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The buoyancy-driven thermogravitational Rayleigh–Benard convection (RBC) occurs in a 1–3 cm-deep layer of normal He-I in a wide experimental cell heated from above at temperatures below the liquid 4He density maximum T

In this paper, we study the ground state of a binary rotating Bose–Einstein condensate with unequal atomic masses. The results are obtained by numerically solving the Gross–Pitaevskii equation. We conclude that the vortex configuration strongly depends on the strength of spin–orbit coupled, rotational frequency as well as on the ratio of atomic mass. A series changes of vortex structure from a single central, triangular, hexagon to linear vortex string are found. In addition, the vortex necklace, giant vortex and linear hidden vortex are observed. Our results are helpful for understanding the artificial gauge field of the binary rotating ultracold Bose gas under realistic imbalanced condition.

In this paper, we study the dynamics of a single vortex and a corotating vortex pair in a quasi-two-dimensional Bose–Einstein condensate. The numerical results are obtained by solving the Gross–Pitaevskii equation. It is shown that the vortex motion is strongly dependent on the dipole–dipole interaction (DDI). For a single vortex, the periodic motion occurs with increasing dipole strength. The x-coordinate and y-coordinate as a function of time close to the shape of cosine wave and triangular wave when DDI is an isotropic repulsive interaction, respectively. In addition, it is evident that strong and anisotropic DDI makes the movement of vortex become fast and the amplitude enlarges. In the case of a corotating vortex pair, the dynamics is qualitatively consistent with a single vortex for weak dipole strength. Moreover, the periodic dynamics only appears for strong and anisotropic DDI and more rapid vortex motion is indicated.

We study the splitting process of a multiply quantized vortex for a trapped highly oblate Bose-Einstein condensate in an optical lattice. Fourfold or sixfold splitting patterns are found in the dynamical evolution in square or triangular optical lattices, respectively. The relaxation time and angular momentum are also investigated to explore the properties of splitting. We find one singly quantized vortex or antivortex could be finally stabilized at the trap center.

Our study sample is a mesoscopic superconducting three-dimensional parallelepiped immersed in a magnetic field $$H_{z}$$ . The sample presents an anisotropy of the Ginzburg–Landau parameter $$\kappa (z)$$ in the z-axis. This dependence allows us to simulate a superconducting three layer system, where the top and bottom layers are made of a type-II superconducting material, and the middle layer is fabricated of a type-I material. We analyzed the superconducting electron density, free energy, and the magnetization curves as functions of H for different values of $$\kappa (z)$$ . Due to the effects of proximity and shielding on the borders of the layers, Abrikosov vortices are present in the type I regions, and a fractional vortex state is present in the type II superconducting region.

We study quantum vortex states consisting of a ring of vortices with alternating sign, in a homogeneous superfluid confined to a circular domain. We find an exact stationary solution of the point vortex model for the neutral vortex necklace. We investigate the stability of the necklace state within both the point-vortex model and the Gross-Pitaevskii equation describing a trapped atomic Bose-Einstein condensate at low temperature. The point-vortex stationary states are found to also be stationary states of the Gross-Pitaevskii equation provided the finite thickness of the outer fluid boundary is accounted for. Under significant perturbation, the Gross-Pitaevskii evolution and point-vortex model exhibit instability as expected for metastable states. The perturbed vortex necklace exhibits sensitivity to the perturbation, suggesting a route to seeding vortex chaos or quantum turbulence., 17 pages, 7 figures, JLTP format, comments welcome

In this paper, we study the von Neumann entanglement entropy as a measure of the quantum entanglement in the spin-1 two-dimensional XX model with single-ion anisotropy. We use the bond operator formalism and consider the range of large anisotropy D and in the neighborhood of the critical point $$D_\mathrm{c}$$ . One discusses the influence of the Berezinskii–Kosterlitz–Thouless phase transition (BKT) that occurs at critical anisotropy point $$D_\mathrm{c}$$ , or the transition of the topological order of vortices and disordered phase on quantum entanglement.

