Component Of Angular Momentum Research Articles

Polarization-Addressable Optical Movement of Plasmonic Nanoparticles and Hotspot Spin Vortices

Spin–orbit coupling in nanoscale optical fields leads to the emergence of a nontrivial spin angular momentum component, transverse to the orbital momentum. In this study, we initially investigate how this spin–orbit coupling effect influences the dynamics in gold monomers. We observe that localized surface plasmon resonance induces self-generated transverse spin, affecting the trajectory of the nanoparticles as a function of the incident polarization. Furthermore, we investigate the spin–orbit coupling in gold dimers. The resonant spin momentum distribution is characterized by the unique formation of vortex and anti-vortex spin angular momentum pairs on opposite surfaces of the nanoparticles, also affecting the particle motion. These findings hold promise for various fields, particularly for the precision control in the development of plasmonic thrusters and the development of metasurfaces and other helicity-controlled system aspects. They offer a method for the development of novel systems and applications in the realm of spin optics.

Spin-orbital angular momentum degeneracy breaking in nanoplasmonic metachain.

The spin and orbital angular momentum (namely SAM and OAM) mode division provides a promising solution to surmount exhausted available degrees of freedom in conventional optical communications. Nevertheless, SAM and OAM are often subjected to the degeneracy of total angular momentum (AM) because they both have integer variables of quantum eigenstates, which inevitably brings about the shortcomings specific to limited signal channels and multiplexing cross talk. Herein, we present a nanoplasmonic metachain that can discriminatively couple any input SAM and OAM components to an extrinsic orbital AM, corresponding to the chirality and topological charge of incident light. Importantly, the unambiguous measurement has a prominent advantage of detecting the arbitrary AM component rather than the total AM. The miniature metadevice offers the possibility of harnessing AM division on chip or in fiber and holds great promise to delve the spin-orbit interactions for topological photonics and quantum cryptography.

Wobbling motion for a triaxial rotor plus a single quasiparticle*

Abstract Wobbling motion in a system comprising a triaxial rotor and a single quasiparticle is studied employing the particle-rotor model. The energy spectra, wobbling frequencies, electromagnetic transition probabilities, g-factors, angular momentum components, spin coherent state maps, and static quadrupole moments are investigated. These investigations were conducted with regard to the Fermi surface transitioning from the lowest orbit to the highest one. As the Fermi surface increases, notable transformations occur in the wobbling mode. Initially, the mode exhibits a transverse revolution around the short axis of the nucleus. However, as the Fermi surface continues to increase, the mode gradually shifts to a longitudinal revolution around the intermediate axis. Eventually, it transitions to a transverse revolution around the long axis. Notably, the stability of the long axis transverse mode diminishes relative to its counterpart along the short axis as the total angular momentum increases at .

Vector Beams with Only Transverse Intensity at Focus

In this work, the tight focusing of vector beams with azimuthal polarization and beams with a V-line of polarization singularity (sector azimuthal polarization) was simulated numerically using the Richards–Wolf formulas. It was demonstrated that in a tight focus for these beams, there is no longitudinal component of the electric field. Previously, a similar effect was demonstrated for azimuthally polarized light only. The longitudinal component of the spin angular momentum for these beams was calculated, and the possibility of creating sector azimuthally polarized beams (beams with V-line singularities) using vector waveplates was demonstrated.

Wobbling Jets in Common Envelope Evolution

We find that the convective motion in the envelopes of red supergiant (RSG) stars supplies a non-negligible stochastic angular momentum to the mass that a secondary star accretes in a common envelope evolution (CEE), such that jets that the secondary star launches wobble. The orbital motion of the secondary star in a CEE and the density gradient in the envelope impose a nonzero angular momentum to the accreted mass with a constant direction parallel to the orbital angular momentum. From one-dimensional stellar evolution simulations with the numerical code mesa we find that the stochastic convection motion in the envelope of RSG stars adds a stochastic angular momentum component with an amplitude that is about 0.1–1 times that of the constant component due to the orbital motion. We mimic a CEE of the RSG star by removing envelope mass at a high rate and by depositing energy into its envelope. The stochastic angular momentum implies that the accretion disk around the secondary star (which we do not simulate), and therefore the jets that it launches, wobble with angles of up to tens of degrees with respect to the orbital angular momentum axis. This wobbling makes it harder for jets to break out from the envelope and can shape small bubbles in the ejecta that compress filaments that appear as arcs in the ejected nebula, i.e., in planetary nebulae when the giant is an asymptotic giant branch star.

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups.

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument's evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups.

