Angular Momentum Channels Research Articles

Optical Orbital Angular Momentum Demultiplexing and Channel Equalization by Using Equalizing Dammann Vortex Grating

A novel equalizing Dammann vortex grating (EDVG) is proposed as orbital angular momentum (OAM) multiplexer to realize OAM signal demultiplexing and channel equalization. The EDVG is designed by suppressing odd diffraction orders and adjusting the grating structure. The light intensity of diffraction is subsequently distributed evenly in the diffraction orders, and the total diffraction efficiency can be improved from 53.22% to 82%. By using the EDVG, OAM demultiplexing and channel equalization can be realized. Numerical simulation shows that the bit error rate (BER) of each OAM channel can decrease to 10-4 when the bit SNR is 22 dB, and the intensity is distributed over the necessary order of diffraction evenly.

Pairing of particle-hole symmetric composite fermions in half-filled Landau level

In a recent proposal of the half-filled Landau level, the composite fermions are taken to be Dirac particles and particle-hole symmetric. Cooper pairing of these composite fermions in different angular momentum channels, $\ell$, can give rise to different kinds of Pfaffian states. In addition to the well known Moore-Read Pfaffian and anti-Pfaffian states, a new putative particle-hole symmetric Pfaffian state, corresponding to the $s-$wave pairing channel, was also proposed. However, the possible underlying pairing mechanism is not clear at all. In this work we provide a specific pairing mechanism for realizing some of these Pfaffian states. We show that there can be nonzero pairing in angular momentum channels $|\ell|\ge 1$ depending on the magnitude of a coupling constant. There is a quantum phase transition from the Dirac composite fermi liquid state to Cooper pairing states in angular momentum channels $|\ell|\ge 1$ as the coupling constant is tuned across its critical point value. Surprisingly the particle-hole symmetric $\ell=0$ channel pairing turns out to be impossible irrespective of the size of the coupling constant.

Delay in Space: Orbital Angular Momentum Beams Transmitting and Receiving in Radio Frequency

ABSTRACTUsing an orbital angular momentum-based communication system to increase the channel capacity has recently attracted more and more attention. This article proposes a novel antenna array to transmit and receive orbital angular momentum beams at a radio frequency (3 GHz) by using delay in space. Different from the well-known uniform circular array which needs a phase-shifting network, every element in the proposed helicoidal array has the same phase. As long there are enough array elements and a power divider, arbitrary orbital angular momentum mode can be generated easily by only changing the positions of the array elements without any phase-shifting. In this experiment, l = 1 and l = 2 helicoidal arrays with eight half-wavelength dipoles are fabricated. The simulated and measured results, such as S parameters, near-field orbital angular momentum properties, far-field orbital angular momentum properties, the channel isolation between different orbital angular momentum channel, and the packet-loss-rate of an orbital angular momentum-based communication system using the helicoidal arrays, are presented, which shows that a helicoidal array can indeed generate arbitrary orbital angular momentum mode. Moreover, different kinds of antenna arrays can be constructed using delay in space and delay in phase together. The authors propose a crossed array to generate orbital angular momentum beams in four directions. The simulation and experimental results of the crossed array are demonstrated. Delay in space is another degree of freedom to generate orbital angular momentum beams in radio frequency.

Rashba scattering in the low-energy limit

We study potential scattering in a two-dimensional electron gas with Rashba spin-orbit coupling in the limit that the energy of the scattering electron approaches the bottom of the lower spin-split band. Focusing on two spin-independent circularly symmetric potentials, an infinite barrier and a delta-function shell, we show that scattering in this limit is qualitatively different from both scattering in the higher spin-split band and scattering of electrons without spin-orbit coupling. The scattering matrix is purely off-diagonal with both off-diagonal elements equal to one, and all angular momentum channels contribute equally; the differential cross section becomes increasingly peaked in the forward and backward scattering directions; the total cross section exhibits quantized plateaus. These features are independent of the details of the scattering potentials, and we conjecture them to be universal. Our results suggest that Rashba scattering in the low-energy limit becomes effectively one-dimensional.

Broadband In-Plane Light Bending With a Doublet Silicon Nanopost Array

The in-plane tailoring of light propagation is significant in on-chip optical interconnections. Recently, an in-plane negative-angle refraction was realized with a thin line of silicon nanoposts, which are at resonance in the first angular momentum channel. This advancement is different from metasurface research, which mostly focuses on out-of-plane operations. In this paper, we experimentally demonstrate that a thin array of doublet silicon nanoposts, in which each unit comprises two tangent nanoposts functioning as an upright interface, remarkably improve efficiency for molding light. The designed upright interface exhibits a broadband response featuring high efficiency in a negative-angle light bending in the wavelength of 1480–1600 nm. The broadband, compactness, low loss, and complementary metal–oxide semiconductor (CMOS) compatibility enable the use of the subwavelength array as an alternative component for on-chip optical control.

