Vortex Nucleation Research Articles

A numerical study of vortex nucleation in 2D rotating Bose–Einstein condensates

This article implements a numerical method for the minimization under constraints of a discrete energy modelling multicomponents rotating Bose–Einstein condensates in the regime of strong confinement and with rotation. Moreover, this method allows to consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). The goal of this paper is to study numerically the structures of the minimizers. In order to do so, we introduce a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.

Hidden vortices and Feynman rule in Bose-Einstein condensates with density-dependent gauge potential.

In this paper, we numerically investigate the vortex nucleation in a Bose-Einstein condensate (BEC) trapped in a double-well potential and subjected to a density-dependent gauge potential. A rotating Bose-Einstein condensate, when confined in a double-well potential, not only gives rise to visible vortices but also produces hidden vortices. We have empirically developed Feynman's rule for the number of vortices versus angular momentum in Bose-Einstein condensates in the presence of density-dependent gauge potentials. The variation of the average angular momentum with the number of vortices is also sensitive to the nature of the nonlinear rotation due to the density-dependent gauge potentials. The empirical result agrees well with the numerical simulations and the connection is verified by means of curve-fitting analysis. The modified Feynman rule is further confirmed for the BECs confined in harmonic and toroidal traps. In addition, we show the nucleation of vortices in double-well and toroidally confined Bose-Einstein condensates solely through nonlinear rotations (without any trap rotation) arising through the density-dependent gauge potential.

Steering of Vortices by Magnetic Field Tilting in Open Superconductor Nanotubes.

In planar superconductor thin films, the places of nucleation and arrangements of moving vortices are determined by structural defects. However, various applications of superconductors require reconfigurable steering of fluxons, which is hard to realize with geometrically predefined vortex pinning landscapes. Here, on the basis of the time-dependent Ginzburg-Landau equation, we present an approach for the steering of vortex chains and vortex jets in superconductor nanotubes containing a slit. The idea is based on the tilting of the magnetic field B at an angle α in the plane perpendicular to the axis of a nanotube carrying an azimuthal transport current. Namely, while at α=0∘, vortices move paraxially in opposite directions within each half-tube; an increase in α displaces the areas with the close-to-maximum normal component |Bn| to the close(opposite)-to-slit regions, giving rise to descending (ascending) branches in the induced-voltage frequency spectrum fU(α). At lower B values, upon reaching the critical angle αc, the close-to-slit vortex chains disappear, yielding fU of the nf1 type (n≥1: an integer; f1: the vortex nucleation frequency). At higher B values, fU is largely blurry because of multifurcations of vortex trajectories, leading to the coexistence of a vortex jet with two vortex chains at α=90∘. In addition to prospects for the tuning of GHz-frequency spectra and the steering of vortices as information bits, our findings lay the foundation for on-demand tuning of vortex arrangements in 3D superconductor membranes in tilted magnetic fields.

Critical velocity and arrest of a superfluid in a pointlike disordered potential

Superfluid flow past a potential barrier is a well studied problem in ultracold Bose gases, however, fewer studies have considered the case of flow through a disordered potential. Here we consider the case of a superfluid flowing through a channel containing multiple point-like barriers, randomly placed to form a disordered potential. We begin by identifying the relationship between the relative position of two point-like barriers and the critical velocity of such an arrangement. We then show that there is a mapping between the critical velocity of a system with two obstacles, and a system with a large number of obstacles. By establishing an initial superflow through a point-like disordered potential, moving faster than the critical velocity, we study how the superflow is arrested through the nucleation of vortices and the breakdown of superfluidity, a problem with interesting connections to quantum turbulence and coarsening. We calculate the vortex decay rate as the width of the barriers is increased, and show that vortex pinning becomes a more important effect for these larger barriers. Published by the American Physical Society 2024

Spontaneous nucleation of vortex–antivortex pairs in confined magnetic microstructures

Vortex–antivortex pairs have shown great potential in spintronics, where they can be used for information storage and logical devices. However, the physical mechanism for the nucleation of vortex–antivortex pairs is still unclear due to its metastability. We report on spontaneous nucleation of vortex–antivortex pairs in patterned Fe20Ni80 films (circular, square, hexagonal islands). By using a complex approach involving micromagnetic simulations, more in-depth understanding of vortex pair nucleation was achieved. A large amount of vortex–antivortex pairs appear in the as-grown magnetic film, which is the unstable high-energy state. Then, vortex and antivortex moves towards each other and annihilate, transforming magnetic structures and lowering the total energy of the system. With the decrease of sizes of microstructures, isolated vortex becomes stabilized due to confinement effect. These results provide a physical view for the nucleation of vortex–antivortex pairs and may be useful for design and optimization of magnetic microstructures for future spintronic applications.