The vortex filament model is used to investigate the interaction of a quantized vortex ring with a straight vortex line and also the interaction of two solitons traveling in opposite directions along a vortex. When a ring reconnects with a line, we find that a likely outcome is the formation of a loop soliton. When they collide, loop solitons reconnect as they overlap each other producing either one or two vortex rings. These simulations are relevant for experiments on quantum turbulence in the zero temperature limit where small vortex rings are expected to be numerous. It seems that loop solitons might also commonly occur on vortex lines as they act as transient states between the absorption of a vortex ring before another ring is emitted when the soliton is involved in a reconnection.

We examine the surface phonon polaritons established on resonance between lossy silicon carbide and vacuum over the Reststrahlen frequency range. To this goal, we investigate two waves counter-propagating along a planar material interface in terms of the orbital and spin parts of the Poynting vector. Vortices of the spin part are thus found to be generated near the collision point of the two waves. In addition, vortex pairs of opposite circulations are identified near the material interface. The locality of the electric permittivity plays an essential role in enabling our simple analysis by neglecting the spatial propagations of phonons while keeping the material damping. The resulting dynamics of the total displacement field turns out to be loss-free in the middle of the lossy dynamics of the other field variables, thus exhibiting a superfluid-like feature in an otherwise normal fluid.

Massive enough particles of frozen hydrogen are known to be captured by quantum vortices in liquid helium. Here, we theoretically demonstrate that the drift of such particles along the vortex is limited by the friction force, which was explicitly calculated. Our hypothesis explains the stabilization of the micron-sized particles’ position on the axis of the vertical vortices despite the significant buoyant force promoting the floating up of the particles.

The coarse-grained hydrodynamics of turbulent superfluid fluids describes the fluid flow in terms of two equations for the averaged normal and superfluid velocities. These two equations are coupled via the mutual friction term, which contains the quantity $${\mathcal {L}}(r,t)$$ –the vortex line density (VLD) of the vortex tangle. The question of how to treat the quantity $${\mathcal {L}}(r,t)$$ –the so-called closure procedure is crucial for the correct description of flow of turbulent superfluids. The article provides a critical analysis of several approaches to the closure procedure. The first one, which is usually referred to as HVBK method suggests to express the quantity $${\mathcal {L}}(r,t)$$ via coarse-grained vorticity $$\nabla \times {\mathbf {v}}_{s}$$ using the famous Feynman rule. This method and idea on the vortex bundle structure, which justifies the use of the HVBK approach, are analyzed and discussed in detail. Another approach that has been popular before, but is still used sometimes, is called the Gorter–Mellink relation. This method suggests that the VLD $${\mathcal {L}}(r,t)$$ is proportional to the squared relative velocity between normal and superfluid components $$\propto (v_{n}-v_{s})^{2}$$ . One more variant of the closure procedure, discussed in the paper, is based on the method in which the vortex line density $${\mathcal {L}}(r,t)$$ is not expressed directly via the velocity (and/or vorticity) field, but is an independent equipollent variable, controlled by a separate equation. The latter approach is called as hydrodynamics of superfluid turbulence (HST). The advantages and disadvantages of each method are discussed.

In this paper, the critical rotation rate for vortex nucleation in ultracold rotating boson atoms in 2D deep optical lattices is calculated. We suggest a semiclassical approach to calculate the critical rotation frequency at finite temperature through extension of Stringari threshold formula. The critical rotation frequency is parametrized in terms of the thermodynamic potential. Depending on the semiclassical approximation, the calculated thermodynamic potential enabled us to investigate the finite size and interatomic interaction effects. The calculated results show that the critical rotation rate, as a function of stirring frequency, shows a peak, while the critical rotation rate as a function of the normalized temperature decreases monotonically with the increase in the temperature. The critical rotation rate depends on the interatomic interaction, atoms number and optical potential depth. The obtained results provide useful theoretical foundation for rotating condensate boson in optical lattice.

