Circulation Quanta Research Articles

Dynamics of quantum vortices in a quasi-two-dimensional Bose–Einstein condensate with two “holes”

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.

Generating and manipulating quantized vortices on-demand in a Bose-Einstein condensate: A numerical study

We numerically investigate an experimentally viable method, that we will refer to as the "chopsticks method", for generating and manipulating on-demand several vortices in a highly oblate atomic Bose-Einstein condensate (BEC) in order to initialize complex vortex distributions for studies of vortex dynamics. The method utilizes moving laser beams (the "chopsticks") to generate, capture and transport vortices inside and outside the BEC. We examine in detail this methodology and show a wide parameter range of applicability for the prototypical two-vortex case, and show case examples of producing and manipulating several vortices for which there is no net circulation, equal numbers of positive and negative circulation vortices, and for which there is one net quantum of circulation. We find that the presence of dissipation can help stabilize the pinning of the vortices on their respective laser beam pinning sites. Finally, we illustrate how to utilize laser beams as repositories that hold large numbers of vortices and how to deposit individual vortices in a sequential fashion in the repositories in order to construct superfluid flows about the repository beams with several quanta of circulation.

Half-quantum vortices

Unlike to superfluid 4He the superfluid 3He-A support the existence of vortices with half-quantum of circulation as well as single quantum vortices. The singular single quanta vortices as well as nonsingular vortices with 2 quanta of circulation have been revealed in rotating 3He-A. However, the half-quantum vortices in open geometry always possess an extra energy due to spin-orbit coupling leading to formation of domain wall at distances larger than dipole length ∼10−3 cm from the vortex axis. Fortunately the same magnetic dipole-dipole interaction does not prevent the existence of half-quantum vortices in the polar phase of superfluid 3He recently discovered in peculiar porous media “nematically ordered” aerogel. Here we discuss this exotic possibility. The discoveries of half-quantum vortices in triplet pairing superconductor Sr2RuO4 as well in the exciton–polariton condensates are the other parts of the story about half-quantum vortices also described in the paper.

Multiply quantized vortices and finite temperature effects in the BEC/BCS crossover regime

The interatomic interaction strength in ultracold fermionic gases can be manipulated using Feshbach resonances, allowing to probe both the regime where atoms form molecules that Bose condense (BEC) and the Bardeen–Cooper–Schrieffer (BCS) regime. We use a path-integral formalism to investigate the properties of multiply quantized vortices in these systems. Although the vortex core region expands when more quanta of circulation are present, the qualitative result is the same: in the BEC regime, the atoms do not penetrate into the vortex core, whereas in the BCS regime they do. The system undergoes a smooth crossover between the two regimes. When the temperature is increased, the penetration of atoms into the vortex core becomes more pronounced.

NMR measurement of quantized vortex lines in rotating 3He-A

The dominant vortex line in 3He-A has singularity-free order parameter structure and low-critical velocity. It is formed in magnetic fields above 1 mT, where the orbital and spin parts of the order parameter are “unlocked”, it carries two quanta of circulation (=2 κ 0), and gives rise to a frequency-shifted satellite peak in the NMR absorption spectrum. We have measured its NMR response with improved resolution and find that the satellite amplitude, in addition to being proportional to the number of vortex lines, also includes a small texture-dependent contribution.

Progress towards a superfluid 4He analog of the superconducting rf squid

Abstract We are working to realize a superfluid 'He analog of the superconducting rf SQUID to be used as a gyroscope. As a first step we developed an experimental method to induce an ac superfluw across a 5 μm radius orifice by using a rotation. The orifice was supported by a septum placed inside a hollow torus filled with liquid helium and the flow was induced by rotating the whole torus, that was the inertial member of a torsional oscillator. We report here measurements of the critical velocity for the orifice, obtained by detecting the occurrence of a dissipation in the oscillator's motion. The energy and the number of circulation quanta involved in the dissipative process are evaluated.

Experiments with negative ions in3He superfluids

The interaction between negative ions and 3 He superfluids was studied by using a time-of-flight spectrometer having a 10−3 relative resolution. The ions guided through a sample of rotating3He-A were found to be focused into the cores of the vortices present in this rotating superfluid. Two different types, with different core structures and presumably different numbers of circulation quanta associated with them, were found. The ion mobility along the vortex cores, μ c , observed in the absence of external magnetic field, can be explained by the mobility anisotropy of the A phase, which indicates that the vortices are continuous, i.e., consist of the A phase even in the core. In finite magnetic fields, a qualitatively similar continuous vortex structure was found, a result compatible with the earlier nuclear magnetic resonance (NMR) experiments, but also a new vortex type with an anomalously high μ c was seen when the vortex sample was prepared “adiabatically.” The observed strong ion focusing indicates broken w-symmetry in the core textures. This is in contradiction with the earlier numerical calculations on the optimal continuous vortex texture. Experiments to observe trapping of ions into the vortex cores were performed both in A and B phases. No trapping could be detected. Mobility measurements in stationary liquid were extended down toT=0.3T c . Comparison with the calculated transport coefficients yieldsΔ A (T)=1.32Δ BCS (T) for the maximal A phase gap atP=29.3 bar, andΔ B (T)=1.12Δ BCS (T) for the B phase gap at 4.8 bar. In the normal Fermi liquid a shallow minimum of ion mobility was detected aroundT≃2T c =5 mK.

