Fractional Vortices Research Articles

Diversified vortex phase diagram for a rotating trapped two-band Fermi gas in the BCS-BEC crossover

We report the equilibrium vortex phase diagram of a rotating two-band Fermi gas confined to a cylindrically symmetric parabolic trapping potential, using the recently developed finite-temperature effective field theory (Klimin et al 2016 Phys. Rev. A 94 023620). A non-monotonic resonant dependence of the free energy as a function of the temperature and the rotation frequency is revealed for a two-band superfluid. We particularly focus on novel features that appear as a result of interband interactions and can be experimentally resolved. The resonant dependence of the free energy is directly manifested in vortex phase diagrams, where areas of stability for both integer and fractional vortex states are found. The study embraces the BCS–BEC crossover regime and the entire temperature range below the critical temperature Tc. Significantly different behavior of vortex matter as a function of the interband coupling is revealed in the BCS and BEC regimes.

Mutual transformations of fractional-order and integer-order optical vortices

We consider the problem of singular beams in optics as a part of the general questions of interactions, shaping and transformations of vortex states with fractional topological charges in physics, in particular, in hydrodynamic and quantum mechanic. Starting from the representation of the fractional-order vortex states as a superposition of infinite number of integer-order vortices with distinctive energy distributions (the vortex spectra) we showed that the smooth wave front of the fractional vortex beam can either decay into an asymmetric array of integer-order vortices or, vice versa, the array of optical vortices can be gathered together forming a smooth wave front with a helicoid-shaped phase distribution under propagation in free space. We revealed that a simple superposition of a finite number of the fractional-order vortex beams enables us to shape symmetric singular beams with the integer-order vortices of the desired topological charges.

Angular Momentum of Topologically Structured Darkness

We theoretically analyze and experimentally measure the extrinsic angular momentum contribution of topologically structured darkness found within fractional vortex beams, and show that this structured darkness can be explained by evanescent waves at phase discontinuities in the generating optic. We also demonstrate the first direct measurement of the intrinsic orbital angular momentum of light with both intrinsic and extrinsic angular momentum, and explain why the total orbital angular momenta of fractional vortices do not match the winding number of their generating phases.

$${\Gamma}$$ Γ -Convergence Analysis of a Generalized XY Model: Fractional Vortices and String Defects

We propose and analyze a generalized two dimensional $XY$ model, whose interaction potential has $n$ weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by $\Gamma$-convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The $\Gamma$-limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings. Our model describes in a simple way several topological singularities arising in Physics and Materials Science. Among them, disclinations and string defects in liquid crystals, fractional vortices and domain walls in micromagnetics, partial dislocations and stacking faults in crystal plasticity.

Appearance of fractional vortex dipoles by using spiral linear zone plate

We present a novel technique based on linear zone plate (LZP) by which linear singularities regarded as fractional vortex dipoles are efficiently generated. Our approach requires applying spiral phase to a LZP, so fractional vortex dipoles are then acquired. By also implementing transverse phase shift to the spiral LZP, we are able to equally divide the number of the produced dark beams carrying mixed phase dislocations into two transverse separate parts. As a result, by varying a so called the controlling parameter the lateral positions of the focused fractional vortex dipoles are changed. Since we are able to generate dark beams in different and specific linear positions, therefore we suggest these features will be of great interest in one-dimensional optical trapping. All results are completely verified by experimental works.

Fractional-topological-charge-induced vortex birth and splitting of light fields on the submicron scale

The formation and dynamics of fractional vortex charge in orbital-angular-momentum states is experimentally investigated. The holographic lithography method developed in this work may be effectively applied to study other structured matter waves.

Fractional vortices in a nano-scaled superconducting composite structure (d-dot) with a twin boundary

In order to investigate effects of twin boundary (TB) on structure of spontaneous half-quantized vortices (SHQVs) in a nano-scaled composite structure that is consisted of d- and s-wave superconductors (d-dot), we investigate magnetic field distribution with a d-dot model which has a single TB using anisotropic two-component Ginzburg-Landau equations and finite element method. We find that fractional vortices appear at the edges of TB and that the fractional vortices merge with SHQVs when effective interaction between d- and s-wave SCs is small.

Dynamically sculpturing plasmonic vortices: from integer to fractional orbital angular momentum.

