NMR experiments on superfluid 3He in a nematic aerogel have shown that the stability of the half-quantum vortex (HQV) realized in the polar phase depends on the relative direction between the magnetic field and the anisotropy axis brought by the aerogel. The vortex energy in the polar phase is examined in terms of the Ginzburg-Landau free energy incorporating the dipole energy, and the reason why the HQV in the polar phase in nematic aerogels became unstable in a transverse magnetic field upon a field-cooling is explained.
We calculate the dynamic vortex mass for clean Fermi superfluids including both s- and d-wave superconductors as a response to a vortex acceleration. Assuming a finite quasiparticle mean free time, the vortex mass appears to be a tensor. The diagonal component dominates in the limit of long mean free time while the off-diagonal mass takes over in the moderately clean regime.
We measure the interaction of a single superfluid vortex with surface irregularities. While vortex pinning in superconductors usually becomes weaker at higher temperatures, we find the opposite behavior. The pinning steadily increases throughout our measurement range, from 0.15Tc to over 0.5Tc. We also find that moving the other end of the vortex decreases the pinning, so we propose Kelvin waves along the vortex as a depinning mechanism.
We review the basic ideas and results on the vortex dynamics in clean superfluid Fermi systems. The forces acting on moving vortices are discussed including the problem of the transverse force which was a matter of confusion for quite a time. Finally, we formulate the equations of the vortex dynamics which include all the forces and the inertial term associated with excitations bound to the moving vortex.
We have measured a precessing superfluid vortex line, stretched from a wire to the wall of a cylindrical cell. By contrast to previous experiments with a similar geometry, the motion along the wall is smooth. The key difference is probably that our wire is substantially off center. We verify several numerical predictions about the motion, including an asymmetry in the precession signature, the behavior of pinning events, and the temperature dependence of the precession.
In-plane complex surface impedance of a Bi2Sr2CaCu2Oy single crystal was measured in the mixed state at 40.8 GHz.The surface reactance, which is proportional to the real part of the effective penetration depth, increased rapidly just above the first-order vortex-lattice melting transition field and the second magnetization peak field.This increase is ascribed to the decrease in the superfluid density rather than the loss of pinning.This result indicates that the vortex melting transition changes the electronic structure as well as the vortex structure.
Quantized vortex core structure is theoretically investigated in Fermion superfluids with population imbalance for two atom species of neutral atom clouds near a Feshbach resonance. In contrast with vortex core in balance case where the quantum depletion makes a vortex visible through the density profile measurement, the vortex core is filled in and becomes less visible because the quantized discrete bound states are occupied exclusively by the majority species. Yet it is shown that the core can be visible through the minority density profile experiment using phase contrast imaging, revealing …
The behavior of a dilute two-component superfluid Fermi gas subjected to rotation is investigated within the context of a weak-coupling BCS theory. The microscopic properties at finite temperature are obtained by iterating the Bogoliubov-de Gennes equations to self-consistency. In the model, alkali atoms are strongly confined in quasi-two-dimensional traps produced by a deep one-dimensional optical lattice. The lattice depth significantly enhances the critical transition temperature and the critical rotation frequency at which the superfluidity ceases. As the rotation frequency increases, the …
Motivated by understanding Majorana zero modes in topological superfluids in particle-number conserving framework beyond the present framework, we study the effect of particle number conservation on the Berry phase resulting from transport of a bound quasiparticle around a superfluid vortex. We find that particle-number non-conserving calculations based on Bogoliubov-de Gennes (BdG) equations are unable to capture the correct physics when the quasiparticle is within the penetration depth of the vortex core where the superfluid velocity is non-zero. Particle number conservation is crucial for d…
We calculate the relaxation of Brinkman-Smith mode via Leggett-Takagi relaxation in the presence of an isolated vortex in superfluid 3He-B. The calculation is based on an analytical solution of the order parameter far from the vortex axis. We obtain an expression for the dissipated power per vortex length as a function of the tipping angle of the magnetization and the orientation of the static magnetic field with respect to the vortex.
Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although any uniaxial deformation leads to a wider A-like phase with the axial pairing in the pressure-temperature phase diagram, the vortex core states in the two phases in aerogel depend highly on the type of deformation. In a compressed aerogel, the first-order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in the B-like…
A trapped degenerate Bose gas exhibits superfluidity with spatially nonuniform superfluid density. We show that the vortex distribution in such a highly inhomogeneous rotating superfluid is nevertheless nearly uniform. The inhomogeneity in vortex density, which diminishes in the rapid-rotation limit, is driven by the discrete way vortices impart angular momentum to the superfluid. This effect favors highest vortex density in regions where the superfluid density is most uniform (e.g., the center of a harmonically trapped gas). A striking consequence of this is that the boson velocity deviates f…
In this letter we show that the vortex lattice structure in the Bose-Fermi superfluid mixture can undergo a sequence of structure transitions when the Fermi superfluid is tuned from the BCS regime to the BEC regime. This is due to different vortex core structure of the Fermi superfluid in the BCS regime and in the BEC regime. In the former the vortex core is nearly filled, while the density at the vortex core gradually decreases until it empties out at the BEC regime. Therefore, with the density-density interaction between the Bose and the Fermi superfluids, the two sets of vortex lattices int…
We present a closed-form expression for the time dynamics of a balanced Fermi superfluid with s-wave pairing and Rashba spin-orbit (SO) coupling. Solving the associated self-consistency conditions for an initial number density given by a Gaussian and an initial gap containing a vortex dipole, we show that Rashba SO coupling results in precession of the vortex dipole. The integrated self-consistent gap decays as a function of time, characterising a "transient Fermi superfluid". Our analytic solution forms a starting point for studies of vortex dynamics -- in particular braiding of Majorana ferm…
The structure of an isolated vortex in a dilute two-component neutral superfluid Fermi gas is studied within the context of self-consistent Bogoliubov-de Gennes theory. Various thermodynamic properties are calculated and the shift in the critical temperature due to the presence of the vortex is analyzed. The gapless excitations inside the vortex core are studied and a scheme to detect these states and thus the presence of the vortex is examined. The numerical results are compared with various analytical expressions when appropriate.