The Neutron Star to Black Hole Mass Gap in the Frame of the Jittering Jets Explosion Mechanism (JJEM)

I build a toy model in the frame of the jittering jets explosion mechanism (JJEM) of core collapse supernovae that incorporates both the stochastically varying angular momentum component of the material that the newly born neutron star (NS) accretes and the constant angular momentum component, and show that the JJEM can account for the ≃2.5–5M ⊙ mass gap between NSs and black holes (BHs). The random component of the angular momentum results from pre-collapse core convection fluctuations that are amplified by post-collapse instabilities. The fixed angular momentum component results from pre-collapse core rotation. For slowly rotating pre-collapse cores the stochastic angular momentum fluctuations form intermittent accretion disks (or belts) around the NS with varying angular momentum axes in all directions. The intermittent accretion disk/belt launches jets in all directions that expel the core material in all directions early on, hence leaving an NS remnant. Rapidly rotating pre-collapse cores form an accretion disk with angular momentum axis that is about the same as the pre-collapse core rotation. The NS launches jets along this axis and hence the jets avoid the equatorial plane region. Inflowing core material continues to feed the central object from the equatorial plane increasing the NS mass to form a BH. The narrow transition from slow to rapid pre-collapse core rotation, i.e., from an efficient to inefficient jet feedback mechanism, accounts for the sparsely populated mass gap.

Spin and orbital angular momentum of coherent photons in a waveguide

Spin angular momentum of a photon corresponds to a polarisation degree of freedom of lights, and such that various polarisation properties are coming from macroscopic manifestation of quantum-mechanical properties of lights. An orbital degree of freedom of lights is also manipulated to form a vortex of lights with orbital angular momentum, which is also quantised. However, it is considered that spin and orbital angular momentum of a photon cannot be split from the total orbital angular momentum in a gauge-invariant way. Here, we revisit this issue for a coherent monochromatic ray from a laser source, propagating in a waveguide. We obtained the helical components of spin and orbital angular momentum by the correspondence with the classical Ponyting vector. By applying a standard quantum field theory using a coherent state, we obtained the gauge-independent expressions of spin and orbital angular momentum operators. During the derivations, it was essential to take a finite cross-sectional area into account, which leads the finite longitudinal component along the direction of the propagation, which allows the splitting. Therefore, the finite mode profile was responsible to justify the splitting, which was not possible as far as we were using plane-wave expansions in a standard theory of quantum-electrodynamics (QED). Our results suggest spin and orbital angular momentum are well-defined quantum-mechanical freedoms at least for coherent photons propagating in a waveguide and in a vacuum with a finite mode profile.

Controlling the Spin Hall Effect in the Sharp Focus of an Axial Superposition of Two Optical Vortices with Left- and Right-Handed Circular Polarization

We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization state of the superposition changes from linear polarization to right-hand circular polarization. Based on the Richards–Wolf theory, exact expressions are obtained for the longitudinal components of the spin angular momentum (SAM) density and orbital angular momentum (OAM) density at the focus of the considered superposition. It follows from these expressions that the sum of the total longitudinal components of the SAM and OAM is conserved upon focusing, and also that, due to the spin-orbit conversion, the total longitudinal component of the SAM decreases during focusing, while the total longitudinal component of the OAM increases by the same amount. By changing the ratio of the amplitudes of the constituent beams from 1 to 0, one can change the value of the spin-orbit conversion from zero (for linear polarization) to a maximum (for circular polarization). Also, by changing this parameter, one can control the spin Hall effect at the focus, which takes place at the focus of the considered beam. This study can be applied for controlling the rotation velocity of microparticles trapped in the focus.

Spin Hall Effect in Paraxial Vectorial Light Beams with an Infinite Number of Polarization Singularities.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements.

QCD angular momentum in N → Δ transitions

N→Δ transitions offer new possibilities for exploring the isovector component of the QCD quark angular momentum (AM) operator causing the Ju−d flavor asymmetry in the nucleon. We extend the concept of QCD AM to transitions between baryon states, using light-front densities of the energy-momentum tensor in transversely localized states. We calculate the N→Δ transition AM in the 1/Nc expansion, connect it with the Ju−d flavor asymmetry in the nucleon, and estimate the values using lattice QCD results. In the same setup we connect the transition AM to the transition GPDs sampled in hard exclusive electroproduction processes with N→Δ transitions, enabling experimental study of the transition AM.

