Superfluid Velocity Research Articles

Nonlinear electrodynamics in cuprate superconductors

We present two types of experiments which probe the high-frequency conductivity of BSCCO films in the presence of large superfluid velocities. In the first the superflow is the static velocity field associated with the vortex lattice. In the second the velocity is dynamic, induced by high-intensity single-cycle electromagnetic pulses. We show that intrinsic pair-breaking in a d-wave superconductor can provide a unified explanation for both effects.

Josephson acoustic radiation in superfluid 4He: Towards a quantum mechanical pressure standard

Below 2.2 K, 4He is a superfluid that exhibits nearly dissipationless flow for velocities less than a well defined critical velocity. For flow through submicron apertures, the superfluid begins to dissipate energy at the critical velocity by the creation and motion of individual quantized vortices across the aperture. Using a recently developed pressure control technique, a constant pressure drop, ΔP, is applied across the aperture. This causes the vortices to cross the aperture at a Josephson frequency given by fj=(m4ΔP)/(ρh) where m4 is the mass of a helium atom and h is Plank’s constant. The periodic vortex crossing causes the superfluid velocity in the aperture to oscillate and emit acoustic radiation at fj. This sound source will radiate a total power of 10−21 W into freespace. Radiation from the vortex motion has been detected using a 1/4 wave resonant detector and a novel cryogenic microphone. This phenomena could lead to a frequency based pressure standard where the frequency is determined by quantum mechanics. [Work partially supported by the Office of Naval Research and NASA.]

The problem of the ‟charge” Q(4) = div vs for superfluid velocity in case of Bose systems

The problem of the ‟charge” <i>Q</i>⁽⁴⁾ = div <b>v</b>_<i>s</i> for superfluid velocity in case of Bose systems

The influence of an external magnetic field and anisotropy on the “charge” [formula omitted] in 3HeA

The normalization condition A ij A ij ★ = 1 for the matrix order parameter describing 3HeA leads to the relation dot A ijA ij ★ + A ijA ij ★ = 0 , where dot A ij denotes the equation of motion for A ij . It was shown that this relation is a condition for superfluid velocity v s of the form div v s = Q(t, x) . If in the system the correlations and nonlocal dependences are important the “charge” Q(t, x) depends on the part of the density of magnetization m connected with the diffusive anisotropic mode and on an external magnetic field H .

Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases.

The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge'' symmetry. This symmetry is manifested by a superfluid velocity ${\mathbf{u}}_{s}$ (or gauge field) generated by the Berry phase of the spin field. In ``static'' traps, ${\mathbf{u}}_{s}$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\mathbf{\ensuremath{\Omega}}}_{c1}$, and can lead to vortex ground states.

Superfluid transition in4He in gravity and heat flow

When4He in a normal fluid state near the superfluid transition is cooled from the bottom below the transition, a superfluid region appears at the bottom and slowly expands in the upward direction. We performed simulations for this case in one dimension fixing the temperature Tb at the bottom and the heat flux at the top Q. We find densely distributed phase slip centers rapidly oscillating in time in the expanding superfluid region. Their role is to produce a temperature gradient compensating the transition temperature gradient (dTλ(p)/dp) pg in gravity and to produce a constant negative reduced temperature T-Tλ(p) with small fluctuations superposed. The superfluid velocity multiplied by the correlation length is found to be violently fluctuating around ħ/√3m.

Boundary layer separation and vortex creation in superflow through small orifices

We report on numerical solutions of the Gross-Pitaevskii equation for twodimensional flow of a super fluid condensate through a small orifice. When the super fluid velocity in the center of the orifice exceeds about 60 % of the speed of sound, the flow in the throat of the orifice becomes unstable to a form of boundary layer separation. Low condensate-density regions bulge away from the walls and form the cores of singly quantized vortices. These detach from the boundary and are convected downstream.