Effects of random depth optical lattice (OL) on vortices in Bose–Einstein condensates (BECs) are studied. By numerically solving Gross–Pitaevskii equation for rotating BECs, we analyzed the property of a single vortex (slow rotating) and vortex lattice structures (fast rotating) in the presence of random depth optical lattice. It is shown that similar to speckle disorder and bichromatic optical lattice pseudorandom potential, random depth optical lattice can also localize a singe vortex. Random depth OL can melt square vortex lattice, while speckle or bichromatic OL disorder can melt triangular vortex lattice. We also show that random depth OL disorder can induce larger angular momentum.

This article reviews, from a very personal point of view, the origins and the early work on the superfluid to normal transition in very thin films of 4He driven by vortex topological defects using a very crude description of the system which contains only the important physics. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the all important experimental verifications of the smoking gun prediction of the universal discontinuity of the superfluid density at $$T=T_{{{\mathrm{c}}}}$$ and the necessary extensions to describe the dynamics necessary to compare with experiment.

Acoustic cavitation is a powerful technique to probe electron bubbles inside the liquid helium. The critical pressure to explode a bubble depends on the number and quantum state of electrons inside the bubble and if the bubble is trapped on a vortex. Here, we report cavitation events that occur at pressure magnitudes approximately 70% lower compared to single electron bubbles. We have considered various possibilities, e.g., single electron bubbles trapped on vortex lines or primary electrons depositing the energy at the acoustic focus and compared the results of our experiments with past measurements reported in the literature. We consider the possibility these new species of bubbles are multielectron bubbles with a small (

A micro-electromechanical resonator, consisting of a $$125 \times 125\,\upmu \hbox {m}^2$$ center plate suspended $$2\,\upmu \hbox {m}$$ above a substrate, was immersed in $$^4$$ He along with a quartz tuning fork. The tuning fork was placed 5 mm above the resonator and was used to generate turbulence. The damping of the resonator was investigated in the presence of turbulence generated by the tuning fork. We observe a velocity, $$v_c \simeq 5\,\hbox {mm}\,\hbox {s}^{-1}$$ , above which the damping on the resonator is drastically reduced for all tuning fork velocities studied. We attribute this change in damping to the shedding and capture of vortices.

We report the spontaneous emission of vortex rings from turbulence induced by a vibrating wire in superfluid $$^4$$ He, and investigate the statistical behavior of quantum turbulence. Using a set of vibrating wires as a turbulence generator and vortex detectors, we measured the distribution of times of flights between the generator and the detectors for emission directions parallel and perpendicular to the vibration direction of the generator wire. We find that the times exhibit a single exponential distribution for emissions in both directions, indicating temporally random emission of vortex rings with a single mean emission rate. When a limit is set on the detection diameter of the vortex rings, the detection times exhibit a double exponential distribution for the perpendicular direction for ring diameters above 10 $$\upmu \hbox {m}$$ , suggesting that large vortex rings reach the detector with a high rate emission at later times. In the parallel emission direction, the emission rate during an equilibrium state exhibits a power law behavior with a minimum diameter of detected vortex rings, implying that a vortex tangle generated by an oscillating object has a self-similar structure of vortex lines.

Using a finite-element method to numerically solve the time-dependent Ginzburg–Landau equations, we studied the dynamic properties of superconducting strips with a central, time-dependent, weakened superconducting region. Through our research, we obtained the voltage oscillation as a function of time. Particularly, a multiharmonic voltage oscillation was found in the superconducting strip. With increasing period of pinning potential, the frequency of the voltage oscillation decreases.

Using Ginzburg–Landau simulations, we study the effect of a multigeometric modulation of the superconducting condensate, imposed by the spatially nanoengineered critical temperature Tc inside a mesoscopic superconductor. A plethora of intriguing vortex states is reported in the presence of the applied magnetic field, reflecting the rich interplay of symmetries imposed by the sample boundary and the chosen polygonal distributions of reduced or enhanced Tc.

The time-dependent Ginzburg–Landau equations have been solved numerically by a finite element method for a hybrid system consisting of a finite-size superconducting film with a magnetic strip on top. It is demonstrated that the coexistence of vortices and antivortices could occur in the mesoscopic superconducting film due to the important influence of the magnetic strip, which could help us to understand the experimental results.