Optical Helicity of Light in the Tight Focus

Using the Richards–Wolf formalism, we obtain explicit analytical expressions for the optical helicity density at the tight focus of four different light beams: a linearly polarized optical vortex, an optical vortex with right-handed circular polarization, superposition of a cylindrical vector beam and a linearly polarized beam, and a beam with hybrid circular-azimuthal polarization. We show that, in all four cases, the helicity density at the focus is nonzero and has different signs in different focal plane areas. If the helicity density changes sign, then the full helicity of the beam (averaged over the beam cross section at the focus) is zero and is conserved upon propagation. We reveal that the full helicity is zero when the full longitudinal component of the spin angular momentum is zero. If the helicity density does not change sign at the focus, such as in a circularly polarized optical vortex, then it is equal to the intensity in the focus, with the full helicity being equal to the beam power and conserving upon propagation. Although the helicity is related to the polarization state distribution across the beam at the focus, the expressions for the helicity density are found to be different from those for the longitudinal component of the spin angular momentum for the beams of interest.

Interpreting ultrafast electron transfer on surfaces with a converged first-principles Newns-Anderson chemisorption function.

We study the electronic coupling between an adsorbate and a metal surface by calculating tunneling matrix elements Had directly from first principles. For this, we employ a projection of the Kohn-Sham Hamiltonian upon a diabatic basis using a version of the popular projection-operator diabatization approach. An appropriate integration of couplings over the Brillouin zone allows the first calculation of a size-convergent Newns-Anderson chemisorption function, a coupling-weighted density of states measuring the line broadening of an adsorbate frontier state upon adsorption. This broadening corresponds to the experimentally observed lifetime of an electron in the state, which we confirm for core-excited Ar*(2p3/2-14s) atoms on a number of transition metal (TM) surfaces. Yet, beyond just lifetimes, the chemisorption function is highly interpretable and encodes rich information on orbital phase interactions on the surface. The model thus captures and elucidates key aspects of the electron transfer process. Finally, a decomposition into angular momentum components reveals the hitherto unresolved role of the hybridized d-character of the TM surface in the resonant electron transfer and elucidates the coupling of the adsorbate to the surface bands over the entire energy scale.

Angular Momentum Variation of the Milky Way Thick Disk: The Dependence of Chemical Abundance and Evidence of the Inside-out Formation Scenario

We investigate the angular momentum of mono-abundance populations (MAPs) of the Milky Way thick disk by using a sample of 26,076 giant stars taken from APOGEE Data Release (DR) 17 and Gaia early DR3. The vertical and perpendicular angular momentum components, L Z and L P , of the MAPs in narrow bins have significant variations across the [α/M]–[M/H] plane. L Z and L P systematically change with [M/H] and [α/M] and can be alternatively quantified by the chemical gradients: d[M/H]/dL Z = 1.2 × 10−3 dex kpc−1 km−1 s, d[M/H]/dL P = −5.0 × 10−3 dec kpc−1 km−1 s, and d[α/M]/dL Z = −3.0 × 10−4 dex kpc−1 km−1 s, d[α/M]/dL P = 1.2 × 10−3 dec kpc−1 km−1 s. These correlations can also be explained as the chemical dependence of the spatial distribution shape of the MAPs. We also exhibit the corresponding age dependence of the angular momentum components. Under the assumption that the guiding radius (R g ) is proportional to L Z , this provides direct observational evidence of the inside-out structure formation scenario of the thick disk, with dR g /dAge = −1.9 kpc Gyr−1. The progressive changes in the disk thickness can be explained by the upside-down formation or/and the consequent kinematical heating.

Effective polarization in proton-induced α knockout reactions

The effective polarization of the residual nucleus in the proton-induced $\alpha$ knockout reaction is investigated within the distorted wave impulse approximation framework. The strong absorption of the emitted $\alpha$ particle results in strong selectivity on the reaction "position" depending on the third component of the single-particle orbital angular momentum of the $\alpha$ particle inside a nucleus, hence on the spin direction of the reaction residue. This is caused by a mechanism that is similar to the Maris effect, the effective polarization in the proton-induced proton knockout reactions. However, as a distinct feature of the effective polarization in the $\alpha$ knockout process, the spin degrees of freedom of the reacting particles play no role. The $\alpha$ knockout process with complete kinematics can be a useful polarization technique for the residual nucleus, without actively controlling the spin of the proton.