Magnetic vortex states manipulation in overlapping ferromagnetic disks

We present the study of vortex magnetic states in a system of two overlapping ferromagnetic disks by Lorenz microscopy (L-TEM) and micromagnetic modeling. It is shown that in the case of small overlaps in this system there are two magnetic configurations Vortex–Antivortex–Vortex (VAV) state and Vortex–Vortex (VV) state. They are promising for phase locking in vortex spin-transfer nanooscillators. However, our experiments show that the nucleation of VV and VAV states is random and, as a result, the arrays consisting of overlapping disks are inhomogeneous. To control the nucleation of vortices with a certain vorticity, we changed the shape of overlapping disks by cutting them off from different edges. Disks of one type have been cut at the same edge (SD), while disks of another type have been cut at different edges (AD). In situ L-TEM experiments showed that after the sample magnetizing in the magnetic field applied in the plane of disks, the VV states have been realized in both SD and AD arrays. On the other hand, when samples were magnetized in a perpendicular magnetic field, the VAV state was realized in SD array, while the VV state was still realized in the AD array. The peculiarities of vortex nucleation in SD and AD in an external magnetic field are analyzed by means of micromagnetic simulations. The proposed method for controlling the configuration of magnetic vortices can be applied to create large arrays of overlapping disks that are in the same magnetic state.

Quantized vortex nucleation in collisions of superfluid nanoscopic helium droplets at zero temperature.

We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40m/s, respectively, induced by the long-range van der Waals attraction between the droplets.

Vortex nucleation processes in rotating lattices of Bose-Einstein condensates ruled by the on-site phases

Vortex nucleation processes in rotating lattices of Bose-Einstein condensates ruled by the on-site phases

Characterization of dissipative regions of a N-doped superconducting radio-frequency cavity

We report radio-frequency measurements of quality factors and temperature mapping of a nitrogen doped Nb superconducting RF cavity. Cavity cutouts of hot and cold spots were studied with low temperature scanning tunneling microscopy and spectroscopy, X-ray photoelectron spectroscopy and secondary electron microscopy. Temperature mapping revealed a substantial reduction of the residual resistance upon cooling the cavity with a greater temperature gradient and hysteretic losses at the quench location, pointing to trapped vortices as the dominant source of residual surface resistance. Analysis of the tunneling spectra in the framework of a proximity effect theory shows that hot spots have a reduced pair potential and a wider distribution of the contact resistance between the Nb and the top Nb oxide. Alone, these degraded superconducting properties account for a much weaker excess dissipation as compared with the vortex contribution. Based on the correlation between the quasiparticle density of states and temperature mapping, we suggest that degraded superconducting properties may facilitate vortex nucleation or settling of trapped flux during cooling the cavity through the critical temperature.

Precursory patterns to vortex nucleation in stirred Bose-Einstein condensates

Within the Gross-Pitaevskii theory, we study precursory pattern formations to the nucleation of vortex dipoles in a two-dimensional Bose-Einstein condensate stirred by a Gaussian potential. We introduce a smooth superfluid vorticity field and its conservative current, which capture very well the gradual process of vortex nucleation as a mechanism of topological singularities acquiring smooth cores. This is characterized by the localization of the superfluid vorticity into core regions which harbor the phase slips. For more impenetrable obstacles, we find that there are additional phase slips that do not acquire cores, thus remaining pinned as ghost vortices to the potential. We show that the vortex kinematics is slaved to the superfluid vorticity current, which determines not only the onset of nucleation but also the shedding dynamics.

Positive Ion Critical Velocity for Nucleation of Quantized Vortices in Isotopically Pure ^4He

The critical velocity for the vortex nucleation of positive ions is determined experimentally in isotopically purified ^4He at temperatures as low as 50 mK. Systematic IV characteristic measurements for a two-dimensional positive ion pool at a depth of 37.6 nm from the surface are carried out with extremely fine control of driving electric fields. The critical velocity of {sim }32 ms^{-1} at 500 mK decreases with decrease in temperature and approaches a temperature-independent value of {sim }18 ms^{-1} below 200 mK. The decrease in critical velocity corresponds to the increase in nucleation rate. The temperature dependence of critical velocity is qualitatively attributed to the “superohmic” macroscopic quantum tunneling of the Caldeira–Leggett theory. The reduction in tunneling rate with increase in temperature is evidence for quantum friction.

