Radial Degrees Of Freedom Research Articles

Role of radial index in self-reconstruction of structured beams

We demonstrate that the self-reconstruction performance of structured light is positively correlated with its radial degrees of freedom; specifically, structured beams with larger radial indices have better self-reconstruction abilities and higher tolerance to obstacles. These results were determined by quantifying the self-reconstruction degree of the Laguerre-Gauss beams. After the beam is partially blocked by an obstacle, we present convincing evidence theoretically and experimentally that an increase in the radial index of the Laguerre-Gauss beam is accompanied by a better self-reconstruction ability. We provide a physical explanation for this result in terms of non-diffraction, traveling-wave solution, and transverse momentum. Finally, we theoretically demonstrate that the contribution of the radial index to the self-reconstruction ability of the Hermite-Gauss and Ince-Gauss modes, the results are consistent. We believe that our results are applicable to all beams with complex radial structure, which provides another perspective on the self-reconstruction of structured beams: the contribution of the radial structure index.

Coherence in the radial degree of freedom.

Coherence quantifies the statistical fluctuations in an optical field and has been extensively studied in the space, time, and polarization degrees of freedom. In the context of space, coherence theory has been formulated between two transverse positions as well as between two azimuthal positions, referred to as transverse spatial coherence and angular coherence, respectively. In this paper, we formulate the theory of coherence for optical fields in the radial degree of freedom and discuss the associated concepts of coherence radial width, radial quasi-homogeneity, and radial stationarity with some physically realizable examples of radially partially coherent fields. Furthermore, we propose an interferometric scheme for measuring radial coherence.

Spin‐Orbit Modal Optical Vortex Beam Shaping from Dielectric Metasurfaces

AbstractOptical information and communication technologies are essentially based on the ability to shape the light field, either at the transmission or at the reception of the optical signal. Nowadays, wavelength and polarization state are already implemented in current telecom architectures and adding the spatial structuring of the light field as a novel degree of freedom to enhance data rate is desirable. In this context, the development of optical devices to shape optical modes belonging to orthogonal basis remains challenging. Here, in the context of singular optics, this work reports on the design, fabrication, and characterization of modal optical vortex beam shaping of paraxial light in the visible domain, in the framework of the Laguerre–Gauss basis. Both the azimuthal and radial degrees of freedom are univocally shaped via optical spin‐orbit interaction mediated by dielectric metasurfaces by combining the spatial modulation of amplitude, geometric phase, and dynamic phase. These results not only demonstrate the realization of new optical components, but also highlight how metasurface‐based technologies can contribute to optical information processing in the classical or quantum regime.

Probing electronic decoherence with high-resolution attosecond photoelectron interferometry

Quantum coherence plays a fundamental role in the study and control of ultrafast dynamics in matter. In the case of photoionization, entanglement of the photoelectron with the ion is a well-known source of decoherence when only one of the particles is measured. Here, we investigate decoherence due to entanglement of the radial and angular degrees of freedom of the photoelectron. We study two-photon ionization via the 2s2p autoionizing state in He using high spectral resolution photoelectron interferometry. Combining experiment and theory, we show that the strong dipole coupling of the 2s2p and 2p^2 states results in the entanglement of the angular and radial degrees of freedom. This translates, in angle-integrated measurements, into a dynamic loss of coherence during autoionization.Graphic

An Overview on Electrodynamic Bearings

In electrodynamics, the levitation ensues when there is a relative motion between a stator and a conductor owing to which high eddy currents are induced. The repulsive forces generated by eddy currents are large enough to carry the moving body passively without violating Earnshaw’s criterion. Electrodynamic bearings (EDB) use this technique to levitate the rotor in axial or radial degrees of freedom. The present article reviews the literature on electrodynamic passive magnetic bearings to provide an in-depth examination of EDB modeling, analysis, and development. Different types of EDB configurations are highlighted, along with improvements in their technology. In addition, essential advancements in mathematical modeling, finite element techniques, and experiments used to determine the bearing characteristics in terms of accuracy are highlighted. Furthermore, critical developments in rotordynamic analysis in terms of high-speed application have been reviewed. Finally, advances in the application of EDB are discussed.

Nanostructured silica spin–orbit optics for modal vortex beam shaping

Abstract Modality is a generic concept of wave-optics at the basis of optical information and communications. One of the challenges of photonics technologies based on optical orbital angular momentum consists in the production of a modal content for both the azimuthal and radial degrees of freedom. This basically requires shaping the complex amplitude of an incident light beam, which is usually made up from adaptive spatial light modulators or bespoke devices. Here, we report on the experimental attempt of a recent theoretical proposal [Opt. Lett. 42, 1966 (2017)] toward the production of various optical vortex modes of the Laguerre–Gaussian type relying on the spin–orbit interaction of light. This is done in the visible domain from optical elements made out of silica glass. The idea consists in exploiting the combined effects of azimuthally-varying geometric phase with that of radially-varying propagation features. The proposed approach can be readily extended to any wavelength as well as to other families of optical modes, although some dynamic phase problems remain to be solved to make it a turnkey technology.

