Total Spin Angular Momentum Research Articles

Angular momentum properties of a circularly polarized vortex beam in the paraxial optical systems

The angular momentum (AM) properties of circularly polarized vortex beams (CPVBs) in two paraxial optical systems [free space and a gradient-index (GRIN) fiber] are demonstrated. The transverse light intensity, the longitudinal light intensity, the phase of the longitudinal electric field, the kinetic momentum, the total spin AM (SAM), the transverse-type SAM (t-SAM), the longitudinal-type SAM (l-SAM), and the orbital angular momentum (OAM) of CPVBs in the two paraxial optical systems are characterized. Spin-orbit coupling of CPVBs is studied during propagation in free space and in a GRIN fiber. When the OAM and the SAM of a CPVB have the same direction of rotation and when they have opposite directions of rotation, the spin-orbit coupling exhibits different characteristics in free space and in the GRIN fiber.

Spin-momentum properties of the spin–orbit interactions of light at optical interfaces

The spin–orbit interaction (SOI) of light manifests as the generation of spin-dependent vortex beams when a spin-polarized beam strikes an optical interface normally. However, the spin-momentum nature of this SOI process remains elusive, which impedes further manipulation. Here, we systematically investigate the spin-momentum properties of the transmitted beam in this SOI process using a full-wave theory. The transmitted beam has three components, a spin-maintained normal mode, a spin-reversed abnormal mode, and a longitudinal component. By decomposing the total spin angular momentum (SAM) into the transverse SAM (T-SAM) and the helicity dependent longitudinal SAM (L-SAM), we demonstrate that the L-SAM dominates the total SAM of the normal mode, while the T-SAM dictates that of the abnormal mode. The underlying physics is that the normal mode exhibits a much larger weight than the longitudinal field, while the abnormal mode has a weight comparable to the longitudinal field. This study enriches the understanding of the spin-momentum nature of light’s SOI and offers new opportunities for manipulating light’s angular momentum.

A decomposition of light’s spin angular momentum density

Light carries intrinsic spin angular momentum (SAM) when the electric or magnetic field vector rotates over time. A familiar vector equation calculates the direction of light’s SAM density using the right-hand rule with reference to the electric and magnetic polarisation ellipses. Using Maxwell’s equations, this vector equation can be decomposed into a sum of two distinct terms, akin to the well-known Poynting vector decomposition into orbital and spin currents. We present the first general study of this spin decomposition, showing that the two terms, which we call canonical and Poynting spin, are chiral analogies to the canonical and spin momenta of light in its interaction with matter. Like canonical momentum, canonical spin is directly measurable. Both canonical and Poynting spin incorporate spatial variation of the electric and magnetic fields and are influenced by optical vortices. The decomposition allows us to show that a linearly polarised vortex beam, which has no total SAM, can nevertheless exert longitudinal chiral pressure due to equal and opposite canonical and Poynting spins.

Spin–Orbital Transformation in a Tight Focus of an Optical Vortex with Circular Polarization

In the framework of the Richards–Wolf formalism, the spin–orbit conversion upon tight focusing of an optical vortex with circular polarization is studied. We obtain exact formulas which show what part of the total (averaged over the beam cross-section) longitudinal spin angular momentum is transferred to the total longitudinal orbital angular momentum in the focus. It is shown that the maximum part of the total longitudinal angular momentum that can be transformed into the total longitudinal orbital angular momentum is equal to half the beam power, and this maximum is reached at the maximum numerical aperture equal to one. We prove that the part of the spin angular momentum that transforms into the orbital angular momentum does not depend on the optical vortex topological charge. It is also shown that by virtue of spin–orbital conversion upon focusing, the total longitudinal energy flux decreases and partially transforms into the whole transversal (azimuthal) energy flow in the focus. Moreover, the longitudinal energy flux decreases by exactly the same amount that the total longitudinal spin angular momentum decreases.

Dramatic improvement in the “Bulk” hyperpolarization of [formula omitted]Xe via spin exchange optical pumping probed using in situ low-field NMR

We report on hyperpolarization of quadrupolar (I=3/2) 131Xe via spin-exchange optical pumping. Observations of the 131Xe polarization dynamics via in situ low-field NMR show that the estimated alkali-metal/131Xe spin-exchange rates can be large enough to compete with 131Xe spin relaxation. 131Xe polarization up to 7.6±1.5% was achieved in ∼8.5×1020 spins—a ∼100-fold improvement in the total spin angular momentum—potentially enabling various applications, including: measurement of spin-dependent neutron-131Xe s-wave scattering; sensitive searches for time-reversal violation in neutron-131Xe interactions beyond the Standard Model; and surface-sensitive pulmonary MRI.