The Kibble–Zurek (Kibble in J Phys A 9:1387–1398, 1976; Zurek in Nature 317:505–508, 1985) scenario predicts that the outcome of a second-order phase transition from a disordered system into an ordered one depends on the quench rate. The emerging order parameter in the ordered state is not spatially uniform, containing topological defects. The faster the transition, the larger the density of defects. In the case of a conductor–superconductor transition, these defects are flux quanta (vortices). To investigate this scenario, we developed a high-resolution magneto-optical imaging system capable of resolving single flux quanta. Using this system, we imaged arrays of spontaneously created vortices in a Nb film. These vortices were formed after the film was rapidly cooled into the superconducting state at rates around 109 K/s. The internal correlations within the vortex array are important in order to differentiate between competing models. In the Kibble–Zurek scenario, neighboring vortices should have a different polarity, while in Hindmarsh–Rajantie (Hindmarsh and Rajantie in Phys Rev Lett 85:4660–4663, 2000) model the polarity should be the same. Our results favor the Kibble–Zurek scenario.

Thermal counterflow in superfluid $$^4$$ He (He II) was studied numerically using the vortex filament model in a spherically symmetric geometry (as resulting from a point heat source). It is found that for the range of temperatures and velocities studied, turbulent tangle of the quantised vortices develops only for sufficiently low temperatures, hinting at the existence of a critical temperature, and only for velocities bounded from above (and presumably from below). A velocity–temperature phase diagram is presented. A simple physical model is proposed that qualitatively explains both observations.

Recently, the authors succeeded in generating a superfluid suction vortex, which is a giant vortex with a hollow core, driven directly by a cryogenic centrifugal pump. The ultimate goal of this study and related work is to determine the distribution of the local density of the quantum vortex lines as a function of the rotational speed and the magnitude of the suction flow. Although the flow of superfluid helium in a rotating bucket, in which the vortex lines are arranged to form a triangular lattice, is known to show rigid body motion, the vortex line distribution of the suction vortex remains an open question. In this study, the attenuation of the second sound across the suction vortex was measured. As a result, it was found that the damping factors of the second sound increased with increasing rotational speed; however, it was found that the apparent vortex line density is not proportional to the rotational speed despite the fact that the total circulation has been previously shown to be proportional to the rotational speed. A possible picture of the quantum vortex lines around the suction vortex is discussed in this paper.

We study the behavior that the inclusion of zones with different Ginzburg–Landau parameters $$\kappa $$ has on the magnetization, Cooper pair density, and $$H_{1}$$ , the magnetic field in which the first vortex penetration occurs, in a superconducting 2D square in the presence of an external applied magnetic field H. We report anomalous vortex configurations and an appreciable variation (no monotonic) of $$H_{1}$$ due to the inhomogeneity of $$\kappa (x,y)$$ . The behavior of the superconducting state for different values of the $$\kappa $$ , along with its respective variations, has been studied by including different convergence ratios in the time-dependent equations of the Ginzburg–Landau model. In addition, the variation of the magnetic susceptibility $$\chi $$ according to the applied magnetic field is shown, and how an understanding of the magnetic moment density $$\mu $$ present in the sample can be established.

A micro-electromechanical plate resonator suspended 2 $$\upmu $$ m above a substrate was immersed in $$^4$$ He at 14 mK at saturated vapor pressure. At these temperatures, four vibrational modes of the device are observed. The corresponding motion of these modes is identified by comparing the observed modes with computer simulations. Owing to its large surface area and small mass, the resonator is sensitive to remnant vortices. The behavior of the modes is studied in the presence of remnant vortices and also in the presence of fully developed turbulence generated by a quartz tuning fork.

To investigate the formation of quantum turbulence in superfluid $$^4\hbox {He}$$ , we have studied the vortex emission from a turbulence region generated by a vibrating wire. The time of flight of vortex rings emitted from a generator to a detector exhibits a single exponential distribution, suggesting that vortex detection is a Poisson process. This means that the detector observes vortex rings at irregular intervals with a mean interval time. Therefore, the single exponential distribution suggests a constant emission rate of vortex rings during turbulence generation, which is proportional to the mean detection rate. By setting a limit on the diameter of detected vortex rings, we find that the emission rate exhibits a power law relationship with the ring diameter. Since the diameter of a vortex ring is related to the vortex line spacing within turbulence when reconnection occurs, the distribution of vortex line spacings is considered to be reflected in the size distribution of the emission rate. Therefore, the power law dependence of the emission rate suggests that the vortex lines within turbulence have a self-similar fractal structure.

