Total Angular Momentum Conservation Research Articles

High-harmonic spin-orbit angular momentum generation in crystalline solids preserving multiscale dynamical symmetry.

Symmetries essentially provide conservation rules in nonlinear light-matter interactions and facilitate control and understanding of photon conversion processes or electron dynamics. Since anisotropic solids have rich symmetries, they are strong candidates for controlling both optical micro- and macroscale structures, namely, spin angular momentum (circular polarization) and orbital angular momentum (spiral wavefront), respectively. Here, we show structured high-harmonic generation linked to the anisotropic symmetry of a solid. By strategically preserving a dynamical symmetry arising from the spin-orbit interaction of light, we generate multiple orbital angular momentum states in high-order harmonics. The experimental results exhibit the total angular momentum conservation rule of light even in the extreme nonlinear region, which is evidence that the mechanism originates from a dynamical symmetry. Our study provides a deeper understanding of multiscale nonlinear optical phenomena and a general guideline for using electronic structures to control structured light, such as through Floquet engineering.

Total angular momentum conservation in Ehrenfest dynamics with a truncated basis of adiabatic states.

We show that standard Ehrenfest dynamics does not conserve linear and angular momentum when using a basis of truncated adiabatic states. However, we also show that previously proposed effective Ehrenfest equations of motion [M. Amano and K. Takatsuka, "Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions," J. Chem. Phys. 122, 084113 (2005) and V. Krishna, "Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum classical limit," J. Chem. Phys. 126, 134107 (2007)] involving the non-Abelian Berry force do maintain momentum conservation. As a numerical example, we investigate the Kramers doublet of the methoxy radical using generalized Hartree-Fock with spin-orbit coupling and confirm that angular momentum is conserved with the proper equations of motion. Our work makes clear some of the limitations of the Born-Oppenheimer approximation when using abinitio electronic structure theory to treat systems with unpaired electronic spin degrees of freedom, and we demonstrate that Ehrenfest dynamics can offer much improved, qualitatively correct results.

Linear mode analysis and spin relaxation

In this paper, a detailed analysis on normal modes of the linearized Hermite collision operator is presented, which follows from linearizing spin Boltzmann equation for massive fermions proposed in [Phys. Rev. D 104, 016022 (2021)] with the nondiagonal part of the transition rate neglected and approximating what we got with a mutilated operator. With the assumption of total angular momentum conservation, the collision term is proven to well describe the equilibrium state and gives proper interpretation for collisional invariants, thus is relevant for the research on local spin polarization. Following the familiar fashion as used in quantum mechanics, we treat the problem of solving normal modes as a degenerate perturbation problem and calculate the dispersion relations for intriguing eleven zero modes, which form one-to-one correspondence to all collisional invariants. We find that the results of spinless modes appearing in ordinary hydrodynamics are consistent with available conclusions in textbooks. As for spin-related modes, we obtain the frequencies up to second order in a wave vector and relate them with the dissipation of spin density fluctuation. In addition, the ratio of two relaxation timescales for spin and momentum is shown as a function of reduced mass, which reads that based on present framework spin equilibration is almost as slow as momentum equilibration as far as the strange quark spins in quark gluon plasma (QGP) are concerned.

Generation of a bright four-photon entangled state from a warm atomic ensemble via inherent polarization entanglement

We report the stable generation of a bright four-photon polarization-entangled Greenberger–Horne–Zeilinger (GHZ) state obtained by the spatial multiplexing of inherently polarization-entangled photons from a warm atomic ensemble of 87Rb. Owing to the total angular momentum conservation of the atomic state in the spontaneous four-wave mixing process of a cascade-type atomic system, the polarizations of the signal and idler photons in the two-photon decay are entangled. With a Rb vapor cell, we realize the generation of robust and bright four-photon GHZ states using two symmetrical spatial modes of inherently polarization-entangled photon pairs without applying an interferometric configuration. The four-photon average coincidence rate of the GHZ state with a fidelity of 0.88(2) is measured as 1.69(7) Hz under a weak pump power of 10 μW. The minimum Allan variance for the stability of the four-photon GHZ state is estimated as 0.92° for an average time of 10 h.

Vector polarizability of an atomic state induced by a linearly polarized vortex beam: External control of magic, tune-out wavelengths, and heteronuclear spin oscillations

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular-momentum conservation of the beam. The theory is employed on $^{87}\mathrm{Sr}^{+}$ to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using the relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes a fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and orbital angular momentum of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}\mathrm{Rb}$ and $^{23}\mathrm{Na}$ atoms.

