Nonzero Orbital Angular Momentum Research Articles

Phase conjugation of twisted Gaussian Schell model beams in stimulated down-conversion

AbstractStimulated parametric down-conversion is a nonlinear optical process that can be used for phase conjugation and frequency conversion of an optical field. A precise description of the outgoing stimulated field has been developed for the case where the input pump and seed fields are coherent. However, partially coherent beams can have interesting and important characteristics that are absent in coherent beams. One example is the twist phase, a novel optical phase that can appear in partially coherent Gaussian beams and gives rise to a nonzero orbital angular momentum. Here, we consider stimulated down-conversion for partially coherent input fields. As a case study, we use twisted Gaussian Schell-Model beams as the seed and pump beams in stimulated parametric down-conversion. It is shown both theoretically and experimentally that the stimulated idler beam can be written as a twisted Gaussian Schell-Model beam, where the beam parameters are determined entirely by the seed and pump. When the pump beam is coherent, the twist phase of the idler is the conjugate of that of the seed. These results could be useful for the correction of wavefront distortion such as in atmospheric turbulence in optical communication channels, and synthesis of partially coherent beams.

Possibility of mixed helical p-wave pairings in Sr2RuO4

The exact nature of unconventional superconductivity in Sr$_2$RuO$_4$ remains a mystery. At the phenomenological level, no superconducting order parameter proposed thus far seems able to coherently account for all essential experimental signatures. Among the latter is the prominent polar Kerr effect, which implies a nonzero ac anomalous Hall conductivity. Assuming the Kerr effect is intrinsic, it can be accounted for by a bulk chiral Cooper pairing with nonzero orbital angular momentum, such as $p+ip$ or $d+id$, which, however, has difficulties in being reconciled with other experimental results. Given the situation, in this paper, we propose alternative possibilities with complex mixtures of distinct helical p-wave order parameters, namely, $A_{1u}+iA_{2u}$ and $B_{1u}+iB_{2u}$ in the group theory nomenclature. These states essentially consist of two copies of chiral p-wave pairings with opposite chirality and different pairing amplitudes, and therefore support intrinsic Hall and Kerr effects. We further show that these states exhibit salient features that may explain several other key observations in this material, including the absence of spontaneous edge current, a substantial Knight shift drop, and possibly signatures in uniaxial strain and ultrasound measurements.

Perturbative QCD analysis of near threshold heavy quarkonium photoproduction at large momentum transfer

We apply perturbative QCD to investigate the near threshold heavy quarkonium photoproduction at large momentum transfer. From an explicit calculation, we show that the conventional power counting method will be modified and the three quark Fock state with nonzero orbital angular momentum dominates the near threshold production. It carries a power behavior of 1/(−t)5 for the differential cross section. We further comment on the impact of our results on the interpretation of the experiment measurement in terms of the gluonic gravitational form factors of the proton.

Critical screening parameters and critical behaviors of one-electron systems with screened Coulomb potentials

The critical screening parameters for one-electron systems screened by Hulthén, Debye–Hückel, and exponential cosine screened Coulomb potentials are calculated with an accuracy close to the precision of numerical arithmetic. The results for a H atom with an infinitely heavy nucleus are reported from the ground to high-lying excited states, and those for arbitrary two-body charged systems are derived from the Zm-scaling law. A thorough comparison of the critical screening parameters for the ground and the first p-wave excited states with previous predictions is made to demonstrate the accuracy of our calculations. The critical behaviors of system-bound and pseudo-continuum eigenenergies for s- and non-s-wave states are shown to follow the quadratic and linear laws, respectively. The variation of the corresponding wave functions is analyzed in detail. For systems with non-zero orbital angular momenta, the bound states convert into shape-type resonances when the screening parameter exceeds the critical value. The resonance energy shares the same linear law as the pseudo-continuum state, while the resonance width varies by an l-dependent power law. It is further shown that the different asymptotic behaviors of the resonance energy and width are consistent with the complex analog of the Hellmann–Feynman theorem.

Decay of the vortex muon

Muon decay is self-analyzing: the spectral-angular distribution of the emitted electron reveals the spin orientation of the polarized muon. Here, we show that the same feature applies to muons in non-plane-wave states and helps reveal the rich polarization opportunities available. We focus on the so-called vortex states, in which the muon carries a non-zero orbital angular momentum with respect to the average propagation direction and exhibits a cone structure in the momentum distribution. We compute the spectrum and the angular distribution of the electrons emitted in decays of vortex muons and show that the most revealing observable is not the angular distribution but the fixed-angle electron spectra. Even for very small cone opening angles of the vortex muons, it will be easy to observe significant modifications of the electron spectra which would allow one to distinguish vortex muons from approximately plane wave muons, as well as to differentiate among various polarization states. These features will be the key to tracking the evolution of vortex muons in external magnetic fields.