New results on the two low-mass-ratio overcontact binaries V1309 Herculis and AS Coronae Borealis

Abstract We present new multi-color light curves of V1309 Her and AS CrB, which were observed by the 60 cm telescope located at the Maidanak Astronomical Observatory. Combined with the Large-Sky-Area Multi-Object Fiber Spectroscopic Telescope atmospheric parameters, we analyzed our BVRCIC light curves for both systems by employing the Wilson–Devinney program. Our results show that both systems are low-mass-ratio overcontact binaries (V1309 Her: q = 0.213, AS CrB: q = 0.16). AS CrB has a high fill-out factor, while that of V1309 Her is moderate. By adding our new times of minimum light, we found the periodic oscillations in their O − C curves, which could be explained by the light travel-time effect of the third bodies. The third lights detected during the light curve analysis support the existence of the third bodies in V1309 Her and AS CrB. Third bodies usually play an important role for the origin and evolution of the central pair by removing their angular momentum. With the angular momentum loss, a moderate-fill-out overcontact binary like V1309 Her will evolve to a deep one like AS CrB. AS CrB lies at the late evolutionary stage of contact binaries. A long-term period increase at a rate of dP/dt = 5.22(± 0.28) × 10−7 d yr−1 was detected in our O − C diagram analysis. When its orbital angular momentum is less than three times the total spin angular momentum, a system may finally evolve into a rapid-rotating single star.

Spin 1/2 one‐ and two‐particle systems in physical space without eigen‐algebra or tensor product

Under the spin–position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra substitutes the vector–matrix spin model built on the Pauli spin operator. The standard quantum operator‐state spin formalism is replaced with vectors transforming by proper and improper rotations in the same 3D space—isomorphic to the space of Pauli matrices. In the single‐spin case, the novel spin 1/2 representation (1) is Hermitian, (2) shows handedness, (3) yields all the standard results and its modulus equals the total spin angular momentum , (4) formalizes irreversibility in measurement, and (5) permits adaptive imbedding of the 2D spin space in 3D. Maximally entangled spin pairs (1) are in phase and have opposite handedness, (2) relate by one of the four basic improper rotations in 3D: plane reflections (triplets) and inversion (singlet), (3) yield the standard total angular momentum, and (4) all standard expectation values for bipartite and partial observations follow. Depending on whether proper and improper rotors act one—or two—sided, the formalism appears in two complementary forms, the “spinor” or the “vector” form, respectively. The proposed scheme provides a clear geometric picture of spin correlations and transformations entirely in the 3D physical orientation space.

Adiabatic spin dynamics and effective exchange interactions from constrained tight-binding electronic structure theory: Beyond the Heisenberg regime

We consider an implementation of the adiabatic spin dynamics approach in a tight-binding description of the electronic structure. The adiabatic approximation for spin-degrees of freedom assumes that the faster electronic degrees of freedom are always in a quasi-equilibrium state, which significantly reduces the numerical complexity in comparison to the full electron dynamics. Non-collinear magnetic configurations are stabilized by a constraining field, which allows to directly obtain the effective magnetic field from the negative of the constraining field. While the dynamics are shown to conserve energy, we demonstrate that adiabatic spin dynamics does not conserve the total spin angular momentum when the lengths of the magnetic moments are allowed to change, which is confirmed by numerical simulations. Furthermore, we develop a method to extract an effective two-spin exchange interaction from the energy curvature tensor of non-collinear states, which we calculate at each time step of the numerical simulations. We demonstrate the effect of non-collinearity on this effective exchange and limitations due to multi-spin interactions in strongly non-collinear configurations beyond the regime where the Heisenberg model is valid. The relevance of the results are discussed with respect to experimental pump-probe experiments that follow the ultra-fast dynamics of magnetism.

