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Vortex reconnections plays an important role in the turbulent flows associated with the superfluids. To understand the dynamics, we examine the reconnections of vortex rings in the superfluids of dilute atomic gases confined in trapping potentials using Gross-Petaevskii equation. Furthermore we study the reconnection dynamics of coreless vortex rings, where one of the species can act as a tracer., Comment: 9 pages, Proceeding from International Conference On Complex Processes in Plasmas and Nonlinear Dynamical Systems, Gandhinagar, India (November 2012)

In this paper, we demonstrate a possible astrophysical application of physics of dense matter, which is related to the r-mode instability of rapidly rotating compact star. We discuss some microscopic consideration to compute the time scale for energy dissipation in the presence of superfluid vortices. As such an example, color-flavor locked (CFL) quark matter is considered.

As the rotation of a neutron star slows down, its density increases, pushing the matter inside the star out of beta equilibrium. The beta decays restoring this equilibrium dissipate energy, which heats the star, making it emit thermal ultraviolet radiation for much longer than the standard cooling times. This effect might have been observed in the nearest millisecond pulsar, J0437‐4715, by Kargaltsev and collaborators. We show how it operates if the nucleons in the star are superfluid. The steady‐state chemical imbalances and temperature increase with the energy gaps, making it possible to constrain the energy gaps from observations. In certain cases, strong oscillations of the temperature can occur. We also analyze competing heating mechanisms, such as vortex friction, and suggest observations that might distinguish between them.

The inner crust of a neutron star is expected to contain a Coulomb lattice of nuclei immersed in a superfluid sea of free neutrons. The rotation of the star induces the formation of vortices in the neutron sea, whose dynamics is influenced by the interaction with the nuclei. In particular, this interaction is important to determine whether it is energetically advantageous for vortices to pin on nuclei or not. We find that the pinning energy is sensitive to quantal size effects. In fact, the nuclear shell structure tends to hinder the formation of vortices inside the nuclear volume.

An experimental study was carried out on the heat transfer properties of pressurized superfluid helium in the Gorter‐Mellink heat transfer region. By using channels of hydraulic diameter from 5.6 × 10− through 4.81 × 10−3 m, the heat transfer properties of pressurized superfluid helium were measured in the experiment. The temperature dependence of Gorter‐Mellink parameter, AGM, is revealed from the experimental results. It is also proven that AGM depend only on temperature, and not on the channel size and shape. The effect of quantized vortices on heat transfer of pressurized superfluid helium is discussed in comparison of the channel diameter with the mean vortex line spacing.

The vortex state of superfluid 3He‐A has been studied under rotation by measuring the change of the width of the main NMR line at rotation speeds up to twice as fast as previously reported. We identify three temperature ranges according to the temperature dependence of the linewidth. These temperature ranges have been predicted by Fomin and Kamenskii. We also report the results of our preliminary NMR linewidth measurements for different rotational speed Ω’s. These are consistent with previously reported results, where they overlap, and reveal a different Ω dependence for each temperature range.

This paper provides a brief history of the evolution of the Berkeley experiments on macroscopic quantum effects in superfluid helium. The narrative follows the evolution of the experiments proceeding from the detection of single vortex lines to vortex photography to quantized circulation in 3He to Josephson effects and superfluid gyroscopes in both 4He and 3He.

We present here a simple model to examine the effect of oscillating superfluid velocity on a quantized vortex. This situation can be realized in vibrating wire or vibrating grid experiments where the vortices are attached to the oscillating wires. Within this model we determine the critical velocity, above which the vortex motion becomes irregular and new vortices are created. We also determine the vortex creation rates.

In rotating superfluid 3He‐B, a sharp transition to turbulence which is insensitive to the fluid velocity is observed in contrast to classical turbulence. Instead, this transition is controlled by an intrinsic parameter, q ≡ α/1 − α′, of the superfluid, where α and α′ are mutual friction parameters depending on temperature. However, rotating superfluid 3He‐B is the only system which shows this kind of transition, and many unsolved mysteries yet remain. Hence, we study numerically the quantum vortex dynamics in thermal (unidirectional) counter flow systems especially at high temperatures, with the goal of proposing a new system which also shows a turbulence transition controlled by q. It is shown that the critical velocity above which the system can sustain a vortex tangle increases sharply at q ≈ 0.4. This means that no vortex tangle state can be stable for q ≳ 0.4. This may be closely relevant to the dramatic vortex dynamics transition caused by q in rotating superfluid 3He‐B.