Current-conserving description of nonlinear transport in NS and NSN structures

Nonlinear transport in NS and NSN structures is studied by means of a self-consistent microscopic description. Current conservation requires the superfluid velocity to be nonzero, causing the various quasiparticle channels within the superconductor to open at different voltages. This effect is responsible for major changes in the current-voltage characteristics. At low temperatures superconductivity, some times in a peculiar gapless form, may survive up to high voltages. The minimum voltage for quasiparticle transmission is shown to decrease strongly with temperature and with the transmittivity of the interfaces. A transport regime is identified where impurities are unable to degrade the quasiparticle electric current.

Heat flow induced anomalies of the entropy and specific heat nearT λ of4He

The effect of a stationary heat currentQ on superfluid4He in a homogeneous metastable state nearT λ (Q) is studied. On the basis of a renormalization-group calculation of the entropy we predict a considerable enhancement ΔC Js=C Js(T,Q)−C Js(T,0) of the specific heatC Js at constant superfluid currentJ s up to a critical heat currentQ c (T) whereC Js is divergent. This result is compared with the cusp anomaly of δC vs of the specific heatCs vs at constant superfluid velocity. In the limitQ→0 we predict the universal ratio lim Q→0ΔC Js/ΔC vs=(1+ν)/(1−ν)=5.08.

Texture of the vortex lattice of superfluid3He-A

In the paper we study the detailed structure of the order parameters in the vortex lattice of superfluid3He-A and compare several vortex lattice structures. Our analysis is confined to a unit cell and assumes a periodic boundary condition for the superfluid velocity field and the order parameter fields. However, we do not assume orthonormality for the order parametersm andn (from which the direction of the orbital angular momentum is given byI=m×n/mn). We obtain a stable configuration for the order parameters and vortex lattice structure using the relaxation technique.

Superfluid density of4He nearT λ in two-loop order

We present the results of a renormalization group calculation of the superfluid density of4He nearT λ at finite superfluid velocity v s . Within the φ4 model for an order parameter with O(n) symmetry and using field theory in three dimensions, we have computed to two-loop order the amplitude function for the superfluid density up to O((v s/v sc)2). We also give the two-loop expression for the amplitude function of the order parameter at v s =0. Applications of these results are briefly discussed.

Multiple quantum phase slips in superfluid4He

Phase slips by 2π in the critical flow of superfluid 4He through an orifice have been known to exist for some time. Besides these small, regular events, large and precipitous drops of the velocity which may cause up to a full collapse of the flow through the orifice have been observed by a number of authors. We have found that collapses are robust and repeatable features during the same cool-down and correspond to events involving n quantized vortices. They depend on temperature, pressure, 3He content and resonator drive level. At a given pressure, their appearance is governed solely by the magnitude of the superfluid velocity vs.

Thermal conductivity study of thin He films adsorbed in porous glasses with well controlled pore sizes

Thermal conductivity study of thin He films adsorbed in porous glasses with well controlled pore sizes[2] is reported. The measurements are performed in a cell where a torsional oscillator monitors the superfluid density change, for the same films for comparison. Since the heat flux through the superfluid is proportional to the superfluid velocity, we discuss the possible observation of the intrinsic critical velocity vsl = h/ml, inherent in superfluid He films in such porous systems with unit pore length l, as discussed by Minoguchi and Nagaoka[3], which marks the velocity at which phase slippages start to occur over macroscopic scales.

Study of rotons in superfluid4He by Raman scattering

There is a long standing disagreement between neutron and Raman scattering from rotons in superfluid4He near Tλ. In neutron scattering the linewidth becomes very large and the roton signal seems to disappear at Tλ. A substantially smaller linewidth is observed with Raman scattering and the roton signal is present even at Tλ. We have interpreted this difference (J. Low Temp. Phys. 93, 879 (1993)) as due to a modulation of the roton energy by a fluctuating local superfluid velocity due to proliferation of vorticity as Tλ is approached. This gives rise to an extra contribution to the roton linewidth in neutron scattering but not in Raman scattering in which two rotons with almost opposite momenta are excited. We propose a test of this explanation with evanescent field Raman scattering. It has been suggested (A. Kuklov, A. Bulatov and J.L. Birman, Phys. Rev. Lett. 72, 3855 (1994)) that in such a measurement the scattering by a single roton should be measurable. In this case the presence of a fluctuating local superfluid velocity should show up as in neutron scattering and corroborate our proposal.

