Orbitronics: Electron orbital angular momentum dynamics in metals

Light orbital angular momentum (OAM) has been recognized as a new promising resource for classical and quantum information applications. In contrast to the spin angular momentum, the OAM is an inherently multidimensional. Thus, the information can be encoded in the higher-dimensional OAM alphabets. Recently, Marrucci et al. have invented a new device named q-plate (QP), made of liquid crystal cell patterned in such a way to introduce a topological charge q at the transverse plane, which is able to generate a well-defined values of photon OAM. My research has been aimed at investigating the physics of the QP, of the optical fields that it generates and of its possible applications for optical communication and quantum information. We studied both theoretically and experimentally a novel set of non-orthogonal but over-complete paraxial modes, named Hypergeometric-Gaussian modes, that is typically associated with OAM-carrying optical fields. We have also found the light propagation kernel inside the QP and we have shown analytically that if small losses due to reflection, absorption, and scattering are neglected, the QP can convert the photon spin into OAM with up to 100 \% efficiency. We implemented a technique to control the QP optical retardation by tuning the QP temperature. At the optimal temperature, the QP can generate a beam with up to 97\% efficiency. Moreover, the OAM state generated by QP can be rotated easily in the 2D OAM Hilbert space by proper manipulation of the input polarization state, a fact which opens a new way of beam shape controlling in MHz scale. We also performed a novel way to encode and read two bits information on the 4D OAM space by using only one QP. Finally, we experimentally demonstrated the transfer of quantum information from spin to OAM and vice versa, including the case of bi-photon states having quantum correlations. Furthermore, by exploiting these quantum information transfer devices, we demonstrated the Hong-Ou-Mandel effect and the optimal quantum cloning with OAM-carrying photons.

A classical derivation is presented for magnetic x-ray scattering from electronic orbital angular momentum. The orbital magnetic scattering factor is identical to that for spin angular momentum, except for the difference in gyromagnetic ratios. Unlike the spin result, which had previously been obtained from both a classical Lagrangian and from quantum mechanics, the classical orbital scattering disagrees with quantum mechanics and with available data. This disagreement between classical and quantum-mechanical results is present for the scattering from a free electron in motion, scattering from an ideal current loop, as well as for scattering from atomic orbital angular momentum.

In a high magnetic field of 3--7 T, nitric oxide (NO) molecules are excited by the double-resonance method through the intermediate $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\ensuremath{\Sigma}}^{+}{F}_{1}({v}^{\ensuremath{'}\ensuremath{'}}=0,{N}^{\ensuremath{'}\ensuremath{'}}=0)$ level to the Landau levels in the energy region above the zero-field ionization limit to the NO${}^{+}\phantom{\rule{0.222222em}{0ex}}X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}({v}^{+}=0,{N}^{+}=0)$ ion. By detecting NO${}^{+}$ ions, the photoionization cross section through the Landau levels is determined as a function of the second laser's frequency. The cross section contains broad structures and fine structures. Fourier analysis of the cross section and classical trajectory calculations of the Rydberg electron demonstrate that the broad structure is formed by the Landau level generated by the cyclotron motion of the electron around the ${N}^{+}=0$ core in a plane perpendicular to the field, while the fine structure is formed by the Landau level generated by the three-dimensional cyclotron motion around the excited ${N}^{+}=2$ core. By simulating the energy structure of the Landau level, the electron's orbital angular momentum is confirmed to be decoupled from the core rotation in the Landau levels. From the selection rules of the excitation, it is demonstrated that the Landau levels with the ${N}^{+}=0$ core are excited using the $s$ character in the $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\ensuremath{\Sigma}}^{+}$ state, while those with the ${N}^{+}=2$ core are excited using the $d$ character. The dominant partial wave, thus determined, explains well the starting direction of the classical trajectory.