Gamma-ray line from electroweakly interacting non-abelian spin-1 dark matter

We study gamma-ray line signatures from electroweakly interacting non-abelian spin-1 dark matter (DM). In this model, Z2-odd spin-1 particles including a DM candidate have the SU(2)L triplet-like features, and the Sommerfeld enhancement is relevant in the annihilation processes. We derive the annihilation cross sections contributing to the photon emission and compare with the SU(2)L triplet fermions, such as Wino DM in the supersymmetric Standard Model. The Sommerfeld enhancement factor is approximately the same in both systems, while our spin-1 DM predicts the larger annihilation cross sections into γγ/Zγ modes than those of the Wino by frac{38}{9} . This is because a spin-1 DM pair forms not only J = 0 but also J = 2 partial wave states where J denotes the total spin angular momentum. Our spin-1 DM also has a new annihilation mode into Z2-even extra heavy vector and photon, Z′γ. For this mode, the photon energy depends on the masses of DM and the heavy vector, and thus we have a chance to probe the mass spectrum. The latest gamma-ray line search in the Galactic Center region gives a strong constraint on our spin-1 DM. We can probe the DM mass for ≲ 25.3 TeV by the Cherenkov Telescope Array experiment even if we assume a conservative DM density profile.

The relativistic spherical top as a massive twistor

We prove the equivalence between two traditional approaches to the classical mechanics of a massive spinning particle in special relativity. One is the spherical top model of Hanson and Regge, recast in a Hamiltonian formulation with improved treatment of covariant spin constraints. The other is the massive twistor model, slightly generalized to incorporate the Regge trajectory relating the mass to the total spin angular momentum. We establish the equivalence by computing the Dirac brackets of the physical phase space carrying three translation and three rotation degrees of freedom. Lorentz covariance and little group covariance uniquely determine the structure of the physical phase space. The Regge trajectory does not affect the phase space but enters the equations of motion. Upon quantization, the twistor model produces a spectrum that agrees perfectly with the massive spinor-helicity description proposed by Arkani-Hamed, Huang and Huang for scattering amplitudes for all masses and spins.

Rotational Doppler Frequency Shift from Time‐Evolving High‐Order Pancharatnam–Berry Phase: A Metasurface Approach

AbstractThe Doppler frequency shift of sound or electromagnetic waves has been widely investigated in many different contexts and, nowadays, represents a formidable tool in medicine, engineering, astrophysics, and optics. Such effect is commonly described in the framework of the universal energy‐momentum conservation law. In particular, the rotational Doppler effect has been recently demonstrated using light carrying orbital angular momentum. When a wave undergoes a cyclic adiabatic transformation of its Hamiltonian, it is known to acquire the so‐called Pancharatnam–Berry (PB) phase. In this work, an experimental evidence of the direct connection between the high‐order PB phase time evolution on the Poincaré sphere and the rotational Doppler frequency shift of light is provided. A metasurface operating at telecom wavelengths is employed to impose a total (spin and orbital) angular momentum (TAM) on the light wave, while two TAM converters ensure a closed cycle on the Poincaré sphere. By rotating one of the converters, a significant Doppler frequency shift is observed without variation of the output TAM. The proposed metasurface‐based approach offers new advanced ways to engineer the frequency content of light.

Spin Quintet in a Silicon Double Quantum Dot: Spin Blockade and Relaxation

Spins in gate-defined silicon quantum dots are promising candidates for implementing large-scale quantum computing. To read the spin state of these qubits, the mechanism that has provided the highest fidelity is spin-to-charge conversion via singlet-triplet spin blockade, which can be detected in-situ using gate-based dispersive sensing. In systems with a complex energy spectrum, like silicon quantum dots, accurately identifying when singlet-triplet blockade occurs is hence of major importance for scalable qubit readout. In this work, we present a description of spin blockade physics in a tunnel-coupled silicon double quantum dot defined in the corners of a split-gate transistor. Using gate-based magnetospectroscopy, we report successive steps of spin blockade and spin blockade lifting involving spin states with total spin angular momentum up to $S=3$. More particularly, we report the formation of a hybridized spin quintet state and show triplet-quintet and quintet-septet spin blockade. This enables studies of the quintet relaxation dynamics from which we find $T_1 \sim 4 ~\mu s$. Finally, we develop a quantum capacitance model that can be applied generally to reconstruct the energy spectrum of a double quantum dot including the spin-dependent tunnel couplings and the energy splitting between different spin manifolds. Our results open for the possibility of using Si CMOS quantum dots as a tuneable platform for studying high-spin systems.

Energy optimization in binary star systems: explanation for equal mass members in close orbits

ABSTRACT Observations indicate that members of close stellar binaries often have mass ratios close to unity, while longer period systems exhibit a more uniform mass-ratio distribution. This paper provides a theoretical explanation for this finding by determining the tidal equilibrium states for binary star systems – subject to the constraints of conservation of angular momentum and constant total mass. This work generalizes previous treatments by including the mass fraction as a variable in the optimization problem. The results show that the lowest energy state accessible to the system corresponds to equal mass stars on a circular orbit, where the stellar spin angular velocities are both synchronized and aligned with the orbit. These features are roughly consistent with observed properties of close binary systems. We also find the conditions required for this minimum energy state to exist: (1) the total angular momentum must exceed a critical value, (2) the orbital angular momentum must be three times greater than the total spin angular momentum, and (3) the semimajor axis is bounded from above. The last condition implies that sufficiently wide binaries are not optimized with equal mass stars, where the limiting binary separation occurs near a0 ≈ 16R*.