Peculiar dynamics of a free surface of the superfluid 4He has been observed experimentally with a newly established technique utilizing a number of electrically charged fine metal particles trapped electrically at the surface by Moroshkin et al. They have reported that some portion of the particles exhibit some irregular motions and suggested the existence of quantized vortices interacting with the metal particles. We have conducted calculations with the vortex filament model, which turns out to support the idea of the vortex-particle interactions. The observed anomalous metal particle motions are roughly categorized into two types; (1) circular motions with specific frequencies, and (2) quasi-linear oscillations. The former ones seem to be explained once we consider a vertical vortex filament whose edges are terminated at the bottom and at a particle trapped at the surface. Although it is not yet clear whether all the anomalous motions are due to the quantum vortices, the vortices seem to play important roles for the motions., Comment: 7 pages, 10 figures

Merging of isolated Bose–Einstein condensates (BECs) is an important topic due to its relevance to matter-wave interferometry and the Kibble–Zurek mechanism. Many past research focused on merging of BECs with uniform initial phases. In our recent brief report (Kanai et al. in Phys Rev A 97:013612, 2018), we showed that upon merging of rotating BECs with non-uniform initial phases, spiral-shaped dark solitons can emerge. These solitons facilitate angular momentum transfer and allow the merged condensate to rotate even in the absence of quantized vortices. More strikingly, the sharp endpoints of these spiral solitons can induce rotational motion in the BECs like vortices but with effectively a fraction of a quantized circulation. This paper reports our systematic study on the merging dynamics of rotating BECs. We discuss how the relative winding number of the rotating BECs and the potential barrier that initially separates the BECs may affect the profile and dynamics of the spiral solitons. The number of spiral solitons created in the BECs is observed to always match exactly the relative winding number of the two BECs. The underlying mechanism for which the solitons can break up to form sharp endpoints with peculiar physical properties and why the number of solitons matches the relative winding number is identified and explained. These results improve our understanding of soliton dynamics, which may allow better manipulation of these non-topological phase defects when they are involved in various quantum transport processes.

We investigate the formation of Shannon information entropy in a rotating Bose–Einstein condensates confined in a harmonic potential combined with an optical lattice (OL) using the mean field Gross–Pitaevskii equation. With the increase of OL depth $$V_0$$ , at the same rotational frequency $$\Omega $$ , we show that the information entropy increases in momentum space $$S_r$$ and total entropy S and it decreases in position space $$S_k$$ . We also calculate the Landsberg order parameter $$\delta $$ and its dependence on $$\Omega $$ . We find that the critical points between the case of OL and non-OL move along the direction of decreasing $$\Omega $$ with the increase of $$V_0$$ . In particular, the dynamics behaviors indicate that the periodicity of S and $$S_{\text{ max }}$$ loses due to the broken symmetry when OL is added.

Free decay of homogeneous vortex tangle in superfluid has been studied for ultra-quantum and quasi-classical regimes at zero temperature limit. It is found that the decay process is associated with heating by means of phonon generation into the system, even at such a zero temperature limit. An explicit expression for the time evolution of temperature due to the heating has been derived. Such heating affects the motion of vortex strings by (a) decreasing their cyclotron frequencies and (b) shortening their length. This length shortening is a secondary decay process initiated by the primary free decay of vortex tangles. The effect of quasiparticles (phonons) on the wave collapse and energy dissipation of the turbulent states has also been studied through the modulation theory.