Fuzzy hyperspheres via confining potentials and energy cutoffs

We simplify and complete the construction of fully O(D)-equivariant fuzzy spheres , for all dimensions , initiated in Fiore and Pisacane (2018 J. Geom. Phys. 132 423–51). This is based on imposing a suitable energy cutoff on a quantum particle in subject to a confining potential well V(r) with a very sharp minimum on the sphere of radius r = 1; the cutoff and the depth of the well diverge with . As a result, the noncommutative Cartesian coordinates generate the whole algebra of observables on the Hilbert space ; applying polynomials in the to any we recover the whole . The commutators of the are proportional to the angular momentum components, as in Snyder noncommutative spaces. , as carrier space of a reducible representation of O(D), is isomorphic to the space of harmonic homogeneous polynomials of degree Λ in the Cartesian coordinates of (commutative) , which carries an irreducible representation of . Moreover, is isomorphic to . We resp. interpret , as fuzzy deformations of the space of (square integrable) functions on S d and of the associated algebra of observables, because they resp. go to as Λ diverges (with fixed). With suitable , in the same limit goes to the (algebra of functions on the) Poisson manifold ; more formally, yields a fuzzy quantization of a coadjoint orbit of that goes to the classical phase space .

The Hamiltonian for von Zeipel–Lidov–Kozai oscillations

ABSTRACT The Hamiltonian used in classical analyses of von Zeipel–Lidov–Kozai or ZLK oscillations in hierarchical triple systems is based on the quadrupole potential from a distant body on a fixed orbit, averaged over the orbits of both the inner and the outer bodies (‘double averaging’). This approximation can be misleading, because the corresponding Hamiltonian conserves the component of angular momentum of the inner binary normal to the orbit of the outer binary, thereby restricting the volume of phase space that the system can access. This defect is usually remedied by including the effects of the octopole potential, or by allowing the outer orbit to respond to variations in the inner orbit. However, in a wide variety of astrophysical systems, non-linear perturbations are comparable to or greater than these effects. The long-term effects of non-linear perturbations are described by an additional Hamiltonian, which we call Brown’s Hamiltonian. At least three different forms of Brown’s Hamiltonian are found in the literature; we show that all three are related by a gauge freedom, although one is much simpler than the others. We argue that investigations of ZLK oscillations in triple systems should include Brown’s Hamiltonian.

Spin-orbit interactions in plasmonic crystals probed by site-selective cathodoluminescence spectroscopy.

The study of spin-orbit coupling (SOC) of light is crucial to explore the light-matter interactions in sub-wavelength structures. By designing a plasmonic lattice with chiral configuration that provides parallel angular momentum and spin components, one can trigger the strength of the SOC phenomena in photonic or plasmonic crystals. Herein, we explore the SOC in a plasmonic crystal, both theoretically and experimentally. Cathodoluminescence (CL) spectroscopy combined with the numerically calculated photonic band structure reveals an energy band splitting that is ascribed to the peculiar spin-orbit interaction of light in the proposed plasmonic crystal. Moreover, we exploit angle-resolved CL and dark-field polarimetry to demonstrate circular-polarization-dependent scattering of surface plasmon waves interacting with the plasmonic crystal. This further confirms that the scattering direction of a given polarization is determined by the transverse spin angular momentum inherently carried by the SP wave, which is in turn locked to the direction of SP propagation. We further propose an interaction Hamiltonian based on axion electrodynamics that underpins the degeneracy breaking of the surface plasmons due to the spin-orbit interaction of light. Our study gives insight into the design of novel plasmonic devices with polarization-dependent directionality of the Bloch plasmons. We expect spin-orbit interactions in plasmonics will find much more scientific interests and potential applications with the continuous development of nanofabrication methodologies and uncovering new aspects of spin-orbit interactions.

Hall Effect at the Focus of an Optical Vortex with Linear Polarization.

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

An odd feature of the “most classical” states of SU(2) invariant quantum mechanical systems

Complex and spinorial techniques of general relativity are used to determine all the states of SU(2) invariant quantum mechanical systems in which the equality holds in uncertainty relations for the components of the angular momentum vector operator in two given directions. The expectation values depend on a discrete quantum number and two parameters, one of them is the angle between two angular momentum components and the other is the quotient of two standard deviations. Allowing the angle between two angular momentum components to be arbitrary, a new genuine quantum mechanical phenomenon emerges: it is shown that although standard deviations change continuously, one of the expectation values changes discontinuously on this parameter space. Since physically neither of the angular momentum components is distinguished over the other, this discontinuity suggests that the genuine parameter space must be a double cover of this classical one: it must be diffeomorphic to a Riemann surface known in connection with the complex function z. Moreover, the angle between angular momentum components plays the role of the parameter of an interpolation between the continuous range of expectation values in the special case of orthogonal angular momentum components and the discrete point spectrum of one angular momentum component. The consequences in the simultaneous measurements of these angular momentum components are also discussed briefly.