Spin-symmetry adaptation to the Monte Carlo correction configuration interaction wave functions.

We propose a method to adapt the spin-symmetry to the Monte Carlo correction configuration interaction (MC3I) wave function which is expanded by the selected Slater determinants (SDs). The spin-symmetry of the MC3I wave function is usually broken because the Monte Carlo method is used to select the SDs, and this problem becomes worse as the electron correlation becomes stronger. In the present method, the S^2 operator is applied to the set of the SDs in the MC3I wave function iteratively until the set becomes closed under S^2. The spin-symmetry adapted MC3I wave functions are calculated by diagonalization of the Hamiltonian matrix which is spanned by the converged set of SDs. The present method is tested by the application to the excited states of C2 in the bond dissociation region and the 100 lowest states of [Fe2S2(SCH3)4]3-. The deviations of S (total spin angular momentum) of some states were too large to assign the electronic states in the original MC3I calculations, while all states have the correct S after spin-symmetry adaptation and become comparable with the full configuration interaction and density matrix renormalization group results. With the present spin-symmetry adaptation, the MC3I method becomes applicable to strong electron correlation systems.

Angular Momentum of Stars and their Planets

To understand the distribution of angular momenta between host stars and their planets, we estimate the spin angular momentum (Jspin) of host stars that follow a power law with stellar mass . Similarly, the orbital angular momenta (Lp) of exoplanets are estimated, and the best fit yields a power law, , with the exoplanetary mass . Furthermore, the total (spin and orbital) angular momentum Jtot of the stellar planetary system is computed, and a power law of the form Jtot = is obtained. In addition, an analysis between specific angular momenta (Ip) of planets and planetary masses reveals that specific angular momentum is nonlinearly related with planetary mass in case of multiplanetary systems and is independent of planetary mass in case of single-planetary systems. We find that the probability of detecting Earth-like planets is more likely for host stars that have total angular momentum ≤1041 kg m2 s−1. Finally, a power-law relationship is obtained between exoplanetary masses and their orbital distances in case of multiplanetary systems and, is independent in case of single-planetary systems.

TY Pup: A Low-mass-ratio and Deep Contact Binary as a Progenitor Candidate of Luminous Red Novae

Abstract TY Pup is a well-known bright eclipsing binary with an orbital period of 0.8192 days. New light curves in B, V, (RI) C bands were obtained with the 0.61 m reflector robotic telescope (PROMPT-8) at CTIO in Chile during 2015 and 2017. By analyzing those photometric data with the W–D method, it is found that TY Pup is a low-mass-ratio (q ∼ 0.184) and deep-contact binary with a high fill-out factor (84.3%). An investigation of all available times of minimum light including three new ones obtained with the 60 cm and the 1.0 m telescopes at Yunnan Observatories in China indicates that the period change of TY Pup is complex. An upward parabolic variation in the O − C diagram is detected to be superimposed on a cyclic oscillation. The upward parabolic change reveals a long-term continuous increase in the orbital period at a rate of dP/dt = 5.57(±0.08) × 10−8 days yr−1. The period increase can be explained by mass transfer from the less massive component (M 2 ∼ 0.3 M ⊙) to the more massive one (M 1 ∼ 1.65 M ⊙). The binary will be merging when it meets the criterion that the orbital angular momentum is less than three times the total spin angular momentum, i.e., J orb < 3J rot. This suggests that the system will finally merge into a rapid-rotating single star and may produce a luminous red nova. The cyclic oscillation in the O − C diagram can be interpreted by the light-travel time effect via the presence of a third body.

Catalystlike effect of orbital angular momentum on the conversion of transverse to three-dimensional spin states within tightly focused radially polarized beams

We report on the catalystlike effect of orbital angular momentum (OAM) on local spin-state conversion within the tightly focused radially polarized beams associated with optical spin-orbit interaction. It is theoretically demonstrated that the incident OAM can lead to a conversion of purely transverse spin state to a three-dimensional spin state on the focal plane. This conversion can be conveniently manipulated by altering the sign and value of the OAM. By comparing the total OAM and spin angular momentum (SAM) on the incident plane to those on the focal plane, it is indicated that the incident OAM have no participation in the angular momentum intertransfer, and just play a role as a catalyst of local SAM conversion. Such an effect of OAM sheds new light on the optical spin-orbit interaction in tight-focusing processes. The resultant three-dimensional spin states may provide more degrees of freedom in optical manipulation and spin-dependent directive coupling.