Molecular hydrodynamics of a weakly degenerate nonideal bose-gas II. Green functions and kinetic coefficients

The nonideal degenerate Bose-system at a temperature close to zero is investigated by N. N. Bogolyubov and D. N. Zubarev's method of collective variables. Applicable to a wide range of frequencies and wave vectors, interpolated expressions for the Green functions of the densities of conserved quantities and for the superfluid velocity potential are derived from exact relations. The criteria defining the validity domain of the hydrodynamic approximation are obtained. The kinetic coefficients of two-liquid hydrodynamics at temperatures close to zero are calculated for a weakly nonideal Bose-gas. A comparison with the method employing the kinetic equation for quasi-particles is made.

Quantum phase of induced dipoles moving in a magnetic field.

We derive the quantum phase accompanying a neutral particle (with no permanent electric dipole moment) moving in an area where a nonuniform electric field and a uniform magnetic field are simultaneously applied. Such a quantum phase can be ascribed to the sum of the Aharonov-Bohm phases of the charges constituting the neutral particle. An experimental configuration much more practical than a previous suggestion is proposed to test for the phase. The possible nonzero superfluid velocity in the ground state of the ${}^{4}\mathrm{He}$ condensate is theoretically demonstrated.

Relationship between the roton minimum and T lambda in 4He.

We present a simple phenomenological relationship between the value of the superfluid transition temperature ${\mathit{T}}_{\ensuremath{\lambda}}$ and the local superfluid flow velocity, the velocity below which no excitations can be formed in $^{4}\mathrm{He}$. We make a direct connection between the local superfluid velocity for a ``dressed'' atom and the parameters of the roton minimum of the $^{4}\mathrm{He}$ dispersion curve as a function of pressure. We suggest that the resulting relation between the \ensuremath{\lambda} transition temperature and the roton minimum is a straightforward consequence of the microscopic conservation laws for energy and momentum.

Mesoscopic Giaever and Josephson junctions

Quasi-particle wave interference controls both the current-voltage characteristics and the current-phase relation of a superconducting device. To illustrate this point, we show that both the Josephson current-phase relation I( φ) = I c sin( φ) and the nonlinear current-voltage characteristic known as Giaever tunneling can be understood only through mesoscopic processes occuring at the interface to the superconductor. The critical current through a one-dimensional superconducting wire or point contact, which has order of magnitude eΔ/ h, is a measure of Landau's superfluid depairing velocity Δ/ p F.

Numerical investigation of the flow properties of He II.

In the framework of the reconnecting vortex-tangle model, flow properties of He II were studied numerically. The Crank-Nicolson method was used to calculate the motion of quantized [sup 4]He vortices, assuming smooth walls in infinitely long channels, applying periodic boundary conditions in the direction of the flow, and with friction coefficients [alpha]=0.1 and [alpha][prime]=0. Flow channels with square and circular cross sections and infinitely wide slits were studied. The superfluid velocity profile was assumed to be flat; the normal-component velocity profile was either flat or parabolic. Special interest was paid to the time-averaged line-length density and the average mutual-friction force density as functions of the difference between the average normal-fluid velocity and the externally applied superfluid velocity. The influence of the periodicity length on the calculated flow properties was determined. The results were compared with experiment.

Instability of second sound under heat flow near the superfluid transition

In heat-carrying superfluids, second sounds become unstable when the difference between the superfluid velocity and the normal fluid velocity exceeds a critical value. We derive a nonlinear evolution equation of the phase of the complex order parameter in this unstable region near the superfluid transition. It indicates emergence of trains of soliton-like heat pulses, which will be nearly periodic in a weakly unstable regime and chaotic in a strongly unstable regime. Experimentally, this instability cannot be observed in usual one-dimensional geometries due to appearance of a normal fluid region at large heat currents. However, we predict that it can be realized in a cell with a constricted part.