Kittel law and domain formation mechanism in PbTiO3/SrTiO3 superlattices

We report second-principles simulations on the structural and energetic properties of domains in (PbTiO$_{3}$)$_{n}$/(SrTiO$_{3}$)$_{n}$ superlattices. For the explored layer thickness ($n$ ranging between 8 and 16 unit cells) and lateral sizes of the domains, the most stable configuration corresponds to polar domains separated by a sequence of counter-rotating vortices (clockwise/counterclockwise) perpendicular to the stacking direction and acting as domain walls. The balance between the domain wall energy and the electrostatic energy yields to an optimal domain period $\omega$ that is proportional to the square-root of the thickness of the PbTiO$_{3}$ layer, following the Kittel law. For a given lateral size of the simulation box, suboptimal domain structures (with a width larger than the one predicted by the Kittel law) can be obtained in a metastable form. However, at finite temperature, molecular dynamics simulations show the spontaneous change of periodicity, which implies the formation of new domains whose generation is initiated by the nucleation of vortices and antivortices at the interface between the SrTiO$_{3}$ and the PbTiO$_{3}$ layers. The vortices progressively elongate and eventually annihilate with the antivortices yielding the formation of new domains to comply the Kittel law via a topological phase transition.

Optimization of the Hysteresis Effect in Superconductor Nb Open Nanotubes

Superconductor Nb open nanotubes are analyzed under a strong transport current in an external magnetic field using the time‐dependent Ginzburg–Landau equations. The geometric properties of the hysteresis loop in current–voltage characteristics are described for nanotubes of different radii from 190 to 440 nm as a function of the magnetic field. The hysteresis effect appears at a constant temperature as a result of the order parameter dynamics. In nanotubes of radii equal to 240 nm and larger, the area of the hysteresis loop manifests a non‐monotonic behavior as a function of the external magnetic field with a maximum ranging from 15 to 20 mT. Normal conductivity is shown to have a crucial impact on the hysteresis effect in superconductor open nanotubes. Namely, a higher normal conductivity leads to the disappearance of the hysteresis effect. As a rule, the upper and lower branches of the hysteresis loop are provided by the phase‐slip and vortex regimes, correspondingly. Just before the transition of the system from the upper branch to the lower one, the way of nucleation and annihilation of vortices in the region with suppressed superconductivity experiences readjustment.

Vortex nucleation in rotating Bose-Einstein condensates with density-dependent gauge potential.

We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, Ω_{cr}, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the Ω_{cr} values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional s-wave scattering lengths through the strength of nonlinear rotation, C, such that Ω_{cr}(C>0)<Ω_{cr}(C=0)<Ω_{cr}(C<0). In an analogous manner, the critical ellipticity (ε_{cr}) for vortex nucleation during an adiabatic introduction of trap ellipticity (ε) depends on the nature of nonlinear rotation besides trap rotation frequency. The nonlinear rotation additionally affects the vortex-vortex interactions and the motion of the vortices through the condensate by altering the strength of Magnus force on them. The combined result of these nonlinear effects is the formation of the non-Abrikosov vortex-lattices and ring-vortex arrangements in the density-dependent BECs.

Dzyaloshinskii-Moriya-Interaction-Like Behavior in Confined Permalloy Nanostructures via Coupled Magnetic Vortices.

Dzyaloshinskii-Moriya interaction (DMI), one of antisymmetric exchanges, originates from the combination of low structural symmetry and large spin-orbit coupling and favors magnetization rotations with fixed chirality. Herein, this work reports a DMI-like behavior in permalloy via coupled vortices in confined structures. Under the in-plane magnetic fields, continuous reversals of different coupled vortices are directly observed by in situ Lorentz transmission electron microscopy, and reproduced by complementary micromagnetic simulations. The statistical results show that coupled vortices with opposite chirality appear more frequently with the frequency up to about 60%. Such an asymmetric phenomenon mainly arises from a DMI-like behavior, associated with the increased total energy difference between different ground-state coupled vortices. Moreover, in the reversal process, the junction between disks accelerates the annihilation of vortices moving toward it and is also the starting point of vortex nucleation. These results provide an effective method to generate a DMI-like behavior in magnetic systems with symmetry breaking surface and benefit the future development of vortex-based spintronic devices.