TYC 1337-1137-1 and TYC 3836-0854-1: Two Low-mass Ratio, Deep Overcontact Systems Near the End Evolutionary Stage of Contact Binaries

New high-precision CCD photometric light curves of two contact binary stars, TYC 1337-1137-1 and TYC 3836-0854-1, are displayed and analyzed by using the Wilson–Devinney (W–D) program. The light curve solutions show that both of them are low-mass ratio, deep overcontact binary systems with a mass ratio of q = 0.1716 ± 0.0010 and a high fillout factor of f = 76.0 ± 2.9% for TYC 1337-1137-1, and q = 0.1900 ± 0.0032 and f = 79.4 ± 7.9% for TYC 3836-0854-1, respectively. These results indicate that they are near the end evolutionary stage of contact binaries. The absolute parameters were calculated by using the new method of mass–radius relationship (0.238 ± 0.009 M⊙ and 1.386 ± 0.050 M⊙ for TYC 1337-1137-1, 0.228 ± 0.014 M⊙ and 1.20 ± 0.07 M⊙ for TYC 3836-0854-1, respectively). The preliminary orbital period analysis suggests that long-term period increases exist for both of them, which may be interpreted in two possible ways. A first possibility is mass transfer conservation from the less massive component to the more massive one leading to an orbital period increase. In this case, when their orbital angular momentum is less than three times the total spin angular momentum, they may evolve into a rapidly rotating single star. A second possibility is that the parabolic variation in the (O − C) diagram is only a part of a long-period cyclic change caused by a potential third body. In future, more high-precision observations of these two binaries are needed to confirm the form of orbital period changes.

Charge Exchange of Highly Charged Ne and Mg Ions with H and He

Abstract Cross sections for single electron capture (SEC), or charge exchange (CX), in collisions of Ne(8–10)+ and Mg(8–12)+ with H and He, are computed using an approximate multichannel Landau–Zener (MCLZ) formalism. Final-state-resolved cross sections for the principal (n), orbital angular momentum (ℓ), and where appropriate, total spin angular momentum (S) quantum numbers are explicitly computed, except for the incident bare ions Ne10+ and Mg12+. In the latter two cases, -resolution is obtained from analytical ℓ-distribution functions applied to n-resolved MCLZ cross sections. In all cases, the cross sections are computed over the collision energy range 1 meV/u to 50 keV/u with LZ parameters estimated from atomic energies obtained from experiment, theory, or, in the case of high-lying Rydberg levels, estimated with a quantum defect approach. Errors in the energy differences in the adiabatic potentials at the avoided crossing distances give the largest contribution to the uncertainties in the cross sections, which are expected to increase with decreasing cross section magnitude. The energy differences are deduced here with the Olson–Salop–Tauljberg radial coupling model. Proper selection of an ℓ-distribution function for bare ion collisions introduces another level of uncertainty into the results. Comparison is made to existing experimental or theoretical results when available, but such data are absent for most considered collision systems. The -resolved SEC cross sections are used in an optically thin cascade simulation to predict X-ray spectra and line ratios that will aid in modeling the X-ray emission in environments where CX is an important mechanism. Details on a MCLZ computational package, Stueckelberg, are also provided.

Two new constraints for the cumulant matrix

We suggest new strict constraints that the two-particle cumulant matrix should fulfill. The constraints are obtained from the decomposition of ⟨Ŝ(2)⟩, previously developed in our laboratory, and the vanishing number of electrons shared by two non-interacting fragments. The conditions impose stringent constraints into the cumulant structure without any need to perform an orbital optimization procedure thus carrying very small or no computational effort. These constraints are tested on the series of Piris natural orbital functionals (PNOF), which are among the most accurate ones available in the literature. Interestingly, even though all PNOF cumulants ensure correct overall ⟨Ŝ(2)⟩ values, none of them is consistent with the local spin structure of systems that dissociate more than one pair of electrons. A careful analysis of the local spin components reveals the most important missing contributions in the cumulant expression thus suggesting a means to improve PNOF5. The constraints provide an inexpensive tool for the construction and testing of cumulant structures that complement previously known conditions such as the N-representability or the square of the total spin angular momentum, ⟨Ŝ(2)⟩.