We present measurements of how a single vortex line in superfluid helium interacts with a macroscopic bump on the chamber wall. At a general level our measurements confirm computational work on vortex pinning by a hemispherical bump, but not all the details agree. Rather than observing a unique pin location, we find that a given applied velocity field can support pinning at multiple sites along the bump, both near its apex and near its edge. We also find that pinning is less favorable than expected. A vortex can pass near or even traverse the bump itself with or without pinning, depending on i…
A profound change occurs in the stability of quantized vortices in externally applied flow of superfluid 3He-B at temperatures ~ 0.6 Tc, owing to the rapidly decreasing damping in vortex motion with decreasing temperature. At low damping an evolving vortex may become unstable and generate a new independent vortex loop. This single-vortex instability is the generic precursor to turbulence. We investigate the instability with non-invasive NMR measurements on a rotating cylindrical sample in the intermediate temperature regime (0.3 - 0.6) Tc. From comparisons with numerical calculations we interp…
We study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimental…
Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when size of the thermal vortex loops is comparable to the film thickness, and the results for T < Tc are found to match very well with perturbative renormalization theories that have only been carried out for T > Tc. When applied to a high-Tc superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and bulk, and estimates show that this may be readily measurable.
We show that the spin quantum Hall effect in the vortex state of two-dimensional rotating superfluid He3 can be described as an adiabatic spin transport of Bloch quasiparticles. We show that the spin Hall conductivity is written by the Berry phase as well as the Chern number. The results have similarity to the adiabatic pumping of Bloch electrons and the spontaneous polarization in crystalline dielectrics.
The integrals of motion for a cylindrically symmetric stationary vortex are obtained in a covariant description of a mixture of interacting superconductors, superfluids and normal fluids. The relevant integrated stress-energy coefficients for the vortex with respect to a vortex-free reference state are calculated in the approximation of a ``stiff'', i.e. least compressible, relativistic equation of state for the fluid mixture. As an illustration of the foregoing general results, we discuss their application to some of the well known examples of ``real'' superfluid and superconducting systems t…
The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems which contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli-de Gennes-Matricon branches with different angular momentum quantum number $n$ approach zero energy level at $p_z\rightarrow 0$. Such condensation of the energy levels is the consequence of the bulk-vortex correspondence in topological superfluids/superconductors. In a given case this is the connection between the Dirac line of zeroes in the bulk spectrum and the level condensatio…
We analyze the vortex core states of two-species (mass imbalanced) superfluid fermion mixtures as a function of two-body binding energy in two dimensions. In particular we solve the Bogoliubov-de Gennes equations for a population balanced mixture of $^{6}$Li and $^{40}$K atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass ($^{6}$Li) fermions and that the core density of the heavy-mass ($^{40}$K) fermions is highly depleted. This is in contrast with the one-species (mass balanced) mixtures with balanced populations where an equal amount of density deplet…
The bound states that can occur in a superfluid vortex have recently called for attention owing to the capability of detecting them experimentally. However, a detailed theoretical account for the presence of these vortex bound states is still lacking, for all temperatures in the superfluid phase and couplings along the BCS-BEC crossover. Here, we fill this gap and present a systematic theoretical study based on the Bogoliubov-de~Gennes equations for the bound states that occur over the two characteristic (inner and outer) spatial ranges in which the extension of a superfluid vortex can be part…
Superfluid $^3$He-B possesses three locally stable vortices known as a normal-core vortex ($o$-vortex), an A-phase-core vortex ($v$-vortex), and a double-core vortex ($d$-vortex). In this work, we study the effects of a magnetic field parallel or perpendicular to the vortex axis on these structures by solving the two-dimensional Ginzburg-Landau equation for two different sets of strong coupling correction. The energies of the $v$- and $d$-vortices have nontrivial dependence on the magnetic field. As a longitudinal magnetic field increases, the $v$-vortex is energetically unstable even for high…
The flow of quantized vortex lines in superfluid 3He-B is laminar at high temperatures, but below 0.6 Tc turbulence becomes possible, owing to the rapidly decreasing mutual friction damping. In the turbulent regime a vortex evolving in applied flow may become unstable, create new vortices, and start turbulence. We monitor this single-vortex instability with NMR techniques in a rotating cylinder. Close to the onset temperature of turbulence, an oscillating component in NMR absorption has been observed, while the instability generates new vortices at a low rate ~ 1 vortex/s, before turbulence se…
Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although the A-like phase with axial pairing is extended by any uniaxial deformation, the vortex core states in the two phases depend highly on the type of deformation in aerogel: In a compressed aerogel, the first order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in B-like phase, while no strange vortex core is expected…
Vortex dynamics in 3He-B is divided by the temperature dependent damping into a high-temperature regime, where the number of vortices is conserved, and a low-temperature regime, where rapid vortex multiplication takes place in a turbulent burst. We investigate experimentally the hydrodynamic transition between these two regimes by injecting seed vortex loops into vortex-free rotating flow. The onset temperature of turbulence is dominated by the roughly exponential temperature dependence of vortex friction, but its exact value is found to depend on the injection method.