Marginal stability in memory training of jammed solids.

Memory encoding by cyclic shear is a reliable process to store information in jammed solids, yet its underlying mechanism and its connection to the amorphous structure are not fully understood. When a jammed sphere packing is repeatedly sheared with cycles of the same strain amplitude, it optimizes its mechanical response to the cyclic driving and stores a memory of it. We study memory by cyclic shear training as a function of the underlying stability of the amorphous structure in marginally stable and highly stable packings, the latter produced by minimizing the potential energy using both positional and radial degrees of freedom. We find that jammed solids need to be marginally stable in order to store a memory by cyclic shear. In particular, highly stable packings store memories only after overcoming brittle yielding and the cyclic shear training takes place in the shear band, a region which we show to be marginally stable.

Quantization of the charge in Coulomb plus harmonic potential

Abstract We consider two models where the wave equation can be reduced to the effective Schrödinger equation whose potential contains both harmonic and the Coulomb terms, $\omega^{2}r^{2}-a/r$. The equation reduces to the biconfluent Heun’s equation, and we find that the charge as well as the energy must be quantized and state-dependent. We also find that two quantum numbers are necessary to count radial degrees of freedom and suggest that this is a general feature of differential equation with higher singularity like the Heun’s equation.

Modeling motional energy spectra and lattice light shifts in optical lattice clocks

We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our model respects the coupling between axial and radial degrees of freedom, as well as other anharmonicities inherent in the confining potential. We further demonstrate how our model can be used to characterize lattice light shifts in optical lattice clocks, including shifts due to higher multipolar (magnetic dipole and electric quadrupole) and higher order (hyperpolarizability) coupling to the lattice field. We compare results for our model with results from other lattice light shift models in the literature under similar conditions.

Dyon in the SU(2) Yang\u2013Mills theory with a gauge-invariant gluon mass toward quark confinement

In the previous paper, we have shown the existence of magnetic monopoles in the pure SU(2) Yang–Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of magnetic monopoles to obtain dyons with both magnetic and electric charges. In fact, we solve under the static and spherically symmetric ansatz the field equations of the SU(2) “complementary” gauge-scalar model, which is the SU(2) Yang–Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the novel dyon solution can be identified with the gauge field configuration of a dyon with a minimum magnetic charge in the massive Yang–Mills theory. Moreover, we compare the dyon of the massive Yang–Mills theory obtained in this way with the Julia–Zee dyon in the Georgi–Glashow gauge-Higgs scalar model and the dyonic extension of the Wu–Yang magnetic monopole in the pure Yang–Mills theory. Finally, we identify the novel dyon solution found in this paper with a dyon configuration on S^1 times {mathbb {R}}^3 space with nontrivial holonomy and propose to use it to understand the confinement/deconfinement phase transition in the Yang–Mills theory at finite temperature, instead of using the dyons constituting the Kraan–van Baal–Lee–Lu caloron.

Using all transverse degrees of freedom in quantum communications based on a generic mode sorter.

The dimension of the state space for information encoding offered by the transverse structure of light is usually limited by the finite size of apertures. The widely used orbital angular momentum (OAM) number of Laguerre-Gaussian (LG) modes in free-space communications cannot achieve the theoretical maximum transmission capacity unless the radial degree of freedom is multiplexed into the protocol. While the methodology to sort the radial quantum number has been developed, the application of radial modes in quantum communications requires an additional ability to efficiently measure the superposition of LG modes in the mutually unbiased basis. Here we develop and implement a generic mode sorter that is capable of sorting the superposition of LG modes through the use of a mode converter. As a consequence, we demonstrate an 8-dimensional quantum key distribution experiment involving all three transverse degrees of freedom: spin, azimuthal, and radial quantum numbers of photons. Our protocol presents an important step towards the goal of reaching the capacity limit of a free-space link and can be useful to other applications that involve spatial modes of photons.

Magnetic monopoles in pure $SU (2)$ Yang–Mills theory with a gauge-invariant mass

In this paper, we show the existence of magnetic monopoles in the pure $SU(2)$ Yang--Mills theory even in absence of scalar fields when the gauge-invariant mass term is introduced. This result follows from the recent proposal for obtaining the gauge field configurations in the Yang-Mills theory from the solutions of the field equations in the "complementary" gauge-scalar model with the radial length of the scalar field being fixed. The gauge-invariant mass term is obtained through a change of variables and a gauge-independent description of the Brout-Englert-Higgs mechanism which neither relies on the spontaneous breaking of gauge symmetry nor on the assumptions of the nonvanishing vacuum expectation value of the scalar field. According to these procedures, we solve under the static and spherically symmetric ansatz the field equations of the $SU(2)$ Yang-Mills theory coupled with an adjoint scalar field whose radial degree of freedom is fixed, and obtain a gauge field configuration of magnetic monopole with a minimum magnetic charge in the massive $SU(2)$ Yang-Mills theory. We compare the magnetic monopole obtained in this way in the massive Yang--Mills theory with the Wu-Yang magnetic monopole in the pure Yang-Mills theory and the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow model.