Landau Theory of Helical Fermi Liquids.

We construct a phenomenological Landau theory for the two-dimensional helical Fermi liquid found on the surface of a three-dimensional time-reversal invariant topological insulator. In the presence of rotation symmetry, interactions between quasiparticles are described by ten independent Landau parameters per angular momentum channel, by contrast with the two (symmetric and antisymmetric) Landau parameters for a conventional spin-degenerate Fermi liquid. We project quasiparticle states onto the Fermi surface and obtain an effectively spinless, projected Landau theory with a single projected Landau parameter per angular momentum channel that captures the spin-momentum locking or nontrivial Berry phase of the Fermi surface. As a result of this nontrivial Berry phase, projection to the Fermi surface can increase or lower the angular momentum of the quasiparticle interactions. We derive equilibrium properties, criteria for Fermi surface instabilities, and collective mode dispersions in terms of the projected Landau parameters. We briefly discuss experimental means of measuring projected Landau parameters.

The Effect of Tilted Magnetic Field in Graphene Cone

We investigate the combined effect of both homogeneous and tilted magnetic fields on the energy spectrum of gapped graphene cones together with long range Coulomb impurity in the framework of perturbation theory. The results illustrate that the tilted magnetic field can significantly affect the spectrum of single particle low-energy effective Hamiltonian, besides lifting the degeneracy of angular momentum channels in the presence of topological defects. The breaking of the electron-hole symmetry by magnetic fields is explained as a direct consequence of sub band Landau-level coupling.

Low energy scattering cross section ratios ofN14(p,p)N14

Background: The slowest reaction in the first CNO cycle is $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$, therefore its rate determines the overall energy production efficiency of the entire cycle. The cross section presents several strong resonance contributions, especially for the ground-state transition. Some of the properties of the corresponding levels in the $^{15}\mathrm{O}$ compound nucleus remain uncertain, which affects the uncertainty in extrapolating the capture cross section to the low energy range of astrophysical interest.Purpose: The $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$ cross section can be described by using the phenomenological $R$ matrix. Over the energy range of interest, only the proton and $\ensuremath{\gamma}$-ray channels are open. Since resonance capture makes significant contributions to the $^{14}\mathrm{N}(p,\ensuremath{\gamma})^{15}\mathrm{O}$ cross section, resonant proton scattering data can be used to provide additional constraints on the $R$-matrix fit of the capture data.Methods: A 4 MV KN Van de Graaff accelerator was used to bombard protons onto a windowless gas target containing enriched $^{14}\mathrm{N}$ gas over the proton energy range from ${E}_{p}=1.0$ to 3.0 MeV. Scattered protons were detected at ${\ensuremath{\theta}}_{\text{lab}}=90, {120}^{\ensuremath{\circ}}, {135}^{\ensuremath{\circ}}, {150}^{\ensuremath{\circ}}$, and ${160}^{\ensuremath{\circ}}$ using ruggedized silicon detectors. In addition, a 10 MV FN Tandem Van de Graaff accelerator was used to accelerate protons onto a solid Adenine (${\mathrm{C}}_{5}{\mathrm{H}}_{5}{\mathrm{N}}_{5}$) target, of natural isotopic abundance, evaporated onto a thin self-supporting carbon backing, over the energy range from ${E}_{p}=1.8$ to 4.0 MeV. Scattered protons were detected at 28 angles between ${\ensuremath{\theta}}_{\text{lab}}=30.{4}^{\ensuremath{\circ}}$ and $167.{7}^{\ensuremath{\circ}}$ by using silicon photodiode detectors.Results: Relative cross sections were extracted from both measurements. While the relative cross sections do not provide as much constraint as absolute measurements, they greatly reduce the dependence of the data on otherwise significant systematic uncertainties, which are more difficult to quantify. The data are fit simultaneously using an $R$-matrix analysis and level energies and proton widths are extracted. Even with relative measurements, the statistics and large angular coverage of the measurements result in more confident values for the energies and proton widths of several levels; in particular, the broad resonance at ${E}_{\text{c.m.}}=2.21$ MeV, which corresponds to the $3/{2}^{+}$ level at ${E}_{x}=9.51$ MeV in $^{15}\mathrm{O}$. In particular, the $s$- and $d$-wave angular-momentum channels are separated.Conclusion: The relative cross sections provide a consistent set of data that can be used to better constrain a full multichannel $R$-matrix extrapolation of the capture data. It has been demonstrated how the scattering data reduce the uncertainty through a preliminary Monte Carlo uncertainty analysis, but several other issues remain that make large contributions to the uncertainty, which must be addressed by further capture and lifetime measurements.

Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings

Data transmission rates in optical communication systems are approaching the limits of conventional multiplexing methods. Orbital angular momentum (OAM) in optical vortex beams offers a new degree of freedom and the potential to increase the capacity of free-space optical communication systems, with OAM beams acting as information carriers for OAM division multiplexing (OAM-DM). We demonstrate independent collinear OAM channel generation, transmission and simultaneous detection using Dammann optical vortex gratings (DOVGs). We achieve 80/160 Tbit s−1 capacity with uniform power distributions along all channels, with 1600 individually modulated quadrature phase-shift keying (QPSK)/16-QAM data channels multiplexed by 10 OAM states, 80 wavelengths and two polarizations. DOVG-enabled OAM multiplexing technology removes the bottleneck of massive OAM state parallel detection and offers an opportunity to raise optical communication systems capacity to Pbit s−1 level. Dammann gratings are used to realize multiplexing based on the generation, transmission and detection of optical angular momentum (OAM). The OAM of optical vortex beams offers a new degree of freedom for multiplexing and hence the promise of higher data communication rates, but massive parallel detection of OAM states has proved challenging. Now, researchers in China, Australia and Singapore have used Dammann optical vortex gratings (DOVGs) to realize multiplexing of massive OAM channels with individual modulation and simultaneous detection capabilities. They achieved a data capacity of 80 Tbit s−1 by multiplexing 1600 channels using ten OAM states, 80 wavelengths and two polarizations. This DOVG-enabled OAM multiplexing technology removes the bottleneck of massive parallel detection of OAM states and has the potential to increase optical communication capacities to the Pbit s−1 level.

Tuning the pseudo-Zeeman splitting in graphene cones by magnetic field

The effect of a homogeneous magnetic field on the energy spectrum of gapped graphene cones with long range charged Coulomb impurity is investigated within the framework of the perturbation theory. It is found that, besides lifting the degeneracy of angular momentum channels due to topological defects, the size of the corresponding splitting is enhanced by the introduction of a homogeneous magnetic field. This indicates that the level splitting may be controlled by the strength of a magnetic field in topological cones. Therefore, our results show that the magnetic field may be used as a tool to tune the pseudo-Zeeman splitting in graphene cones.

Nuclear pairing from two-body microscopic forces: analysis of the Cooper pair wavefunctions

In a recent paper we studied the behavior of the pairing gaps $\Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations employed realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. In this contribution, after a detailed description of the numerical method we employed in the solution of the BCS equations, we will show a preliminary analysis of the Cooper pair wavefunctions.

Nuclear pairing from two-body microscopic forces: analysis of the Cooper pair wavefunctions

In a recent paper we studied the behavior of the pairing gaps $\Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations employed realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. In this contribution, after a detailed description of the numerical method we employed in the solution of the BCS equations, we will show a preliminary analysis of the Cooper pair wavefunctions.

Nuclear pairing from microscopic forces: Singlet channels and higher-partial waves

Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process. Purpose: We plan to study the behavior of the pairing gaps $\Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations will employ realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. Methods: The superfluid states of neutron and nuclear matter are studied by solving the BCS gap equation for chiral nuclear potentials using the method suggested by Khodel et al., where the original gap equation is replaced by a coupled set of equations for the dimensionless gap function $\chi(p)$ defined by $\Delta(p) = \Delta_F \chi(p)$ and a non-linear algebraic equation for the gap magnitude $\Delta_F = \Delta(p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled $^3PF_2$ partial wave. Results: We have successfully applied Khodel's method to singlet ($S$) and coupled channel ($SD$ and $PF$) cases in neutron and nuclear matter. Our calculations agree with other ab-initio approaches, where available, and provide crucial inputs for future applications in superfluid systems.

Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance

We study massless Dirac fermions in a supercritical Coulomb potential with the emphasis on that its low-energy physics is universal and parametrized by a single quantity per supercritical angular momentum channel. This low-energy parameter with the dimension of length is defined only up to multiplicative factors and thus each supercritical channel exhibits the discrete scale invariance. In particular, we show that the induced vacuum polarization has a power-law tail whose coefficient is a sum of log-periodic functions with respect to the distance from the potential center. This coefficient can also be expressed in terms of the energy and width of so-called atomic collapse resonances. Our universal predictions on the vacuum polarization and its relationship to atomic collapse resonances shed light on the longstanding fundamental problem of quantum electrodynamics and can in principle be tested by graphene experiments with charged impurities.