We study the ferromagnetic (FM)-core spin vortex of spin-1 condensate in a 2D harmonic trap with homogeneous magnetic field. It is shown that such a topological excitation may exist when the system stays at the easy-axis phase with the negative quadratic-Zeeman-energy parameter larger than a critical value. The exact spatial distributions of number density and local spin are obtained with a variational method. A polar ring with local spin $$ F=0$$ appears in the FM-core spin vortex. The density–density interaction can significantly affect both the spatial distribution of local spin and the position of the polar ring. The local spin in most areas is larger for the stronger ferromagnetic interaction. More interestingly, a local minimum emerges near the polar ring in the curve of total number density when the spin–spin interaction is large enough. In such easy-axis phase, the quadratic-Zeeman-energy parameter cannot control the FM-core spin vortex. An easily controlled experiment scheme is provided to realize the FM-core spin vortex.

The problem of Abrikosov vortices depinning from extended linear (columnar) defect in 3D-anisotropic superconductor film under non-uniformly distributed Lorentz force is studied for the case of low temperatures, disregarding thermal activation processes. We treat it as a problem of mechanical behavior of an elastic vortex string settled in a potential well of a linear defect and exerted to Lorentz force action within the screening layer about the London penetration depth near the specimen surface. The stability problem for the vortex pinning state is investigated by means of numerical modeling, and conditions for the instability threshold are obtained as well as the critical current density $$j_\mathrm{c}$$ and its dependence on the film thickness and magnetic field orientation. The instability leading to vortex depinning from extended linear defect first emerges near the surface and then propagates inside the superconductor. This scenario of vortex depinning mechanism at low temperatures is strongly supported by some recent experiments on high-Tc superconductors and other novel superconducting materials, containing columnar defects of various nature.

Confocal Annular Josephson Tunnel Junctions (CAJTJs) which are the natural generalization of the circular annular Josephson tunnel junctions, have a rich nonlinear phenomenology due to the intrinsic non-uniformity of their planar tunnel barrier delimited by two closely spaced confocal ellipses. In the presence of a uniform magnetic field in the barrier plane, the periodically changing width of the elliptical annulus generates a asymmetric double-well for a Josephson vortex trapped in a long and narrow CAJTJ. The preparation and readout of the vortex pinned in one of the two potential minima, which are important for the possible realization of a vortex qubit, have been numerically and experimentally investigated for CAJTJs with the moderate aspect ratio 2:1. In this work we focus on the impact of the annulus eccentricity on the properties of the vortex potential profile and study the depinning mechanism of a fluxon in more eccentric samples with aspect ratio 4:1. We also discuss the effects of the temperature-dependent losses as well as the influence of the current and magnetic noise., Comment: arXiv admin note: text overlap with arXiv:1707.01672

Recent observation of quantum vortices in superfluid $$^{4}$$ He droplets measuring a few hundreds of nanometers in diameter involved decoration of vortex cores by clusters containing large numbers of Xe atoms, which served as X-ray contrast agents. Here, we report on the study of the kinematics of the combined vortex–cluster system in a cylinder and in a sphere. Equilibrium states, characterized by total angular momentum, L, were found by minimizing the total energy, E, which sums from the kinetic energy of the liquid due to the vortex and due to orbiting Xe clusters, as well as solvation energy of the cluster in the droplet. Calculations show that, at small mass of the cluster, the equilibrium displacement of the system from the rotation axis is close to that for the bare vortex. However, upon decrease in L beyond certain critical value, which is larger for heavier clusters, the displacement bifurcates toward the surface region, where the motion of the system is governed by the clusters. In addition, at even smaller L, bare orbiting clusters become energetically favorable, opening the possibility for the vortex to detach from the cluster and to annihilate at the droplet’s surface.

Static and non-static properties of the superconducting vortex state in a splice of weak and strong superconducting regions were studied. We considered a superconducting disk with triangular and circular defects, which lead to the appearance of anisotropy in the sample. This anisotropy is included in the time-dependent Ginzburg–Landau equations through a varied $$T_\mathrm{c}$$ , which leads to distinct differences in the magnetization, supercurrent, vorticity, and free energy curves. Several unconventional vortex states were found, some comprising vortex clusters or exhibiting asymmetry, which are formed owing to the competing interactions of vortices with different Meissner currents that can be found in the sample due to anisotropy.