentum and energy and the seemingly natural separation of the angular momentum into spin and orbital components in the paraxial approximation, are investigated for a general nonparaxial form of monochromatic beam with near cylindrical symmetry.     

A simple analytical model of the angular momentum transformation in strongly focused light beams

A ray-optics model is proposed to describe the vector beam transformation in a strongly focusing optical system. In contrast to usual approaches based on the focused field distribution near the focal plane, we use the beam pattern formed immediately after the exit aperture. In this cross section, details of the output field distribution are of minor physical interest but proper allowance is made for transformation of the beam polarization state. This enables the spin and orbital angular momentum representations to be obtained, which are valid for any cross section of the transformed beam. Simple analytical results are available for a transversely homogeneous, circularly polarized incident beam confined by a circular aperture. Variations of the spin and orbital angular momenta of the output beam with change of the focusing strength are analyzed. The analytical results are in good qualitative and reasonable quantitative agreement with the results of numerical calculations performed for the Gaussian and Laguerre-Gaussian beams. The model supplies an efficient and physically transparent means for qualitative analysis of the spin-to-orbital angular momentum conversion. It can be generalized to incident beams with complex spatial and polarization structure.     

标量算符本征值对g壳层LSQ耦合态的完全分类计算

按（Ｕ,Ｄ）Ｌ－ＬＳＱ格式构造ｌ壳层ＬＳＱ耦合态,这里Ｕ（Ｄ）是自旋向上（向下）电子的轨道角动量,Ｌ、Ｓ、Ｑ是总轨道角动量、总自旋和准旋。由４个产生－湮灭算符构造与轨道、自旋准旋算符均为易的标量算符并用基本征值对ＬＳＱ耦合态进上步分类,实现了对ｆ、ｇ壳层耦合态的完全分类,列出了ｇ壳层耦合态完全分类的主要结果。     

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

Effect of relativistic many-electron interactions on photoelectron partial wave probabilities

We obtain relative cross sections for the production of photoelectrons with specific angular momentum quantum numbers. These cross sections are obtained from the polarization analysis of the visible fluorescence of ions produced when circularly polarized vacuum ultraviolet radiation photoionizes ground state Ar. The ratio of cross sections for the production of photoelectrons with the same orbital angular momentum but different total angular momenta shows strong deviations from the statistical ratio, demonstrating the importance of relativistic interactions in many-electron photoionization dynamics.     

Remarks on the signs of g factors in atomic and molecular Zeeman spectroscopy

This paper draws attention to the advantages that would be obtained by adopting a new convention for the sign of g factors that would make the g factor for electron spin a negative quantity (g ≈ ?2), rather than a positive quantity as generally adopted at present. The editors are aware that the proposal made in this paper concerning the conventional sign of the g factor for electron spin will be seen by some readers as controversial. We have nonetheless agreed to publish this paper in the hope that it will stimulate discussion. The editors would welcome comments on this proposal in the form of short papers, which they will then be happy to consider for publication together at a later date.

Various magnetic moments, associated with rotational, vibrational, nuclear spin, electron orbital and electron spin angular momenta, can contribute to the Zeeman effect in atoms and molecules. They are considered in this paper in the context of the effective Hamiltonian where relativistic and other corrections as well as the effects of mixing with other electronic states are absorbed in appropriate g factors. In spherically symmetric systems, the magnetic dipole moment arising from a specific angular momentum can be written as the product of three factors: the nuclear or Bohr magneton (which is positive), the g factor (which may be positive or negative), and the corresponding angular momentum (which is a vector). A convention is discussed, in which the sign of the g factor is positive when the dipole moment is parallel to its angular momentum and negative when it is antiparallel. This would have the advantage that it could be applied consistently in any situation. Such a choice would require the g factors for the electron orbital and electron spin angular momenta to be negative. This concept can easily be extended to the case of a general molecule where the relation between the dipole and angular momentum vectors has tensorial character.