Classification of magnetic vortices by angular momentum conservation

Superfluid vortices are quantum excitations carrying quantized amount of orbital angular momentum in a phase where global symmetry is spontaneously broken. We address a question of whether magnetic vortices in superconductors with dynamical gauge fields can carry nonzero orbital angular momentum or not. We discuss the angular momentum conservation in several distinct classes of examples from crossdisciplinary fields of physics across condensed matter, dense nuclear systems, and cosmology. The angular momentum carried by gauge field configurations around the magnetic vortex plays a crucial role in satisfying the principle of the conservation law. Based on various ways how the angular momentum conservation is realized, we provide a general scheme of classifying magnetic vortices in different phases of matter.

Vortex states in an acoustic Weyl crystal with a topological lattice defect

Crystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

Formation of Millimeter Waves with Electrically Tunable Orbital Angular Momentum

A method for forming electromagnetic waves with a tunable nonzero orbital angular momentum (OAM) is proposed. The approach is based on transforming an incident plane wave into a helical one using an electrically tunable ferroelectric lens. It uses high-resistive thin/thick film electrodes with a special discrete topology. The correlation between film electrodes topology and the highest order of OAM modes that the lens can form is described. A lens prototype based on Ba0.55Sr0.45TiO3 ferroelectric material and operating at a frequency of 60 GHz was designed, manufactured, and tested. The amplitude and phase distribution of the OAM wave with l = +1 formed by prototype were measured to confirm the effectiveness of the proposed method. The proposed lens has a combination of advantages such as low dimensions, electrical control over the OAM modes, and the possibility to operate in the millimeter wavelength range.

Converting an array of edge dislocations into a multi-vortex beam.

We theoretically show how, using a cylindrical lens, a Gaussian beam with a finite number of parallel zero-intensity lines (edge dislocations) is transformed into a vortex beam that carries orbital angular momentum (OAM) and topological charge (TC). Remarkably, while the original beam is assumed to carry a non-zero OAM and have no TC, the latter is shown to appear during free-space propagation. Considering two parallel center-symmetric zero-intensity lines located as an example, we look into the dynamics of generating two intensity nulls at the double focal length: with increasing distance between the vertical zero-intensity lines, two optical vortices are first generated on the horizontal axis before converging at the origin and then diverging along the vertical axis. Irrespective of the between-line distance, such an optical vortex has ${\rm TC} = - {2}$ at any distance from the optical axis, except for the original plane. With changing distance between the zero-intensity lines, the OAM that the beam carries is changing, taking positive and negative values, or a zero value at a certain between-line distance. We also show that if the number of zero-intensity lines is infinite, a vortex beam with finite OAM and infinite TC is generated.

Synthetic ultrawideband orbital angular momentum radar

Control of orbital angular momentum (OAM) offers the potential for increases in control and sensitivity for high-performance microwave systems. EM waves with properties dependent on spatial distribution are said to be “structured.” Control of OAM in microwave systems is an example of a wave structure that exploits EM degrees of freedom, which most conventional systems do not use. OAM is characterized by an integer OAM mode in which zero represents the case of a plane wave and nonzero OAM modes propagate with a helical wavefront. A uniform circular phased array approach is utilized to produce helix-shaped OAM wavefronts. This method offers a critical advantage over common fixed-frequency dielectric lenses; the phases of all antenna elements are programmable across a wide frequency range, which is necessary for ultrawideband (UWB) radar imaging. Simulations and laboratory experiments are performed to determine the requirements and capabilities of an UWB OAM radar that uses the circular phased array approach. Key results include OAM phase front characterization, detection of specified OAM modes, and configuration of a network analyzer UWB radar with synthetic OAM mode-control via signal post-processing.

Higher-order topology in plasmonic Kagome lattices

We study the topological properties of a Kagome plasmonic metasurface, modeled with a coupled dipole method that naturally includes retarded long range interactions. We demonstrate that the system supports an obstructed atomic limit phase through the calculation of Wilson loops. Then, we characterize the hierarchy of topological boundary modes hosted by the subwavelength array of plasmonic nanoparticles: both one-dimensional edge modes and zero-dimensional corner modes. We determine the properties of these modes, which robustly confine light at subwavelength scales, calculate the local density of photonic states at edge and corner modes frequencies, and demonstrate the selective excitation of delocalized corner modes in a topological cavity, through nonzero orbital angular momentum beam excitation.