The Orbital Angular Momentum (OAM) carried by light beams with helical phasefront (vortex beams) has been widely employed in many applications such as optical tweezers, optical drives of micro-machines, atom trapping, and optical communication. OAM provides an additional dimension (diversity) to multiplexing techniques, which can be utilized in addition to conventional multiplexing methods to achieve higher data rates in wireless communication. OAM beams have been thoroughly studied and used in the optical regime but in the mm-wave and THz-wave region, they are still under investigation. In these frequency bands, there are difficulties associated with beam-splitting and beam-combining processes as well as with the use of spiral phase plates and other methods for OAM generation, since the wavelength is much larger compared to those at optical frequencies, leading to higher diffraction losses. The present paper describes the natural generation of high-power OAM modes by gyro-type vacuum electron devices with cylindrical interaction circuit and axial output of the generated rotating higher-order transverse electric mode TEm,n, where m > 1 and n are the azimuthal and radial mode index, respectively. The ratio between the total angular momentum (TAM) JN and total energy WN of N photons is given by m/ω, where ω is the angular frequency of the operating mode, which in a gyrotron oscillator is close to the TEm,n-mode cutoff frequency in the cavity. Therefore, m/ω = Rc/c, where Rc is the caustic radius and c the velocity of light in vacuum. This means that the OAM is proportional to the caustic radius and at a given frequency the same for all modes with the same azimuthal index m. Right-hand rotation (co-rotation with the electrons) corresponds to a positive value of m and left-hand rotation to negative m. The corresponding OAM mode number (topological charge) is l = m – 1. Circularly polarized TE1n modes only possess a Spin Angular Momentum (SAM: s = ±1). TE0n modes have neither SAM nor OAM. This is the result of the photonic (quasi-optical) approach to derive the TAM of modes generated in gyrotrons. The same result follows from the electromagnetic (EM) wave approach for the TAM within a given waveguide volume per total energy of the EM wave in the same volume. Such high-power output beams with very pure higher-order OAM, generated by gyrotron oscillators or amplifiers (broadband) could be used for multiplexing in long-range wireless communications. The corresponding mode and helical wavefront sensitive detectors for selective OAM-mode sorting are available and described in the present paper.

Angular momentum of light can be divided into spin angular momentum and orbital angular momentum (OAM). Due to the theoretically unlimited orthogonal states, the physical dimension of OAM provides a potential solution to boost the information capacity. The OAM multiplexing and modulation techniques have been implemented to meet the continuous growth of bandwidth requirements, resulting in the concept of OAM optical communication. However, the performances of the traditional optical OAM detection techniques degrade seriously in the practical application of OAM optical communications. Thanks to the powerful data analysis advantages, the cutting-edge machine learning (ML) algorithms have been widely used in the field of image processing, laying the technical foundation for OAM recognition. This paper reviews the recent advances on OAM optical communications that are enhanced by ML methods. More than the traditional OAM detection methods, the OAM demodulation methods based on multiple network architectures, including the support vector machine, self-organizing map, feed-forward neural network, convolutional neural network, and diffractive deep optical neural network (D2NN), have been summarized. We also discuss the development of the spiking neural network and on-chip D2NN, opening a possible way to facilitate the future ultra-low power and ultra-fast OAM demodulation technology.

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries and for extracting NS information from GW data. In this paper, we use semianalytic methods to carry out a systematic study on the tidal excitation of fundamental modes ($f$-modes) of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is antialigned with the orbital angular momentum---where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigenmodes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. (Our treatment is at Newtonian order, including a gravitational radiation reaction at quadrupole order.) We then find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and postresonance. Using the method of osculating orbits, we obtain semianalytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in our understanding of the system's dynamics. In particular, we recover both the averaged postresonance evolution, which differs from the preresonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that, for a system with component masses of $(1.4,1.4)\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ at 100 Mpc, the constraints on the effective Love number of the (2,2) mode at Newtonian order can be improved by a factor of $3\ensuremath{\sim}4$ if spin frequency is as high as 500 Hz. The relative errors are $0.7\ensuremath{\sim}0.8$ in the Cosmic Explorer, and they might be further improved by post-Newtonian effects. The constraints on the $f$-mode frequency and the spin frequency are improved by factors of $5\ensuremath{\sim}6$ and $19\ensuremath{\sim}27$, respectively. In the Cosmic Explorer case, the relative errors are $0.2\ensuremath{\sim}0.4$ and $0.7\ensuremath{\sim}1.0$, respectively. Hence, the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to $f$-mode; it can also be applied to other types of tides.

Optical vortices carrying orbital angular momentum (OAM) have attracted extensive attention in recent decades because of their interesting applications in optical trapping, optical machining, optical communication, quantum information, and optical microscopy. Intriguing effects induced by OAMs, such as angular momentum conversion, spin Hall effect of light (SHEL), and spin–orbital interaction, have also gained increasing interest. In this article, we provide an overview of the modulations of OAMs on the propagation dynamics of scalar and vector fields in free space. First, we introduce the evolution of canonical and noncanonical optical vortices and analyze the modulations by means of local spatial frequency. Second, we review the Pancharatnam–Berry (PB) phases arising from spin–orbital interaction and reveal the control of beam evolution referring to novel behavior such as spindependent splitting and polarization singularity conversion. Finally, we discuss the propagation and focusing properties of azimuthally broken vector vortex beams.