Fast and efficient detection of a single photon with hole-patterned superconductor microstrips

In this Letter, we report on pattern engineering in superconducting microstrips to achieve a fast and efficient detection of a single-photon over a large detection area. The proposed detector is composed of hole-patterned superconductor microstrips fabricated with a 5-nm-thick amorphous molybdenum silicide film. It exhibits a saturated internal detection efficiency at 1550 nm with a negligible dark count rate and a recovery time of 9 ns with a large detection area (50 × 50 μm2). The simulation reveals that the holes patterned in the superconductor microstrip stimulate the nucleation of the vortex, which constitutes a major key to achieving the efficient detection of photons. This work paves the way for the facile and prolonged regulation of vortex nucleation in superconductors, which shows promise for developing high-performance large-area superconductor single-photon detectors.

Response of a θSOT sensor to the magnetic field's in-plane and out-of-plane components

Nano-sized three-junctions superconducting quantum interference device (θSOT) demonstrates tunable sensitivity to the multi-directional magnetic fields for its 3D unique structure. We report the magnetic properties of this device using the state-of-the-art 3D simulations within the Ginzburg–Landau formalism. The stability range of the Meissner state, in other words, the vortex nucleation point of the device for two fluxes (in the left and right loop), is studied in detail. Static properties such as the distribution of Cooper pairs and screening current density of θSOT device are observed. Response of the θSOT sensor to the magnetic field’s in-plane and out-of-plane components is investigated.

Field-driven side-by-side magnetic domain wall dynamics in ferromagnetic nanostrips

There has been a plethora of studies on domain wall dynamics in magnetic nanostrips, mainly because of its versatile non-linear physics and potential applications in data storage devices. However, most of the studies focus on out-of-plane domain walls or in-plane head-to-head (tail-to-tail) domain walls. Here, we numerically study the field-driven dynamics of in-plane side-by-side domain walls in ferromagnetic strips, which can be stable in the presence of an in-plane easy-axis anisotropy transverse to the strip. The domain walls move in a rigid-body manner at low field, and show complex Walker breakdown behavior at high field. We observe a multi-step Walker breakdown through vortex nucleation in wide strips. In the presence of Dzyaloshinskii-Moriya interaction (DMI), the first Walker breakdown field first decreases then increases with interfacial DMI, while keeps increasing with bulk DMI. These findings complement the current understanding on domain wall dynamics.

Vortex nucleation barriers and stable fractional vortices near boundaries in multicomponent superconductors

The magnetization process of a superconductor is determined by the potential barrier for vortex nucleation and escape. In multicomponent superconductors, fractional vortices with a winding in the phase of only one of the components can be stable topological solitons that carry a fraction of the flux quantum. While the formation of such objects in the bulk costs logarithmically or linearly divergent energy, these objects were shown to be stable near the samples' boundaries in the two-component London model. Therefore the conventional Bean-Livingston picture of magnetic flux entry does not apply to these superconductors, since the entry process can involve fractionalization of a vortex. In this paper, we address the nonlinear problem of determining the potential barrier for fluxoid penetration in a multicomponent superconductor, including the effects of various intercomponent couplings, by using the recently developed gauged string method. The method allows numerically exact (i.e., convergent) calculation of a sphaleron configuration in a gauge theory and thus the height of the nucleation barrier. We show how the fractionalized nucleation processes result in multiple sphalerons and intermediate states due to the complex shape of the energy landscape of multicomponent superconductors.

Vortices nucleation by inherent fluctuations in nematic liquid crystal cells

Multistable systems are characterized by exhibiting domain coexistence, where each domain accounts for the different equilibrium states. In case these systems are described by vectorial fields, domains can be connected through topological defects. Vortices are one of the most frequent and studied topological defect points. Optical vortices are equally relevant for their fundamental features as beams with topological features and their applications in image processing, telecommunications, optical tweezers, and quantum information. A natural source of optical vortices is the interaction of light beams with matter vortices in liquid crystal cells. The rhythms that govern the emergence of matter vortices due to fluctuations are not established. Here, we investigate the nucleation mechanisms of the matter vortices in liquid crystal cells and establish statistical laws that govern them. Based on a stochastic amplitude equation, the law for the number of nucleated vortices as a function of anisotropy, voltage, and noise level intensity is set. Experimental observations in a nematic liquid crystal cell with homeotropic anchoring and a negative anisotropic dielectric constant under the influence of a transversal electric field show a qualitative agreement with the theoretical findings.