THE EFFECT OF RVB FLUX CONFIGURATION ON THE SUPERCONDUCTING STATE

The RVB state is a singlet quantum liquid which can support periodic or fluid-like quantum circulation around the elementary plaquette in two dimensions. In the s + id phase there is a half flux quanta of circulation in every elementary plaquette. We show that the holons in the presence of this lattice of circulation have a two-valley structure, as opposed to "s"or "d" states, which have a single valley. Using an effective holon Hamiltonian, we study the mean-field properties of the two-valley holon condensate, and compare its energy with the single valley case. A transition from the "d" to the "s + id" state is predicted with increasing hole concentration for sufficiently large Hubbard U. Some speculations are offered about the general case of a fluid-like distribution of flux quanta.

Rotating superfluid 3He

The significance of the order parameter is reviewed for the familiar case of vortices in the rotating Bose superfluid 4He. The triplet p-wave Cooper pairing in the Fermi superfluid 3He introduces new and unusual possibilities. In the rotating B phase, all vortices have singular cores, and several different structures have been investigated. In the rotating A phase, an additional feature is a nonsingular vortex with two quanta of circulation.

Orbital Dynamics of Superfluid 3He

Because the gap of superfluid 3He is anisotropic, any motion of the anisotropy axis will lead to a non-equilibrium quasiparticle distribution. Equilibrium can only be restored through quasiparticle collisions which lead to dissipation. This dissipation was measured using the damping of torsional oscillations of a powder-filled torus about its axis of symmetry. In both the A and B phases, the orbital viscosity coefficient, µ, extracted from the damping was proportional to (1-T/Tc) near Tc. At low temperatures µ, is independent of temperature. Both observations are in contrast with theoretical predictions. The dissipation is also sensitive to the presence of a d.c. supercurrent. This was used to study persistent currents in the A-phase, where the flow decayed in discrete jumps of approximately 5 circulation quanta.

Vortices in Rotating Superfluid 3He

Four different types of vortices and one metastable vortex state have been observed in the rotating superfluid 3He. In the A-phase, both continuous vortices with two circulation quanta and singular vortices with one circulation quantum have been identified. The rotating B-phase displays two regions in the pT-plane with different stable vortex structures separated by a first order phase transition. A metastable vortex state is obtained when cooling, during rotation, through the first order phase transition line. The relevant experimental data for these identifications are reviewed and their interpretation is discussed on the basis of the present theoretical understanding.

Phase transitions in two-dimensional uniformly frustratedXY models. II. General scheme

For two-dimensional uniformly frustratedXY models the group of symmetry spontaneously broken in the ground state is a cross product of the group of two-dimensional rotations by some discrete group of finite order. Different possibilities of phase transitions in such systems are investigated. The transition to the Coulomb gas with noninteger charges is widely used when analyzing the properties of relevant topological excitations. The number of these excitations includes not only domain walls and traditional (integer) vortices, but also vortices with a fractional number of circulation quanta which are to be localized at bends and intersections of domain walls. The types of possible phase transitions prove to be dependent on their relative sequence: in the case the vanishing of domain wall free energy occurs earlier (at increasing temperature) than the dissociation of pairs of ordinary vortices, the second phase transition is to be associated with dissociation of pairs of fractional vortices. The general statements are illustrated with a number of examples.

Phase transitions in two-dimensional uniformly frustratedXY models. I. Antiferromagnetic model on a triangular lattice

A most popular model in the family of two-dimensional uniformly-frustratedXY models is the antiferromagnetic model on a triangular lattice [AFXY(t) model]. Its ground state is both continuously and twofold discretely degenerated. Different phase transitions possible in such systems are investigated. Relevant topological excitations are analyzed and a new class of such (vortices with a fractional number of circulation quanta) is discovered. Their role in determining the properties of the system proves itself essential. The characteristics of phase transitions related to breaking of discrete and continuous symmetries change. The phase diagram of the “generalized” AFXY(t) model is constructed. The results obtained are rederived in the representation of the Coulomb gas with half-integer charges, equivalent to the AFXY(t) model with the Berezinskii-Villain interaction.

Discontinuous field-velocity relation for vortex rings in superfluid solutions

The simultaneous existence of two different ring velocities observed in dilute 3He- 4He solutions below 45 mK can be interpreted as evidence for the existence of rings with different quanta of circulation or a resonance in the ring- 3He scattering cross section.

Heat Torques and Circulation in Superfluid Helium

The small torques experienced by heated cylinders immersed in rotating superfluid helium have been measured and the results are compared with the predictions made for "heat-exchange" torques by Penney and Overhauser. They have pointed out that whenever there is a net superfluid circulation about a heated object, the object should experience a torque proportional to the circulation and power input and inversely proportional to the absolute temperature. The measured torques show this expected dependence on power and temperature. The existence of such torques is inherent in the two-fluid thermohydrodynamics of He II and is a result of the transfer of superfluid angular momentum to the object as superfluid is converted to normal fluid at the heated surface. Torques of order ${10}^{\ensuremath{-}6}$ to ${10}^{\ensuremath{-}7}$ dyn cm are observed at 1.30\ifmmode^\circ\else\textdegree\fi{}K for power inputs of a few milliwatts and for cylinders 2 mm in diameter and 1 cm long. If the superfluid circulation is quantized, as first suggested by Onsager and Feynman, the torque should also be quantized. The torque values measured in the present experiment correspond to those expected for a few quanta of circulation about the cylinder, but the present experimental noise levels do not permit clear resolution of individual quantum levels.