Orbital angular momentum for spintronics

We show that when an electron or photon propagates in a cylindrically symmetric waveguide, its spin angular momentum (SAM) and its orbital angular momentum (OAM) interact. Remarkably, we find that the dynamics resulting from this spin-orbit interaction are quantitatively described by a single expression applying to both electrons and photons. This leads to the prediction of several novel rotational effects: the spatial or time evolution of either particle's spin/polarization vector is controlled by the sign of its OAM quantum number, or conversely, its spatial wavefunction is controlled by its SAM. We show that the common origin of these effects in electrons and photons is a universal geometric phase. We demonstrate how these phenomena can be used to reversibly transfer entanglement between the SAM and OAM degrees of freedom of two-particle states.

Spin-orbit interactions are inherent in many basic optical processes in anisotropic and inhomogeneous materials, under tight focusing or strong scattering, and have attracted enormous attention and research efforts. Since the spin-orbit interactions depend on the materials where they occur, the study of the effects of materials on the spin-orbit interactions could play an important role in understanding and utilizing many novel optical phenomena. Here, we investigate the effect of negative-index material on the spin-orbit interactions in a plasmonic lens structure in the form of a circular slot in silver film. Numerical simulations are employed to study the influence of the negative-index material on the plasmonic vortex formation and the plasmonic focusing in the structure under circularly polarized excitations bearing different orbital angular momentum. We reveal that the presence of negative-index material leaves the plasmonic vortex field distribution and the corresponding topological charge unaltered during the spin-to-orbital angular momentum conversion, whereas reverses the rotation direction of in-plane energy flux of the plasmonic vortex and shifts the surface plasmon polariton focus position to the opposite direction compared to the case without negative-index material. This work will help further the understanding of the regulation of optical spin-orbital interactions by material properties and design optical devices with novel functions.

Optical vortices are a new kind of laser beam and receiving more and more attention currently.The complex amplitudes of optical vortices comprise a helical term exp (il),with l being the topological charge and the azimuthal angle.Each photon in optical vortices carries the orbital angular momentum (OAM) with a value of lħ,where ħ is the Planck's constant divided by 2.The topological charge l is the eigenvalue of optical vortices,and determines the helical wavefront distribution,thus also known as OAM state.Moreover,such an OAM state can be an infinite integer state. And vortices with various OAM states are orthogonal to each other,making it possible to be employed in high capacity data-transmission system.In addition,the above unique features contribute to their widely applications in lots of areas such as optical tweezers and spanners,rotation detection,quantum entanglement,etc.In these applications,detecting OAM states is basic,and greatly significant.Recently researchers have developed lots of approaches to detecting the OAM states,including the methods of interference,diffraction gratings,metasurface,etc.Of such approaches,the scheme of diffraction gratings is the simplest and most widely used,where one or more diffraction gratings are employed. When optical vortices propagate through such gratings,the OAM states are acquired immediately through capturing and analyzing the distinct OAM-related diffraction patterns.In this review,we focus on the techniques of detecting OAM states through diffraction gratings,which have been demonstrated by our group and other researchers.Some of the main detection gratings,including double-slit,triangle aperture and slit,angular slit,cylindrical lens,graduallychanging-period grating,annular grating,are introduced.In addition,schemes like composite fork grating,Dammann vortex grating and integrated Dammann grating,are presented to detect the OAM state for coaxial multiplexed vortices. Besides diagnosing OAM state,measuring the intensity proportion of each OAM channel,known as OAM spectrum, in multiplexed vortices is also necessary in some cases.Therefore we also introduce the ways to measure the OAM spectrum,e.g.the OAM mode sorter,the gray-scale algorithm.

Light beams carrying multiple orbital angular momentum (OAM) states, which can be realized by the structured media with phase singularities, have attracted great attentions in the fields of high dimensional optical information processing. Alternatively, a simple uniaxial crystal can be used to simultaneously generate four OAM states of light through the second harmonic generation and cascaded optical spin–orbit interaction (SOI) processes. However, two of the OAM states realized in the crystal are very weak and limit the practical applications. Here, we aim to circumvent this constraint by using the sequential optical SOI processes in two crystals with threefold rotational symmetry. Four angular momentum states of the fundamental waves are prepared after the first crystal and then are utilized to generate the corresponding second harmonic waves (SHWs) with opposite spin and doubled OAM in the second crystal. Further through a sequential SOI process, totally eight angular momentum states of the SHWs with nearly equal energy are experimentally observed. The proposed methodology may find potential applications in optical communications, parallel optical computing, optical manipulation and so on.