As a fundamental tool for light-matter interactions, plasmonic vortex (PV) is extremely useful due to the unique near field property. However, it is a pity that, up to now, the orbital angular momentum (OAM) carried by PVs could not be dynamically and continuously tuned in practice as well as the properties of fractional PVs are still not well investigated. By comparing with two previously reported methods, it is suggested that our proposal of utilizing the propagation induced radial phase gradient of incident Laguerre-Gaussian (LG) beam is a promising candidate to sculpture PVs from integer to fractional OAM dynamically. Consequently, the preset OAM of PVs could have four composing parts: the incident spin and orbital angular momentum, the geometric contribution of chiral plasmonic structure, and the radial phase gradient dependent contribution. Moreover, an analytical expression for the fractional PV is derived as a linear superposition of infinite numbers of integer PVs described by Bessel function of the first kind. It is also shown that the actual mean OAM of a fractional PV would deviate from the preset value, which is similar with previous results for spatial fractional optical vortices.

Probing the fractional topological charge of a vortex light beam by using dynamic angular double slits

Vortex beams with fractional topological charge (FTC) have many special characteristics and novel applications. However, one of the obstacles for their application is the difficulty of precisely determining the FTC of fractional vortex beams. We find that when a vortex beam with an FTC illuminates a dynamic angular double slit (ADS), the far-field interference patterns that include the information of the FTC of the beam at the angular bisector direction of the ADS vary periodically. Based on this property, a simple dynamic ADS device and data fitting method can be used to precisely measure the FTC of a vortex light beam with an error of less than 5%.

Reverse propagation and negative angular momentum density flux of an optical nondiffracting nonparaxial fractional Bessel vortex beam of progressive waves.

Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.

Negative optical spin torque wrench of a non-diffracting non-paraxial fractional Bessel vortex beam

An absorptive Rayleigh dielectric sphere in a non-diffracting non-paraxial fractional Bessel vortex beam experiences a spin torque. The axial and transverse radiation spin torque components are evaluated in the dipole approximation using the radiative correction of the electric field. Particular emphasis is given on the polarization as well as changing the topological charge α and the half-cone angle of the beam. When α is zero, the axial spin torque component vanishes. However, when α becomes a real positive number, the vortex beam induces left-handed (negative) axial spin torque as the sphere shifts off-axially from the center of the beam. The results show that a non-diffracting non-paraxial fractional Bessel vortex beam is capable of inducing a spin reversal of an absorptive Rayleigh sphere placed arbitrarily in its path. Potential applications are yet to be explored in particle manipulation, rotation in optical tweezers, optical tractor beams, and the design of optically-engineered metamaterials to name a few areas.

Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems

We analyze the superconducting instabilities in the vicinity of the quantum-critical point of an inversion symmetry breaking order. We first show that the fluctuations of the inversion symmetry breaking order lead to two degenerate superconducting (SC) instabilities, one in the $s$-wave channel, and the other in a time-reversal invariant odd-parity pairing channel (the simplest case being the same as the of $^3$He-B phase). Remarkably, we find that unlike many well-known examples, the selection of the pairing symmetry of the condensate is independent of the momentum-space structure of the collective mode that mediates the pairing interaction. We found that this degeneracy is a result of the existence of a conserved fermionic helicity, $\chi$, and the two degenerate channels correspond to even and odd combinations of SC order parameters with $\chi=\pm1$. As a result, the system has an enlarged symmetry $U(1)\times U(1)$, with each $U(1)\times U(1)$ corresponding to one value of the helicity $\chi$. Because of the enlarged symmetry, this system admits exotic topological defects such as a fractional quantum vortex, which we show has a Majorana zero mode bound at its core. We discuss how the enlarged symmetry can be lifted by small perturbations, such as the Coulomb interaction or Fermi surface splitting in the presence of broken inversion symmetry, and we show that the resulting superconducting state can be topological or trivial depending on parameters. The $U(1)\times U(1)$ symmetry is restored at the phase boundary between the topological and trivial SC states, and allows for a transition between topologically distinct SC phases without the vanishing of the order parameter. We present a global phase diagram of the superconducting states and discuss possible experimental implications.

21pAR-7 d-dotにおいて双晶境界により生じうる分数自発磁束の理論解析

21pAR-7 d-dotにおいて双晶境界により生じうる分数自発磁束の理論解析

Fractional vortex Hilbert’s Hotel

We demonstrate how the unusual mathematics of transfinite numbers, in particular, a nearly perfect realization of Hilbert’s famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a fractional vortex plate can be used, in principle, to create any number of “open rooms,” i.e., topological charges, simultaneously. Fractional vortex plates are therefore demonstrated to create a singularity of topological charge, in which the vortex state is completely undefined and in fact arbitrary. These results hint that transfinite mathematics is much more common and important to optical systems than previously imagined.