Size-dependent optical properties of shallow quantum dot excitons close to a dielectric-hyperbolic material interface.

The resonance frequency shift and the radiative decay rate of single quantum dot excitions in close proximity to a dielectric-hyperbolic material interface are theoretically investigated. The previous nonlocal susceptibility model for a quantum-confined exciton in inhomogeneous surroundings has been substantially upgraded in a way to incorporate exciton's envelope functions with a non-zero orbital angular momentum and a dyadic Green function tensor for uniaxially anisotropic multilayer structures. Different eigenstates of spatially localized excitons are considered with a distance to the interface of half-infinite Tetradymites(Bi2Se3), a natural hyperbolic material in a visible-to-near infrared wavelength range. From numerically obtained self-energy corrections (SEC) of the exciton as a function of its spatial confinement, eigenfunction, and distance, where the real and imaginary parts correspond to the resonance frequency shift and the radiative decay rate of the exciton, respectively, both optical properties show a significant dependence on the spatial confinement of the exciton than expected. The SEC of very weakly confined (quasi free) two-dimensional excitons is almost immune to specific choice of the eigenfunction and to anisotropic properties of the hyperbolic material even at a close distance, while such conditions are decisive for the SEC of strongly confined excitons.

Spontaneous Emission of Vector Vortex Beams

Harnessing the spontaneous emission of incoherent quantum emitters is one of the hallmarks of nano-optics. Yet, an enduring challenge remains-making them emit vector beams, which are complex forms of light associated with fruitful developments in fluorescence imaging, optical trapping and high-speed telecommunications. Vector beams are characterized by spatially varying polarization states whose construction requires coherence properties that are typically possessed by lasers-but not by photons produced by spontaneous emission. Here, we show a route to weave the spontaneous emission of an ensemble of colloidal quantum dots into vector beams. To this end, we use holographic nanostructures that impart the necessary spatial coherence, polarization and topological properties to the light originating from the emitters. We focus our demonstration on vector vortex beams, which are chiral vector beams carrying non-zero orbital angular momentum, and argue that our approach can be extended to other forms of vectorial light.

Laser cooling of transition-metal atoms

We propose the application of laser cooling to a number of transition-metal atoms, allowing numerous bosonic and fermionic atomic gases to be cooled to ultra-low temperatures. The non-zero electron orbital angular momentum of these atoms implies that strongly atom-state-dependent light-atom interactions occur even for light that is far-detuned from atomic transitions. At the same time, many transition-metal atoms have small magnetic dipole moments in their low-energy states, reducing the rate of dipolar-relaxation collisions. Altogether, these features provide compelling opportunities for future ultracold-atom research. Focusing on the case of atomic titanium, we identify the metastable $a ^5F_5$ state as supporting a $J \rightarrow J+1$ optical transition with properties similar to the D2 transition of alkali atoms, and suited for laser cooling. The high total angular momentum and electron spin of this state suppresses leakage out of the the nearly closed optical transition to a branching ratio estimated below $\sim 10^{-5}$. Following the pattern exemplified by titanium, we identify optical transitions that are suited for laser cooling of elements in the scandium group (Sc, Y, La), the titanium group (Ti, Zr), the vanadium group (V, Nb), the manganese group (Mn, Tc), and the iron group (Fe, Ru).

Generation of twisted photons by undulators filled with dispersive medium

The radiation of twisted photons by undulators filled with a homogeneous dielectric dispersive medium is considered. The general formulas for the average number of radiated twisted photons are obtained. The radiation of undulators in the dipole regime and the radiation of the helical and planar wigglers are studied in detail. It is shown that the selection rules for radiation of twisted photons established for undulators in a vacuum also holds for undulators filled with a dielectric medium. In the case of a medium with plasma permittivity the lower undulator harmonics do not form. This fact can be used for generation of twisted photons with nonzero orbital angular momentum on the lowest admissible harmonic. The use of the effect of inverse radiation polarization for generation of twisted photons with larger orbital angular momentum is described. The influence of the anomalous Doppler effect on the projection of the total angular momentum of radiated twisted photons is investigated. The parameters of the undulator and the charged particles are found such that the produced radiation, in particular, the Vavilov-Cherenkov radiation, is a pure source of twisted photons with definite nonzero orbital angular momentum. The developed theory is used to describe the radiation of twisted photons by beams of electrons and protons in the undulators filled with helium. We also consider the radiation of X-ray twisted photons by electrons in the undulator filled with xenon. The parameters are chosen so as to be achievable at the present experimental facilities.