Phenomenology of the Pauli exclusion principle violations due to the non-perturbative generalized uncertainty principle

New phenomenological implications of the Generalized Uncertainty Principle (GUP), a modification of the Heisenberg Uncertainty Principle (HUP) are explored in light of constraints arising from underground experiments. An intimate link intertwines the symplectic structure of a theory, which is at the very base of the formulation of the HUP and thus a pillar of quantum mechanics, with the symmetries of space-time and the spin-statistics. Within this wide framework, a large class of non-perturbative GUPs inevitably lead to energy-dependent violations of the total angular momentum conservation rules, and imply hence tiny Pauli Exclusion Principle (PEP) violating transitions. Exotic PEP violating nuclear transitions can be tested, for example, through extremely high precision data provided by the DAMA/LIBRA experiment. We show that several GUP violations are already ruled out up to the quantum gravity Planck scale.

Orbital angular momentum of a π-pulse emission by dense relativistic cold electron beam

Using a quantum fluid model, a set of three paraxial coupled equations to describe the free-electron laser instability is derived. These equations are solved numerically considering Laguerre-Gaussian modes as the initial conditions to study the transfer of orbital angular momentum between them, which satisfies the total angular momentum conservation as matching condition. The amplification and compression of the output radiation is observed. Using the method of separation of variables, the set of coupled equations, which describes a π-pulse solution, is obtained in such a way that a transverse overlapping factor, R, governs the energy exchange efficiency of the process.

Variational-based energy–momentum schemes of higher-order for elastic fiber-reinforced continua

This paper contributes to the improvement of recently published higher-order accurate energy–momentum schemes for an anisotropic hyperelastic material formulation based on the concept of structural tensors. These Galerkin-based energy–momentum schemes are developed by means of time finite elements with the focus on improving numerical stability and robustness in the presence of stiffness and large rotations. They show advantages over conventional time stepping schemes in combination with anisotropic materials formulated with polyconvex strain energy density functions. In this paper, higher-order energy–momentum schemes are developed by using a differential variational principle in order to remedy the drawbacks of these Galerkin-based schemes, namely a variationally inconsistent time approximation of the strains in the higher-order case, no coordinate free superimposed stress tensor and an unseparated time approximation of the fibers and the matrix material. These new structure-preserving time integrators preserve all conservation laws of a free flying hyperelastic anisotropic continuum, namely the total linear and the total angular momentum conservation as well as the total energy conservation. Numerical examples demonstrate dynamic behavior of anisotropic continua, discrete conservation properties of flying continua and the effect of higher-order accuracy subject to transient loads.

A general realistic treatment of the disk paradox

Mechanical angular momentum is not conserved in systems involving electromagnetic fields with non-zero electromagnetic field angular momentum. Conservation is restored only if the total (mechanical and field) angular momentum is considered. Previous studies have investigated this effect, known as ‘Feynman’s Electromagnetic Paradox’ or simply ‘Disk Paradox’ in the context of idealized systems (infinite or infinitesimal solenoids and charged cylinders etc). In the present analysis we generalize previous studies by considering more realistic systems with finite components and demonstrating explicitly the conservation of the total angular momentum. This is achieved by expressing both the mechanical and the field angular momentum in terms of charges and magnetic field fluxes through various system components. Using this general expression and the closure of magnetic field lines, we demonstrate explicitly the conservation of total angular momentum in both idealized and realistic systems (finite solenoid concentric with two charged cylinders, much longer than the solenoid) taking all the relevant terms into account including the flux outside of the solenoid. This formalism has the potential to facilitate a simpler and more accurate demonstration of total angular momentum conservation in undergraduate physics electromagnetism laboratories.

On the macroscopic quantization in mesoscopic rings and single-electron devices

In this letter we investigate the phenomenon of macroscopic quantization and consider particle on the ring interacting with the dissipative bath as an example. We demonstrate that even in presence of environment, there is macroscopically quantized observable which can take only integer values in the zero temperature limit. This fact follows from the total angular momentum conservation combined with momentum quantization for bare particle on the ring. The nontrivial thing is that the model under consideration, including the notion of quantized observable, can be mapped onto the Ambegaokar–Eckern–Schon model of the single-electron box (SEB). We evaluate SEB observable, originating after mapping, and reveal new physics, which follows from the macroscopic quantization phenomenon and the existence of additional conservation law. Some generalizations of the obtained results are also presented.

