Orbital Angular Momentum Quantum Number Research Articles

The dynamical evolution of exciton-polaritons in asymmetric ring-step potential well

Abstract The exciton-polariton, a quasi-particle formed by the coupling of excitons and photons, exhibits a semi-light-semi-matter nature, inheriting the advantages of both constituents and capable of achieving Bose-Einstein condensation at room temperature. This paper investigates the evolution of superposition states of semiconductor microcavity exciton-polariton Bose-Einstein condensate (BEC) within a ring-shaped structure. By employing theoretical modeling, the time-dependent dynamics of the superposition states of exciton-polaritons bound within a unique ring-step asymmetric potential well structure are analyzed. The study reveals correlations between the potential well structure of this step-like configuration and the transitions of exciton-polariton BEC superposition states, shedding light on the evolution paths of BEC systems under specific structural influences and the fluctuation patterns of excitonic fields. These findings hold relevance for experimental manipulations of exciton-polariton superposition states within microcavities. The research demonstrates that ring-step potential well structures influence the excitation and evolution of exciton-polariton BEC superposition states, leading to transitions towards higher or lower order states. This transition is reflected macroscopically in alterations in the number and spatial distribution of interference petals in the superposition states. We consider initial states with orbital angular momentum quantum number l = 2, 3, 4, respectively. By exploiting the different structural relationships of ring-step potential wells, we achieve controlled evolutions of macroscopic occupation states, with interference petal numbers ranging from 4 to 6, 4 to 8, 6 to 8, 6 to 10, 8 to 10, 8 to 12, and 6 to 4.

Modulation effect of focusing mirror on beam propagation through anisotropic turbulence

In this study, we modulated the Bessel-Gaussian (BG) beam using a focusing mirror to enhance the performance of wireless optical communication (WOC) while considering the angles between turbulence cells and the transmitted direction when beams propagate through anisotropic atmospheric turbulence along a slant path. Numerical results reveal that when the BG beam is modulated by a focusing mirror with a focusing length of 1 km, the detection probability of orbital angular momentum (OAM) is increased by 9.06% compared with the unmodulated BG beam when the OAM quantum number is 1. Simultaneously, this modulation method effectively reduces the bit error rate and enhances the channel capacity in OAM-based WOC. Furthermore, we observed that the smaller the OAM number, the better the effect of the modulation. Through our analysis, we identified that the most significant distortions in OAM mode propagation occur at the exponential parameter approximately 3.1 in the modified von Karman spectrum. Moreover, we demonstrated that the effects of the anisotropic tilt angle can not be negligible for beams through a slant path. Therefore, the modulation of the focusing mirror, in combination with a well-designed propagation direction that takes appropriate angles into account, can significantly improve the overall quality and performance of optical communication systems.

Analytical solutions for the Klein–Gordon equation with combined exponential type and ring-shaped potentials

In this study, we have successfully obtained the analytical solutions for the Klein–Gordon equation with new proposed a non-central exponential potential Vr=D1-σ0coth(αr)2+(η1+η2cosθ)/r2sin2θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V\\left( r \\right) = D\\left[ {1 - \\sigma_{0} \\coth (\\alpha r)} \\right]^{2} + (\\eta_{1} + \\eta_{2} \\cos \ heta )/r^{2} \\sin^{2} \ heta$$\\end{document}. Our approach involves a proper approximation of the centrifugal term, with l′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${l}{\\prime}$$\\end{document} representing the generalized orbital angular momentum quantum number, and the utilization of the Nikiforov–Uvarov method. The resulting radial and angular wave functions are expressed in terms of Jacobi polynomials, and the corresponding energy equation is also derived. Our calculations of the eigenvalues for arbitrary quantum numbers demonstrated significant sensitivity to potential parameters and quantum numbers. Additionally, we evaluate the dependence of energy eigenvalues on screening parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} for arbitrary quantum numbers nr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_{r}$$\\end{document} and N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N$$\\end{document} to establish the accuracy of our findings. Furthermore, we determine the non-relativistic limits of the radial wave function and energy equation, which align with corresponding previous results in the case where η1=η2=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta_{1} = \\eta_{2} = 0$$\\end{document}.