Pairing in half-filled Landau level

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current–current interactions. Our results show that there can be a continuous transition from the Halperin–Lee–Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that ℓ=1 angular momentum channel is quite different from higher angular momenta ℓ≥3. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction ν=12+12 is quantitatively changed from the previously established results but not qualitatively.

Polarization effect in scattering of Dirac particles by a central potential in the zero-energy limit

The scattering of Dirac particles by a central potential is revisited. An analytic analysis is carried out for the behavior of the phase shifts and the cross sections for unpolarized and polarized particles in the zero-energy limit. Special attention is paid to the polarization effect in the zero-energy limit. For incident particles with longitudinal polarization, it turns out that their polarization is in general kept unchanged after scattering, consistent with naive physical judgement. However, when the central potential takes some special form such that it supports a critical-energy solution in some specific angular momentum channel, the situation is dramatically changed, and a considerable part of the scattered particles have their original polarization reversed. For a spherical square well potential with appropriate depth, up to 53.8% of the scattered particles may have their polarization reversed.

High-capacity millimetre-wave communications with orbital angular momentum multiplexing.

One property of electromagnetic waves that has been recently explored is the ability to multiplex multiple beams, such that each beam has a unique helical phase front. The amount of phase front ‘twisting’ indicates the orbital angular momentum state number, and beams with different orbital angular momentum are orthogonal. Such orbital angular momentum based multiplexing can potentially increase the system capacity and spectral efficiency of millimetre-wave wireless communication links with a single aperture pair by transmitting multiple coaxial data streams. Here we demonstrate a 32-Gbit s−1 millimetre-wave link over 2.5 metres with a spectral efficiency of ~16 bit s−1 Hz−1 using four independent orbital–angular momentum beams on each of two polarizations. All eight orbital angular momentum channels are recovered with bit-error rates below 3.8 × 10−3. In addition, we demonstrate a millimetre-wave orbital angular momentum mode demultiplexer to demultiplex four orbital angular momentum channels with crosstalk less than −12.5 dB and show an 8-Gbit s−1 link containing two orbital angular momentum beams on each of two polarizations.

Importance of high-angular-momentum channels in pseudopotentials for quantum Monte Carlo

Quantum Monte Carlo methods provide in principle a highly accurate treatment of the many-body problem of calculating the ground and excited states of condensed systems. In practice, however, uncontrolled errors, such as those arising from the fixed-node and pseudopotential approximations can be problematic. We show that the accuracy of some quantum Monte Carlo calculations is limited by the properties of currently available pseudopotentials. The use of pseudopotentials involves several approximations, and we will focus on one that is relatively simple to correct during the pseudopotential design phase. It is necessary to include angular-momentum channels in the pseudopotential for excited angular-momentum states and to choose the local channel appropriately to obtain accurate results. Variational and diffusion Monte Carlo calculations for Zn, O, and Si atoms and ions demonstrate these issues. Adding higher-angular-momentum channels into the pseudopotential description reduces such errors without a significant increase in computational cost.

Rotational properties of two-component Bose gases in the lowest Landau level

We study the rotational (yrast) spectra of dilute two-component atomic Bose gases in the low angular momentum regime, assuming equal interspecies and intraspecies interaction. Our analysis employs the composite fermion (CF) approach including a pseudospin degree of freedom. While the CF approach is not {\it a priori} expected to work well in this angular momentum regime, we show that composite fermion diagonalization gives remarkably accurate approximations to low energy states in the spectra. For angular momenta $0 < L < M$ (where $N$ and $M$ denote the numbers of particles of the two species, and $M \geq N$), we find that the CF states span the full Hilbert space and provide a convenient set of basis states which, by construction, are eigenstates of the symmetries of the Hamiltonian. Within this CF basis, we identify a subset of the basis states with the lowest $\Lambda$-level kinetic energy. Diagonalization within this significally smaller subspace constitutes a major computational simplification and provides very close approximations to ground states and a number of low-lying states within each pseudospin and angular momentum channel.

Insight into the skew-scattering mechanism of the spin Hall effect: Potential scattering versus spin-orbit scattering

We present a detailed analysis of the skew-scattering contribution to the spin Hall conductivity using an extended version of the resonant scattering model of Fert and Levy [Phys. Rev. Lett. {\bf 106}, 157208 (2011)]. For $5d$ impurities in a Cu host, the proposed phase shift model reproduces the corresponding first-principles calculations. Crucial for that agreement is the consideration of two scattering channels related to $p$ and $d$ impurity states, since the discussed mechanism is governed by a subtle interplay between the spin-orbit and potential scattering in both angular-momentum channels. It is shown that the potential scattering strength plays a decisive role for the magnitude of the spin Hall conductivity.