Generation of optical orbital angular momentum light by an azimuthally-graded refractive index plate

We propose and numerically demonstrate a method to generate orbital angular momentum (OAM) light by using an azimuthally graded index (AGI) plate of uniform subwavelength thickness. We illustrate, theoretically, through numerical simulations, how a plane polarized fundamental gaussian beam incident onto such an AGI plate acquires a nonzero orbital angular momentum, and exhibits an annular far-field intensity profile with a phase singularity line along its axis. We further confirm the OAM property of the output beam by calculations of the overlap integral between its far-field and the paraxial Laguerre Gaussian modes of nonzero OAM. We also highlight the advantages of the proposed AGI plate over existing methods to generate OAM light.

Phase-matching analysis in high-order harmonic generation with nonzero orbital angular momentum Laguerre-Gaussian beams

Through high-order harmonic generation driven by intense ultrashort vortex infrared or midinfrared lasers, a nonzero orbital angular momentum can be imprinted onto extreme ultraviolet (XUV) or soft-x-ray (SXR) light pulses. Here we simulate the generation of vortex XUV harmonics in the gas medium as well as their propagation in vacuum till reaching the far field. We find that the intensity and phase of generated high harmonics are very sensitive to the position of gas jet with respect to the laser focus. The topological charge of the $q\mathrm{th}$ harmonic is found to be $q$ times that of the driving Laguerre-Gaussian beam. Each harmonic in the far field appears as a single ring in the transverse plane with an invariant diameter which is scalable with the fundamental topological charge only when the gas jet is placed after the laser focus. The underlying phase-matching mechanism is analyzed by examining the spatial map of the coherence length and by calculating the evolution of harmonic emission in the medium. We anticipate this work to stimulate interest in generating intense vortex XUV or SXR attosecond pulses for probing dynamics of molecules where special molecular features are difficult to be detected with linear or circular XUV or SXR pulses.

Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces

The breathing honeycomb lattice hosts a topologically non-trivial bulk phase due to the crystalline-symmetry of the system. Pseudospin-dependent edge states, which emerge at the interface between trivial and non-trivial regions, can be used for the directional propagation of energy. Using the plasmonic metasurface as an example system, we probe these states in the near- and far-field using a semi-analytical model. We provide the conditions under which directionality was observed and show that it is source position dependent. By probing with circularly-polarised magnetic dipoles out of the plane, we first characterise modes along the interface in terms of the enhancement of source emissions due to the metasurface. We then excite from the far-field with non-zero orbital angular momentum beams. The position-dependent directionality holds true for all classical wave systems with a breathing honeycomb lattice. Our results show that a metasurface in combination with a chiral two-dimensional material, could be used to guide light effectively on the nanoscale.

Twisted particle collisions: A new tool for spin physics

Collisions of twisted particles --- that is, non-plane-wave states of photons, electrons, or any other particle, equipped with a non-zero orbital angular momentum (OAM) with respect to its propagation direction --- offer novel ways to probe particle structure and interactions. In the recent paper \cite{Ivanov:2019vxe}, we argued that resonance production in twisted photon collisions or twisted $e^+e^-$ annihilation gives access to parity- and spin-sensitive observables in inclusive cross sections, even when the initial particles are unpolarized. Here, we explore these features in detail, providing a qualitative picture and illustrating it with numerical examples. We show how one can detect parity-violating effects in collisions of unpolarized twisted photons and how one can produce almost $100\%$ polarized vector mesons in unpolarized twisted $e^+e^-$ annihilation. These examples highlight the unprecedented level of control over polarization offered by twisted particles, impossible in the usual plane wave collisions.

Doing Spin Physics with Unpolarized Particles

Twisted, or vortex, particles refer to freely propagating non-plane-wave states with helicoidal wave fronts. In this state, the particle possesses a nonzero orbital angular momentum with respect to its average propagation direction. Twisted photons and electrons have been experimentally demonstrated, and creation of other particles in twisted states can be anticipated. If brought in collisions, twisted states offer a new degree of freedom to particle physics, and it is timely to analyze what new insights may follow. Here, we theoretically investigate resonance production in twisted photon collisions and twisted e^{+}e^{-} annihilation and show that these processes emerge as a completely novel probe of spin and parity-sensitive observables in fully inclusive cross sections with unpolarized initial particles. This is possible because the initial state with a nonzero angular momentum explicitly breaks the left-right symmetry even when averaging over helicities. In particular, we show how one can produce almost 100% polarized vector mesons in unpolarized twisted e^{+}e^{-} annihilation and how to control its polarization state.