Optically controlled ultrafast dynamics of skyrmion in antiferromagnets

The optical vortex, an optical beam carrying orbital angular momentum (OAM), has been demonstrated to be promising in manipulating magnetic structure and its dynamics in various systems. In this work, by using numerical and analytical methods, we investigate the optical vortex control of the ultrafast dynamics of skyrmion in antiferromagnets. It is shown that an isolated skyrmion can be generated/erased in an ultrashort time of $\ensuremath{\sim}\mathrm{ps}$ by beam focusing through the Zeeman effect. Subsequently, the OAM can be transferred to the skyrmion and results in its rotation. Different from the case of ferromagnets, the skyrmion rotation direction in antiferromagnets depends on the light frequency, allowing an easy control of the skyrmion rotation via tuning the frequency of light beam. Furthermore, the skyrmion Hall motion, driven by multipolar spin waves that are excited by optical vortex, is revealed in our calculations, demonstrating the dependence of the Hall angle on the OAM quantum number. This work unveils the interesting optical control of the skyrmion dynamics in antiferromagnets, which is a crucial step towards the development of magneto-optic and spintronic applications.

Generation and characteristics of an anomalous Airy vortex beam from a Lommel vortex beam

A practical method for generating an anomalous Airy vortex beam is proposed, and characteristics of this novel kind beam are investigated. Results show that orbital angular momentum (OAM) quantum number n could be used to modulate the profiles of vortex rings, asymmetric parameter c would cause the beam rotation and phase distortion, and when increase control parameters α and β, more energy would concentrate on the side lobes, and the side lobes in the x-direction and y-direction separately would expand laterally and longitudinally, respectively. Particularly, the position and moving direction of the light spot could be controlled precisely according to the actual needs by altering the phase shift proportional coefficients p and q. Our work would extend potential applications of the mixed vortex beams in optical micro-manipulation and optical trapping.

Spin-textured neutron beams with orbital angular momentum

We present a rigorous theoretical framework underpinning the technique of spin-echo modulated small-angle neutron scattering (SEMSANS), and show how the technique can be extended in order to generate spin-textured neutron beams with orbital angular momentum (OAM) via birefringent neutron spin-polarization devices known as magnetic Wollaston prisms. Neutron OAM beams are mathematically characterized by a ``cork-screw'' phase singularity ${e}^{i\ensuremath{\ell}\ensuremath{\phi}}$ about the propagation axis where $\ensuremath{\ell}$ is the OAM quantum number. To understand the precise relationship between the emergent OAM state and the variety of spin textures realized by various setups, we have developed a path-integral approach that in the interferometric limit makes a judicious use of magnetic Snell's law. We show that our proposed technique produces a complex two-dimensional pattern of spin-OAM entangled states which may be useful as a probe of quantum magnetic materials. We compare our path-integral approach to the well-known single-path Larmor precession model and present a pedagogical derivation of magnetic Snell's law of refraction for both massive and massless particles based on Maupertuis's action principle.

Vortex X-wave propagation through von Kármán oceanic turbulence with anisotropy.

Vortex X-waves with coupling effects of orbital angular momentum (OAM) and spatiotemporal invariance are introduced into the research of underwater wireless optical communication systems (UWOCSs). We establish the OAM probability density of vortex X-waves and channel capacity of UWOCS using Rytov approximation and correlation function. Furthermore, an in-depth analysis of OAM detection probability and channel capacity is performed on vortex X-waves carrying OAM in von Kármán oceanic turbulence with anisotropy. The results show that an increase in OAM quantum number results in a "hollow X" shape in the received plane, where the energy of vortex X-waves is injected into the lobes, reducing the received probability of the vortex X-waves transmitted to the receiving end. As the Bessel cone angle increases, the energy gradually concentrates toward the energy distribution center, and the vortex X-waves become more localized. Our research may trigger the development of UWOCS for bulk data transfer based on OAM encoding.

Fully-Stripped Beryllium-Ion Collisions with 2ℓm States of Atomic Hydrogen: Target Excitation and Ionisation cross Sections

The wave-packet convergent close-coupling approach is used to calculate integrated target excitation and ionisation cross sections in bare beryllium-ion collisions with the 2ℓm states of atomic hydrogen (where n, ℓ and m are the principal, orbital angular momentum and magnetic quantum numbers, respectively). The calculations are performed at representative projectile energies between 10 keV/u to 1 MeV/u. The calculated cross sections for collisions with H(2s) are compared with recent theoretical results. Generally, good agreement is observed for the n-partial excitation and total ionisation cross sections. However, a significant discrepancy is found for excitation into the dominant n=3 states at 100 keV/u, where the target excitation cross-section peaks. We also present the first calculations of the excitation and ionisation cross sections for Be4+ collisions with H(2p0) and H(2p±1).