The quantum dynamics of the electron's spin and orbital angular momenta in semiconductor quantum rings is analyzed. Both Rashba and Dresselhaus spin-orbit interactions (SOIs) in their quasi-two-dimensional forms are taken into account. The narrow quantum rings are treated with models including one and two radial modes. We find that when either Rashba or Dresselhaus SOI acts alone, the different angular momentum states are coupled in blocks of two (for a single radial mode) or four (for two radial modes). We also show that the full Hilbert space splits into two disjoint subspaces, which are not coupled by either of the two SOIs, thereby decoupling accordingly the state evolution. When both SOI mechanisms are present, in principle infinitely many states are coupled, but we find by numerical computation of the quantum dynamics that for typical evolution times in practice only a few neighboring states are involved in the dynamics. Thus the exchange of angular momenta proceeds only via very few states. Furthermore, we find a trend that when initially high orbital momenta are prepared, the time evolution of spin and orbital momenta is almost unaffected by the availability of a second radial mode, in sharp contrast to the case of preparing the system in low orbital angular momentum states. The implications of our findings for the coherent control of angular momentum in quantum rings are pointed out.

Summary form only given.The orbital angular momentum of light is distinct from the intrinsic angular momentum associated with the polarization state of the light. Thus linearly polarized laser modes can carry angular momentum. Such orbital angular momentum is associated with light beams with helical wave fronts, one class of which are Laguerre-Gaussian laser modes. The azimuthal phase factor exp(il/spl phi/) in their field distribution, gives rise to an orbital angular momentum equivalent to l/spl planck/ per photon. Our previous investigations of second-harmonic generation using Laguerre-Gaussian modes confirmed that the conservation of orbital angular determines the mode structure of the frequency-doubled beam. It was shown that a Laguerre-Gaussian mode with an azimuthal index l is transformed into a frequency-doubled mode with twice the azimuthal index 2l, thus conserving the angular momentum within the light fields. Degenerate parametric downconversion can be considered as the inverse process to second-harmonic generation. An incoming pump wave generates two new fields, signal and idler, with half the pump frequency. Accordingly, a Laguerre-Gaussian pump beam with an even value of the azimuthal index l produces signal and idler beams that can both have integer azimuthal mode indices of l/2. Away from degeneracy, the signal and idler frequencies do not in general have an integer ratio. Consequently, the orbital angular momentum of the pump cannot be divided to give integer l-values for the signal and idler beams in the same ratio as their energy. Even for degenerate phase matching, an integer division of the orbital angular momentum will not be possible when the pump mode has an odd value of l. We investigate the role that the conservation of orbital angular momentum plays in the downconversion process.

Reactions for which the reactant (r)-to-product (p) mass ratio (mu(r)/mu(p)) is high, the well-known H + LH --> HH + L processes, convert most of available energy to product rotation, while that disposed as recoil is often regarded as negligible. In angular momentum (AM) terms, however, this recoil orbital AM (l(p)) is shown to be a critical component of the overall AM balance. For products of light mu(p), the maximum value of l(p) is energy limited and as a result the formation of products in low rotational (j(p)) states is severely restricted. Here energy constraints on recoil orbital AM and the consequent restrictions on j(p)-state populations are quantified using novel diagrammatic methods that illustrate how constraints on l(p) determine the j(p) states that are allowed or forbidden by the need to conserve energy and AM for each state-to-state transition. The method accurately predicts j(BaI)j (v=0,1,2) peaks from crossed-beam Ba + HI experiments, providing a quantitative and physically transparent rationale for the observed BaI rotational distributions. Extension to a wider range of reactions having mu(r)mu(p)>1 shows that at least some j(p) are formally forbidden for each given reactant relative velocity or, more accurately, l(r). The fraction of inaccessible product states for a given initial velocity rises rapidly with mu(r)/mu(p) (>96% in Ba + HI). The method is also used to demonstrate that recoil orbital AM will be strongly aligned parallel to product rotational AM for high mu(r)/mu(p), although this correlation is generally lost in the low j(p) region as the parallel vector requirement is relaxed.