We argue that the critical velocity for intrinsic nucleation of quantized vortices in isothermal flow of He II at low temperature can be viewed as approaching the spinodal limit in pressure and breakdown of superfluidity as a consequence of the Bernoulli equation. Breaking the liquid by cavitation that changes the topology from simply to multiply connected seems an essential requirement for intrinsic vortex nucleation and serves as an additional criterion of superfluidity, of the form Vc = [2(pext − psp)/ρs]1/2, where pext is the external pressure, psp denotes the spinodal limit, and ρs stands for the superfluid density. This criterion can be viewed as additional to the well‐known Landau criterion for breakdown of superfluidity due to emission of quasiparticles.We argue that the critical velocity for intrinsic nucleation of quantized vortices in isothermal flow of He II at low temperature can be viewed as approaching the spinodal limit in pressure and breakdown of superfluidity as a consequence of the Bernoulli equation. Breaking the liquid by cavitation that changes the topology from simply to multiply connected seems an essential requirement for intrinsic vortex nucleation and serves as an additional criterion of superfluidity, of the form Vc = [2(pext − psp)/ρs]1/2, where pext is the external pressure, psp denotes the spinodal limit, and ρs stands for the superfluid density. This criterion can be viewed as additional to the well‐known Landau criterion for breakdown of superfluidity due to emission of quasiparticles.

At sufficiently low temperatures, electron bubbles (negative ions) can become trapped on quantized vortices in superfluid helium. Previously, the escape of electron bubbles from vortices by thermal excitation and through quantum tunneling has been studied. In this paper, we report on an experiment in which light is used to release bubbles from quantized vortices (photoemission). A CO2 laser is used to excite the electron from the 1S to the 1P state, and it is found that each time a photon is absorbed there is a small probability that the bubble containing the electron escapes from the vortex.

In atomic Fermi gases, the pairing character changes from BCS‐like to BEC‐like when one decreases the threshold energy of the Feshbach resonance. With this crossover, the system enters the strong‐coupling regime through the population enhancement of diatom molecules, and the vortex structure becomes much different from well‐known core structures in BCS superfluid since the superfluid order parameter is given by a sum of BCS pairs and BEC molecular condensates. In this paper, we study the structure of a vortex by numerically solving the generalized Bogoliubov‐de Gennes equation derived from the fermion‐boson model and clarify how the vortex structure changes with the threshold energy of the Feshbach resonance. We find that the diatom boson condensate enhances the matter density depletion inside the vortex core and the discreteness of localized quasi‐particle spectrum.

We describe measurements of the decay of quantum turbulence produced by a vibrating grid in superfluid 3He‐B at low temperatures. Two nearby NbTi vibrating wire resonators at different distances from the grid are used to detect the turbulence via a reduction in the quasiparticle damping owing to Andreev reflection by the flow around the vortex lines. The decay time constant of this turbulence, after stopping the grid motion, is longer at the wire furthest from the grid. This suggests that either the tangle evolves and moves away from the grid once the grid motion has been stopped, or that there is a faster decay mechanism in operation close to the grid.

Recently there have been reports of superfluidity in solid 4He and possibly in other solids. One of the common features of these systems is their small superfluid density. This would imply a rather long three dimensional (3D) coherence length. Sub‐monolayer superfluid 4He films condensed on 3D connected surfaces show 3D superfluid transitions, in some cases with a rather small 3D superfluid density and a long 3D coherence length, which implies a large 3D vortex core size. We have previously detected 3D vortex lines in a 3D superfluid made of a sub‐monolayer 4He film condensed on the pore surface of large pore diameter porous glass, by measuring the energy dissipation in a torsional oscillator under rotation. We propose application of this method to the new supersolids.

Following the injection of vortex loops into an originally vortex‐free sample of superfluid 3He‐B at T < 0.6Tc, transient states appear which exhibit a modified response in transverse NMR experiments when compared with the response from the final equilibrium state of rectilinear vortices. Here we investigate the NMR response of a model state where a random vortex tangle is assumed to be superimposed on the equilibrium vortex state. We show that this model can qualitatively account for the experimental findings, provided that the tangle is anisotropic.