Spectroscopy of nanoantenna-covered Cu2O : Towards enhancing quadrupole transitions in Rydberg excitons

Plasmonic antennas channel incoming light into a confined near field that comes along with strong field gradients at the edges. Transverse field gradients are capable of driving quadrupole transitions in a more effective way than the weak longitudinal field gradient in dipolar light. Cuprous oxide Rydberg excitons with principal quantum number $n$ between 5 and 15 are several tens to a few hundreds of nanometers in diameter and can have different orbital angular momentum quantum numbers. Usually, only $P$- and $F$-excitons are electric dipole allowed, while $S$- and $D$-excitons remain dark. Here, we use 30-nm-wide and 60- to 110-nm-long plasmonic aluminum nanoantennas deposited on the cuprous oxide crystal surface to create transverse field gradients in similar spatial dimensions as the size of the Rydberg excitons. This way, light field and matter wave function overlap spatially and quadrupole transitions of $S$excitons are enhanced. The relative enhancement of the $S$-exciton oscillator strength with respect to the $P$-exciton oscillator accounts for a factor of up to 1.4.

Twisted Magnon Frequency Comb and Penrose Superradiance.

Quantization effects of the nonlinear magnon-vortex interaction in ferromagnetic nanodisks are studied. We show that the circular geometry twists the spin-wave fields with spiral phase dislocations carrying quantized orbital angular momentum (OAM). Meanwhile, the confluence and splitting scattering of twisted magnons off the gyrating vortex core (VC) generates a frequency comb consisting of discrete and equally spaced spectral lines, dubbed as twisted magnon frequency comb (TMFC). It is found that the mode spacing of the TMFC is equal to the gyration frequency of the VC and the OAM quantum numbers between adjacent spectral lines differ by one. By applying a magnetic field perpendicular to the plane of a thick nanodisk, we observe a magnonic Penrose superradiance inside the cone vortex state, which mimics the amplification of particles scattered from a rotating black hole. It is demonstrated that the higher-order modes of TMFC are significantly amplified while the lower-order ones are trapped within the VC gyrating orbit which manifests as the ergoregion. These results suggest a promising way to generate twisted magnons with large OAM and to drastically improve the flatness of the magnon comb.

Three-dimensional photoelectron holography with trichromatic polarization-tailored laser pulses

We present a three-dimensional (3D) photoelectron wave packet holography scheme based on polarization-tailored trichromatic femtosecond laser pulses for the determination of quantum phases in atomic multiphoton ionization (MPI). Experimentally, we combine supercontinuum polarization pulse shaping with photoelectron tomography for the reconstruction of the 3D photoelectron momentum distribution (PMD). To demonstrate the 3D photoelectron holography scheme, we superimpose a sculptured wave packet encoding a relative continuum phase with a reference wave packet. In particular, we create a sculptured angular momentum superposition wave packet by (2 + 1) resonance-enhanced MPI of potassium atoms using a counter-rotating circularly polarized bichromatic pulse sequence. The sculptured wave packet, consisting of states with different orbital angular momentum quantum numbers, interferes with the reference wave packet generated by direct three-photon ionization with a circularly polarized pulse of the third color. Depending on the circularity of the reference pulse, interference of both wave packets gives rise to 3D photoelectron holograms with c 2 or c 4 rotational symmetry in the laser polarization plane, i.e., in the azimuthal direction. In the polar direction, the azimuthal interference pattern undergoes a phase-shift revealing the relative quantum phase between the p- and f-type continuum partial waves in the sculptured wave packet. We determine the relative continuum phase by fitting the parameters of an analytical model of the hologram to the measured 3D PMD and confirm the result by direct extraction of the continuum phase difference from the polar-angle-dependent azimuthal phase-shift of the photoelectron angular distribution.