Fractional-charge vortex in a spinor Bose-Einstein condensate

We classify all possible fractional charge vortices of charge less than unity in spin-1 and spin-2 polar and cyclic Bose-Einstein condensates (BECs) with zero magnetization. Statics and dynamics of these vortices in quasi-two-dimensional spinor BECs are studied employing accurate numerical solution and a Lagrange variational approximation. The results for density and collective-mode oscillation are illustrated using fractional-charge BEC vortex of $^{23}$Na and $^{87}$Rb atoms with realistic interaction and trapping potential parameters.

Gradual edge enhancement in spiral phase contrast imaging with fractional vortex filters.

In the spiral phase contrast imaging, the integer spiral phase plate (SPP) are generally employed to perform the radial Hilbert transform on the object. Here we introduce fractional SPP filters, instead of the integer ones, to investigate the gradual formation of edge enhancement for pure phase objects. Two spatial light modulators are used in our experimental configuration. One is addressed to display the pure phase object of a five-pointed star, while the other serves as a dynamic filter of fractional topological charge Q. Of interest is the observation of the complete reversal of the edge and background brightness by gradually changing the fractional vortices from Q = 0 to 1. The experimental results were well interpreted based on the OAM spectra of fractional SPP, which indicates that the filtered output image can be considered as a coherent superposition of all possible images that are individually resulted from the integer OAM filtering. Besides, we show that the spiral phase contrast effect can still be observed in real time for a rotating three-leaf clover. Our results may find potential applications in the optical microscopic imaging.

Fractional Solitons in Excitonic Josephson Junctions.

The Josephson effect is especially appealing to physicists because it reveals macroscopically the quantum order and phase. In excitonic bilayers the effect is even subtler due to the counterflow of supercurrent as well as the tunneling between layers (interlayer tunneling). Here we study, in a quantum Hall bilayer, the excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. The system is mapped into a pseudospin ferromagnet then described numerically by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, we identify a family of fractional sine-Gordon solitons which resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Each fractional soliton carries a topological charge Q that is not necessarily a half/full integer but can vary continuously. The calculated current-phase relation (CPR) shows that solitons with Q = ϕ0/2π is the lowest energy state starting from zero ϕ0 – until ϕ0 > π – then the alternative group of solitons with Q = ϕ0/2π − 1 takes place and switches the polarity of CPR.

Spontaneously broken time-reversal symmetry in high-temperature superconductors

Conventional superconductors are strong diamagnets that through the Meissner effect expel magnetic fields. It would therefore be surprising if a superconducting ground state would support spontaneous magnetics fields. Such time-reversal symmetry broken states have been proposed for the high-temperature superconductors, but their identification remains experimentally controversial. Here we show a route to a low-temperature superconducting state with broken time-reversal symmetry that may accommodate currently conflicting experiments. This state is characterised by an unusual vortex pattern in the form of a necklace of fractional vortices around the perimeter of the material, where neighbouring vortices have opposite current circulation. This vortex pattern is a result of a spectral rearrangement of current carrying states near the surfaces.

On the radiation force fields of fractional-order acoustic vortices

Here we report the creation and observation of acoustic vortices of fractional order. Whilst integer orders are known to produce axisymmetric acoustic fields, fractional orders are shown to break this symmetry and produce a vast array of unexplored field patterns, typically exhibiting multiple closely spaced phase singularities. Here, fractional acoustic vortices are created by emitting ultrasonic waves from an annular array of sources using multiple ramps of phase delay around its circumference. Acoustic radiation force patterns, including multiple concentration points, short straight lines, triangles, squares and discontinuous circles are simulated and experimentally observed. The fractional acoustic vortex leading to two closely spaced phase singularities is used to trap, and by controlling the order, reversibly manipulate two microparticles to a proximity of 0.3 acoustic wavelengths.

Simulation of two-flavor symmetry-locking phases in ultracold fermionic mixtures

We describe an ultracold fermionic set-up where it is possible to synthesize a superfluid phase with symmetry obtained by locking independent invariance groups of the normal state. In this phase, named two-flavor symmetry-locking (TFSL) phase, non-Abelian fractional vortices with semi-integer flux and gapless non-Abelian Goldstone modes localized on them appear. Considerations on the possible experimental realization of the TFSL are also provided.