We present measurements on both energy loss and pinning for a vortex terminating on the curved surface of a cylindrical container. We vary surface roughness, cell diameter, fluid velocity, and temperature. Although energy loss and pinning both arise from interactions between the vortex and the surface, their dependences on the experimental parameters differ, suggesting that different mechanisms govern the two effects. We propose that the energy loss stems from reconnections with a mesh of microscopic vortices that covers the cell wall, while pinning is dominated by other influences such as the…
The superfluid transition of $^3$He-$^4$He mixture films adsorbed on alumina powder is studied, with a $^4$He superfluid coverage near one layer. With up to 1.3 layers of $^3$He added, the transition becomes strongly broadened, indicating a linear increase in the vortex core size for $^3$He coverages below one layer. Annealing of the sample mixture at 4.2 K is found to be critically important in ensuring a homogeneous film across the porous substrate.
The microscopic properties of a single vortex in a dilute superfluid Fermi gas at zero temperature are examined within the framework of self-consistent Bogoliubov-de Gennes theory. Using only physical parameters as input, we study the pair potential, the density, the energy, and the current distribution. Comparison of the numerical results with analytical expressions clearly indicates that the energy of the vortex is governed by the zero-temperature BCS coherence length.
Employing the fracton-elastic duality, we develop a low-energy effective theory of a zero-temperature vortex crystal in a two-dimensional bosonic superfluid which naturally incorporates crystalline topological defects. We extract static interactions between these defects and investigate several continuous quantum transitions triggered by the Higgs condensation of vortex vacancies/interstitials and dislocations. We propose that the quantum melting of the vortex crystal towards the hexatic or smectic phase may occur via a pair of continuous transitions separated by an intermediate vortex superso…
Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles a…
We study quantized vortices in ${}^{3}P_{2}$ superfluids using a microscopic theory for the first time. The theory is based on the Eilenberger equation to determine the order parameters and the Bogoliubov-de Gennes (BdG) equation to obtain the eigenenergies and the core magnetization. Within axisymmetric vortex configurations, we find several stable and metastable vortex configurations which depend on the strength of a magnetic field, similar to a $v$ vortex and $o$ vortex in $^3$He superfluids. We demonstrate that the $o$ vortex is the most stable axisymmetric vortex in the presence of a stro…
Using a generalized reciprocity relation between charge and vortex conductivities at complex frequencies in two space dimensions, we identify the capacitance in the insulating phase as a measure of vortex condensate stiffness. We compute the ratio of boson superfluid stiffness to vortex condensate stiffness at mirror points to be 0.21(1) for the relativistic O(2) model. The product of dynamical conductivities at mirror points is used as a test of charge-vortex duality. We propose the finite wave vector compressibility as an experimental measure of the vortex condensate stiffness for neutral la…
A microscopic, quantum mechanical model for neutron vortices in the crust of a neutron star is presented. After a brief introduction to the Bogoliubov- de Gennes equations, which form the basis for our calculations, we present results for density distributions, vortex core sizes and vortex energies, both for an isolated neutron vortex and for the case when the vortex core overlaps with a cylindrical nucleus. Earlier results on the vortex core size are confirmed, indicating a much less dramatic variation of the vortex core size with density than predicted by the BCS formula.
We present an efficient framework to numerically treat infinite periodic vortex lattices in rotating superfluids described by the Gross-Pitaevskii theory. The commonly used split-step Fourier (SSF) spectral methods are inapplicable to such systems as the standard Fourier transform does not respect the boundary conditions mandated by the magnetic translation group. We present a generalisation of the SSF method which incorporates the correct boundary conditions by employing the so-called magnetic Fourier transform. We test the method and show that it reduces to known results in the lowest-Landau…
Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by mapping the dynamics of certain quantum theories onto the dynamics of classical gravity. We use this gravitational description to numerically construct turbulent flows in a holographic superfluid in two spatial dimensions. We find that the superfluid kinetic energy spectrum obeys the Kolmogorov -5/3 scaling law, as it does for turbulent flows in normal fluid…