Effects of ocean turbulence on photon orbital angular momentum quantum communication

The effect of the turbulent motion of ocean on the quantum communication based on the orbital angular momentum in an underwater quantum channel is studied in this work. Based on the power spectrum model of ocean turbulence proposed by Elamassie, the quantitative relationships of different ocean turbulence parameters with the single photon detection probability of orbital angular momentum photons, the channel capacity, the key generation rate, the concurrence of two entangled photons are proposed. The maximum entanglement distance of the orbital angular momentum entangled photon-pairs in the ocean turbulence is further studied by the universal entanglement decay of the concurrence of entangled photon-pairs in the ocean turbulence. The results show that the detection probability of single photon, the channel capacity, the key generation rate, and the concurrence of entangled photon-pairs decrease with the increase of the dissipation rate of turbulent kinetic energy and the decrease of the rate of dissipation of mean-squared temperature. The influence of the temperature and salinity balance parameter of ocean turbulence on the performance of underwater quantum communication are significantly different under the condition of whether the stable stratification of seawater is assumed or not. In the ocean turbulent environment, the increasing of the initial orbital angular momentum quantum number of signal photons can improve the key generation rate of quantum key distribution and the resistance of entangled photons to entanglement decay.

Optical trapping force on two types of particles with a focused partially coherent Lommel-Gaussian beam

In order to explore the capture of two types of particles with different refractive-indexes with focused partially coherent Lommel-Gaussian beam (PCLGB), we numerically derived the expressions of the intensity, and its distribution is also simulated. We found that the focused PCLGB is able to capture two high refractive-index particles at different positions on the focal plane and a low refractive-index particle at the focus, respectively. when the orbital angular momentum (OAM)quantum number, lens focal length, asymmetry parameter decreased, and the spatial correlation length and beam waist increased, the transverse gradient force of the focused PCLGB increased; when the OAM quantum number, lens focal length, asymmetry parameter, spatial correlation length decreased and the beam waist increased, the axial gradient force and scattering force of the focused PCLGB increased. We can choose the optimum optical and lens parameters, a large range and stable trapping can be achieved. The obtained results have certain reference value for the focused PCLGB applied in micromanipulation technology and biotechnology.

Received probability of perfect optical vortex in absorbent and weak turbulent seawater links.

We investigated the effects of absorbent and weak turbulent seawater channels on the orbital angular momentum (OAM) mode carried by perfect optical vortex (POV) based on the Rytov approximation. After deriving the received probability of OAM modes, some numerical results are worked out to show that the receiving probability of OAM modes decreases linearly with the increase of virtual refractive index of the water body. An underwater communication link with POV as the signal carrier can obtain high receiving probability by adopting long signal wavelength in intervals of "seawater window wavelength," low OAM quantum number, a POV with a larger ring radius, and a transmitter as well as receiver with a smaller aperture. The transmission distance of OAM mode carried by POV in four kinds of seawater is better than that of a Bessel-Gaussian beam.

Probability of orbital angular momentum for square Hermite–Gaussian vortex pulsed beam in oceanic turbulence channel

By the theory of localized waves and the vectorial solution of the Maxwell equation, we develop and explore the vector characteristics of the new square Hermite–Gaussian vortex pulsed beam possessing orbital angular momentum (OAM). To investigate the propagation performance of this new beam, the measurement probability model of OAM states for square Hermite–Gaussian vortex pulsed beam propagation through oceanic turbulence is built. We discover through the numerical simulation that a large propagation distance causes a large delay of arrival time for this vortex pulsed beam. Under the same conditions, both the measurement signal probability and the measurement crosstalk probability of OAM states reach the peak at the arrival time. The wide initial half-pulse width and the low OAM quantum number can improve a measurement signal probability and decrease a measurement crosstalk probability of OAM states. Oceanic turbulence with a weak dissipation rate of mean-squared temperature, a small temperature and salinity ratio, a long inner scale and a strong dissipation rate of turbulent kinetic energy has a weak disturbance on the measurement signal probability and a strong disturbance on the measurement crosstalk probability of OAM states for the square Hermite–Gaussian vortex pulsed beam.

Variational Method for Hydrogen Atom Embedded in Non-ideal Classical Plasmas

The energies, radial moments, and radial distributions of different bound states [ $$n=1-6$$ , $$l=0-5$$ ; n and l being the principal and orbital angular momentum quantum numbers, respectively] of hydrogen atom embedded in non-ideal plasma background have been estimated under the framework of variational method. In order to study the effect of non-ideality, the same structural properties are also determined under the ideal classical plasma environment.

Structural properties of Na atom under impenetrable spatial confinement

The structural properties and radial distributions of the valence electron in different excited levels of Na atom (n = 3–5, l = 0–4; n and l being the principal and orbital angular momentum quantum numbers, respectively) under impenetrable spherical confinement have been studied, where the interaction between the frozen core and the valence electron is mimicked by a model potential available in the literature. The effect of the core on the valence electron has been investigated by estimating the structural properties of Na10+ ion under similar confinement. Scaled radial densities at the nucleus and related ratios are presented for a few excited states of the valence electron of Na atom and the corresponding analytic results have been tested numerically.