To investigate the hydraulic cavitation and the motion of cavity in superfluid helium, an observation system was constructed. The system contains a cryostat for superfluid helium experiment and a high-speed video camera system. Using this apparatus, observations of cavitation which accompanies the flow around a metal sphere falling in the sample liquid were carried out. The hydraulic cavitation in superfluid helium was successfully observed for the first time. Experimental results of negative pressures were compared with cavitation theory. It follows that experimental values were three orders of magnitude smaller than theoretical values. Disagreements are discussed in viewpoints of turbulent flow and quantized vortex.

Using a focused laser beam we stir a Bose-Einstein condensate confined in a magnetic trap. When the stirring frequency reaches a critical value, we observe the formation of a vortex at the center of the condensate. Using the quadrupolar excitation of the condensate we measure the angular momentum of the condensate with the vortex, and we find that it is ∼ℏ per particle, as expected. For larger stirring frequencies, regular arrays of vortices are observed.

Vortices for 2D superfluids are introduced and are described in terms of a 2D Coulomb gas. The 2D classical JJ array is modeled by a 2D XY-model and a mapping between the XY-model and the Coulomb gas is given. The physical properties of a JJ array are then given in terms of the corresponding Coulomb gas properties. First aspects of the Kosterlitz-Thouless vortex unbinding transitions are reviewed. Consequencies for the resistance as well as the frequency dependent conductivity are described. Next the vortex unbinding induced by an external current is considered with Consequencies for the non-linear IV-characteristics. Finally some some effects of a perpendicular magnetic field are discussed in terms of an interplay between free vortices and bound vortex pairs.

The superfluid transition for 4He films adsorbed in porous materials is discussed using a theory which emphasizes topological excitations of the superfluid associated with the multiple connectivity of the porous material. The coupling constant for these excitations is renormalized by the polarization of quantized vortices and is obtained from a generalization of the Kosterlitz‐Thouless theory. Within this picture, the crossover from two‐dimensional, Kosterlitz‐Thouless behavior, to three‐dimensional critical behavior may be understood.

The effects of vortex pinning on the superfluid velocity of the He4 films is discussed.(AIP)

Results from cw NMR measurements on superfluid 3He‐B in rotation are discussed. The measurements have been performed with the magnetic field oriented at different angles with respect to the rotation axis. The results illustrate the effect of rotation on different order parameter textures in a cylindrical container. In particular, they allow the textural vortex free energy to be determined. The influence of boundary conditions on different textures has been investigated.

Theoretical principles underlying the unusual signatures of vortices in textural NMR on rotating superfluid 3He are summarized here. We emphasize the evidence for continuous vorticity in the A‐phase and a complicated structure of the vortex core in the B‐phase, manifested through the observed first‐order phase transition of the core of vortices. Textures in a rotating cylinder of 3He‐B which result under various combined orientating effect of surfaces, vortices, and the normal fluid‐superfluid counterflow are discussed.

The coupling of the real squashing collective mode to the zero sound in rotating superfluid 3He‐B has been investigated. In a magnetic field rotation enhances the coupling of the non‐zero mJ substrates, and the five or sometimes six‐fold line splitting becomes observable even when H is parallel to Ω and to the direction of sound propagation. Equilibrium vortex lattices and vortex free states can be distinguished by their characteristic absorption spectra. The data are compared with microscopic calculations and a recent phenomenological theory. In the A‐phase the anisotropy of the sound attenuation serves as a powerful means to detect the 1 texture rearrangement when a vortex lattice is formed; measurements have been made in zero and in weak (1.7 mT) magnetic fields.

Muirhead, Vinen and Donnelly have argued that vortex nucleation by negative ions in superfluid 4He involves small vortex loops emerging in the equatorial plane of the ion. These loops have to overcome an energy barrier of about 3 °K. They do this either by thermal activation (involving a phonon or roton) or by tunnelling. Recent experiments have observed this thermally activated process and found an energy barrier of order 3 °K.Another feature of their model is that vortex lines undergo a sort of cyclotron motion at a frequency ωc=ℏ/(mπa2) where a is the vortex core radius. When quantized these cyclotron levels are about 50 °K apart. The presence of these levels can be inferred from measurements of the vortex nucleation rate at low temperatures as a function of electric field.

Finite frequency dissipation near the superfluid transition of Helium 4 films adsorbed on porous substances is discussed.(AIP)

Recent works on analytic vortices in rotating 3He‐A are reviewed. It is shown that the circular‐hyperbolic vortex lattice has the lowest free energy in an axial magnetic field. The associated nuclear magnetic resonance satellites account for not only the observed satellite frequencies in a rotating 3He‐A experiment but also the observed intensity of the satellite resonances.