Phonon coupling effects in magnetic moments of magic and semimagic nuclei

Phonon coupling (PC) corrections to magnetic moments of odd neighbors of magic and semi-magic nuclei are analyzed within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional by Fayans et al. The perturbation theory in g_L^2 is used where g_L is the phonon-particle coupling vertex. A model is developed with separating non-regular PC contributions, the rest is supposed to be regular and included into the standard TFFS parameters. An ansatz is proposed to take into account the so-called tadpole term which ensures the total angular momentum conservation with g_L^2 accuracy. An approximate method is suggested to take into account higher order terms in g_L^2. Calculations are carried out for four odd-proton chains, the odd Tl, Bi, In and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to the magnetic moment in magic nuclei is, as a rule, negligible. In non-magic nuclei considered it is noticeable and, with only one exception, negative. On average it is of the order of -(0.1 - 0.5) \mu_N and improves the agreement of the theory with the data. Simultaneously we calculated the gyromagnetic ratio g_L^{ph} of all low-lying phonons in 208Pb. For the 3^-_1 state it is rather close to the Bohr-Mottelson model prediction whereas for other L-phonons, two 5^- and six positive parity states, the difference from the Bohr-Mottelson values is significant.

Fragmentation of spin-orbit-coupled spinor Bose-Einstein condensates

The fragmentation of spin-orbit-coupled spin-1 Bose gas with a weak interaction in external harmonic trap is explored by both exact diagonalization and mean-field theory. This fragmentation tendency, which originates from the total angular momentum conservation, is affected obviously by the spin-orbit-coupling strength and the spin-dependent interaction. Strong spin-orbit interaction raises the inverse participation ratio, which describes the number of significantly occupied single-particle states. As the spin-dependent interaction changes from antiferromagnetic to ferromagnetic, the peak values in the inverse participation ratio become lower. Without the confinement of the appointed total angular momentum, the condensate chooses a zero or finite total angular momentum ground state, which is determined by both the interaction and the spin-orbit-coupling strength.

A model for phonon coupling contributions to electromagnetic moments of odd spherical nuclei

Within the Theory of Finite Fermi Systems (TFFS), a model is developed to describe Phonon Coupling (PC) effects in odd magic and semi-magic nuclei. It is based on the perturbation theory in , where gL is the vertex of the L-phonon creation. Among all diagrams the set is separated which depends significantly on the nucleus under consideration and the state λ of the odd nucleon. An ansatz is proposed to take into account the phonon tadpole diagram which ensures the total angular-momentum conservation. Calculations are carried out for three odd-proton chains, the odd Tl, In and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to magnetic moments in magic nuclei is, as a rule, negligible. In the non-magic nuclei considered it is noticeable and improves the agreement with data.

Quantum entangled ground states of two spinor Bose-Einstein condensates

We revisit in detail the non-mean-field ground-state phase diagram for a binary mixture of spin-1 Bose-Einstein condensates including quantum fluctuations. The non-commuting terms in the spin-dependent Hamiltonian under single spatial mode approximation make it difficult to obtain exact eigenstates. Utilizing the spin z-component conservation and the total spin angular momentum conservation, we numerically derive the information of the building blocks and evaluate von Neumann entropy to quantify the ground states. The mean-field phase boundaries are found to remain largely intact, yet the ground states show fragmented and entangled behaviors within large parameter spaces of interspecies spin-exchange and singlet-pairing interactions.

Spin Hall effect of light in photon tunneling

We resolve the breakdown of angular momentum conservation on two-dimensional photon tunneling by considering the spin Hall effect (SHE) of light. This effect manifests itself as polarization-dependent transverse shifts of the field centroid when a classic wave packet tunnels through a prism-air-prism barrier. For the left or the right circularly polarized component, the transverse shift can be modulated by altering the refractive index gradient associated with the two prisms. We find that the SHE in conventional beam refraction can be evidently enhanced via photon tunneling mechanism. The transverse spatial shift is governed by the total angular momentum conservation law, while the transverse angular shift is governed by the total linear momentum conservation law. These findings open the possibility for developing new nanophotonic devices and can be extrapolated to other physical systems.