Switchable X-Ray Orbital Angular Momentum from an Artificial Spin Ice.

Artificial spin ices (ASI) have been widely investigated as magnetic metamaterials with exotic properties governed by their geometries. In parallel, interest in x-ray photon orbital angular momentum (OAM) has been rapidly growing. Here we show that a square ASI with a patterned topological defect, a double edge dislocation, imparts OAM to scattered x rays. Unlike single dislocations, a double dislocation does not introduce magnetic frustration, and the ASI equilibrates to its antiferromagnetic (AFM) ground state. The topological charge of the defect differs with respect to the structural and magnetic order; thus, x-ray diffraction from the ASI produces photons with even and odd OAM quantum numbers at the structural and AFM Bragg conditions, respectively. The magnetic transitions of the ASI allow the AFM OAM beams to be switched on and off by modest variations of temperature and applied magnetic field. These results demonstrate ASIs can serve as metasurfaces for reconfigurable x-ray optics that could enable selective probes of electronic and magnetic properties.

VPA: Computer program for the computation of the phase shift in atom–atom potential scattering using the Variable Phase Approach

A computer code for the computation of the phase shift in atom–atom and electron–atom potential scattering is presented. The phase shift is the central quantity required for the calculation of all types of scattering cross sections. The program uses the Variable Phase Approach (VPA). This is the only exact method for the direct calculation of the scattering phase shift. All other methods are based on examining the large distance behavior of the exact solution of the Schrödinger equation. Such methods yield the phase shift only modulo π. The absolute value of the phase shift and its variation with scattering energy is, however, needed for a full understanding of the scattering process, such as for instance in the study of shape resonances and Glory oscillations. The VPA has been sparingly used owing to the instability of the underlying equations and the consequent difficulty of writing computer code to solve them. We present a computer code for the efficient implementation of the VPA method for atom–atom scattering problems over a wide range of scattering energies. The code works for potentials which are singular and for those that are non-singular at the origin. An example of the implementation of the code is given for both an interaction potential with an attractive well and for a purely repulsive potential. Program summaryProgram title: VPA:Variable Phase ApproachCPC Library link to program files: https://dx.doi.org/10.17632/zh248d2362.1Code Ocean capsule: https://dx.doi.org/10.24433/CO.8146850.v1Licensing provisions: GNU General Public License 3 (GPL)Programming language: Fortran 90Nature of problem: To compute the quantum mechanical phase shift in an atom–atom or an electron–atom potential scattering problem. The interaction potential, dependent on a single radial coordinate, is defined by the user.Solution method: The Variable Phase Approach is used. This is the only available method for the direct calculation of the phase shift. The initial internuclear separation for the integration is chosen with the help of the analytical solution for a hard sphere core for all orbital angular momentum quantum numbers L of interest. The first-order nonlinear equation is integrated numerically with a modified LSODA19,20 program. The analytic formula for calculation of the Jacobian of the equation is also provided.Additional comments including restrictions and unusual features: Computer codes for the atom–atom interaction potential, POTENT1, and for its derivative with respect to the inter nuclear separation, DPOTENT1, must be supplied by a user. The calculation of the spherical Bessel and Neumann functions required is performed explicitly for large l angular momentum quantum numbers where the standard upward iterative generation of the functions becomes unstable.

Structural properties of Li atom under quantum and classical plasmas: A composite variational framework

AbstractStructural properties of 1s2nl (2L) [n = 2–5, l = 0–4; where, n and l are the principal quantum number and orbital angular momentum quantum number, respectively] states of Li atom embedded in classical weakly coupled plasma (WCP) and dense quantum plasma (DQP) have been discussed. The Debye‐Hckel potential or the screened‐Coulomb potential (SCP) and exponential‐cosine‐screened Coulomb potential (ECSCP) have been used to mimic the WCP and DQP, respectively. Li atom has been treated as a composite system with a frozen core Li+ ion and a chemically active valence electron. The Rayleigh‐Ritz variational method with Hylleraas‐type basis set has been used to estimate the energy eigenvalue of 1s2 (1S) state of Li+ ion core and a pure exponential basis has been considered to compute the energy of nl (2L) states of the valence electron of Li atom. The influence of ECSCP and SCP on the radial probability distribution of the valence electron of the Li atom has also been studied.