Gauge-independent Brout\u2013Englert\u2013Higgs mechanism and Yang\u2013Mills theory with a gauge-invariant gluon mass term

For the Yang–Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout–Englert–Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang–Mills theory with an adjoint scalar field. Moreover, we show that the Yang–Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin–Shenker continuity and Osterwalder–Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout–Englert–Higgs mechanism by starting with the complementary gauge-scalar model.

Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

Ab-initio modeling of an anion C- 60 pseudopotential for fullerene-based compounds

A pseudopotential of $C_{60}^-$ has been constructed from ab-initio quantum-mechanical calculations. Since the obtained pseudopotential can be easily fitted by rather simple analytical approximation it can be effectively used both in classical and quantum molecular dynamics of fullerene-based compounds.

Thermoelectric effect of correlated metals: Band-structure effects and the breakdown of Mott's formula

We study the thermoelectric effect of two-dimensional metals on a square lattice within semiclassical Boltzmann transport theory with particular focus on electron-electron scattering. We compute the electrical conductivity and the Seebeck coefficient as a function of band filling and temperature for generically chosen hopping parameters in a two-dimensional tight-binding model. The Boltzmann equation is solved numerically after computing the full collision integral, taking the angular and radial degrees of freedom into account. These degrees of freedom of the collision integral, neglected in the standard single-relaxation-time approximation, play an important role if the transport coefficients show unconventional features. Within our detailed numerical simulation, we show that the widely used Mott formula to compute the Seebeck effect is not sufficient to describe the thermoelectric effect in the presence of strong electron-electron scattering. Furthermore, we study the Seebeck coefficient and its temperature dependence in the vicinity of a Lifshitz transition and demonstrate that it shows remarkable parallels to transport features near a quantum critical point.

Two-photon optics of Bessel-Gaussian modes

In this paper we consider geometrical two-photon optics of Bessel-Gaussian modes generated in spontaneous parametric down-conversion of a Gaussian pump beam. We provide a general theoretical expression for the orbital angular momentum (OAM) spectrum and Schmidt number in this basis and show how this may be varied by control over the radial degree of freedom, a continuous parameter in Bessel-Gaussian modes. As a test we first implement a back-projection technique to classically predict, by experiment, the quantum correlations for Bessel-Gaussian modes produced by three holographic masks, a blazed axicon, binary axicon and a binary Bessel function. We then proceed to test the theory on the down-converted photons using the binary Bessel mask. We experimentally quantify the number of usable OAM modes and confirm the theoretical prediction of a flattening in the OAM spectrum and a concomitant increase in the OAM bandwidth. The results have implications for the control of dimensionality in quantum states.

Advanced Adaptive Vibration Controller for Active Magnetic Bearing with Application to Energy Storage Flywheel

This work introduced a kind of advanced adaptive control approach applied in Active magnetic bearing (AMB) to suppress the rotors vibrations in Flywheel Energy Storage System (FESS). The bearings system was built as a five degree-of-freedom (DOF) system and the four radial DOF among these were adopted AMB. Based on the Lyapunov theory, the proposed adaptive control law was designed to compensate various disturbance factors by controlling the AMBs. Finally, the simulation result illustrates that the proposed adaptive control law is effective to reduce the rotors vibration and improve the systems stability.

Electronuclear multiconfiguration time-dependent hartree calculations on the confined H atom with mobile electron and nucleus

A multiconfiguration time-dependent Hartree method oriented toward calculations of a non-Born-Oppenheimer nature has been applied to the calculation of the dynamical properties of a confined H atom. The calculation is fully six-dimensional and does not take into account constraints arising from linear or angular momentum conservation. The orbital evolution is monitored and the energy level spectrum of the system, as well as the dependence of the results on the decomposition of the Hamiltonian and on the correlation between radial degrees of freedom, is determined. © 2012 Wiley Periodicals, Inc.

Magnetic Force Characteristics and Structure of a Novel Radial Hybrid Magnetic Bearing

There are some problems in the permanent magnetic circuit of the current permanent magnet biased magnetic bearings, such as small magnetic force, low magnetic flux density and lack of self-stabilization. To solve this problem, a new hybrid radial magnetic bearing structure has been proposed. The nonlinear model and linearization equation of the new hybrid radial magnetic bearing capacity has been established by current molecular method and virtual displacement theorem. It is found that the permanent magnetic bearing can achieve self-stabilization in the radial degrees of freedom and can reduce the total displacement of negative stiffness. The results show that the air gap flux density is greatly improved by the new hybrid magnetic bearing with Halbach array structure. Current stiffness and displacement rigidity is closely related to initial current and initial gap of the equilibrium position. Near the equilibrium position, current stiffness and displacement rigidity are linear relationship. With the increase of air gap, it remains a good linearity. While with the decrease of air gap, it presents nonlinear characteristics..