Secular Increase of the Astronomical Unit: a Possible Explanation in Terms of the Total Angular-Momentum Conservation Law

Abstract We give an idea and order-of-magnitude estimations to explain a recently reported secular increase of the Astronomical Unit ($AU$) by Krasinsky and Brumberg (2004, Celest. Mech. Dyn. Astron., 90, 267). The idea proposed is analogous to tidal acceleration in the Earth–Moon system, which is based on conservation of the total angular momentum; we apply this scenario to the Sun–planets system. Assuming the existence of some tidal interactions that transfer the rotational angular momentum of the Sun, and using a reported value of the positive secular trend in the Astronomical Unit, $\displaystyle\frac{d}{dt}{AU}$$=$ 15$ \pm $4 (m cy$^{-1}$), the suggested change in the period of rotation of the Sun is about 21 ms cy$^{-1}$ in the case that the orbits of the eight planets have the same “expansion rate.” This value is sufficiently small, and at present it seems there are no observational data that exclude this possibility. The effects of a change in the Sun’s moment of inertia is also investigated. It is pointed out that a change in the moment of inertia due to radiative mass loss by the Sun may be responsible for the secular increase of $AU$, if orbital “expansion” is happening only in the inner-planets system. Although the existence of some tidal interactions is assumed between the Sun and the planets, concrete mechanisms of angular-momentum transfer are not discussed in this paper, which remain to be pursued as future investigations.

Angular momentum transport in a multicomponent solar wind with differentially flowing, thermally anisotropic ions

Context. The Helios measurements of the angular momentum flux L of the fast solar wind lead to a tendency for the fluxes associated with individual ion angular momenta of protons and alpha particles, Lp and Lα, to be negative (i.e., in the sense of counter-rotation with the Sun). However, the opposite holds for the slow wind, and the overall particle contribution LP = Lp + Lα tends to exceed the magnetic contribution LM. These two aspects are at variance with previous models. Aims. We examine whether introducing realistic ion temperature anisotropies can resolve this discrepancy. Methods. From a general set of multifluid transport equations with gyrotropic species pressure tensors, we derive the equations governing both the meridional and azimuthal dynamics of outflows from magnetized, rotating stars. The equations are not restricted to radial flows in the equatorial plane but valid for general axisymmetric winds that include two major ion species. The azimuthal dynamics are examined in detail, using the empirical meridional flow profiles for the solar wind, constructed mainly according to measurements made in situ. Results. The angular momentum flux L is determined by the requirement that the solution to the total angular momentum conservation law is unique and smooth in the vicinity of the Alfven point, defined as where the combined Alfvenic Mach number MT = 1. MT has to consider the contributions from both protons and alpha particles. Introducing realistic ion temperature anisotropies may introduce a change of up to 10% in L and up to ∼1. 8k m s −1 in azimuthal speeds of individual ions between 0.3 and 1 AU, compared with the isotropic case. The latter has strong consequences on the relative importance of LP and LM in the angular momentum budget. Conclusions. However, introducing ion temperature anisotropies cannot resolve the discrepancy between in situ measurements and model computations. For the fast-wind solutions, while in extreme cases LP may become negative, Lp never does. On the other hand, for the slow solar wind solutions examined, LP never exceeds LM, even though LM may be less than the individual ion contribution, since Lp and Lα always have opposite signs for the slow and fast wind alike.

Total angular momentum conservation in laser-induced femtosecond magnetism

Total angular momentum conservation in laser-induced femtosecond magnetism

Morphology-induced oscillations of the electron-spin precession in Fe films onAg(001)

Spin-polarized electron reflection experiments on Fe films on $\mathrm{Ag}(001)$ show oscillations of the electron-spin precession as a function of the Fe thickness with monolayer periodicity. They are attributed to morphological changes of the Fe film. This shows---because of total angular momentum conservation---that the transfer of spin-angular momentum from the incident electrons to the ferromagnetic film can be extremely sensitive to the morphology and structure of the film.

Orbital elements of the mild and strong barium stars formed through a wind accretion scenario

Taking account of the metallicity dependence of the s-process nucleosynthesis in the AGB stars, we adopted the wind accretion model with the condition of total angular momentum conservation and used the Monte-Carlo method to study the variations and the distributions of the orbital elements of the mild and strong Ba stars. The calculated results show that the level of heavy-element overabundance in a Ba star depends on the orbital period. Since there is a strong dependence of s-process yields on the initial stellar metallicity of the AGB star and a strong increase of the s-process yields in AGB stars with decreasing metallicity, the calculated results strongly suggest that the initial metallicity of the Ba star systems is another important parameter for the level of heavy-element overabundance in a Ba star. The strong Ba stars generally have lower metallicities than mild Ba stars. The masses of AGB progenitor and Ba star are other two parameters which also have some impact on the heavy-element overabundance in the Ba star.