We have studied the resonance of a commercial quartz tuning fork immersed in superfluid 4 He, at temperatures between 5 mK and 1 K, and at pressures between zero and 25 bar. The force-velocity curves for the tuning fork show a linear damping force at low velocities. On increasing velocity we see a transition corresponding to the appearance of extra drag due to quantized vortex lines in the superfluid. We loosely call this extra contribution "turbulent drag". The turbulent drag force, obtained after subtracting a linear damping force, is independent of pressure and temperature below 1 K, and is easily fitted by an empirical formula. The transition from linear damping (laminar flow) occurs at a well-defined critical velocity that has the same value for the pressures and temperatures that we have measured. Later experiments using the same fork in a new cell revealed different behaviour, with the velocity stepping discontinuously at the transition, somewhat similar to previous observations on vibrating wire resonators and oscillating spheres. We compare and contrast the observed behaviour of the superfluid drag and inertial forces with that measured for vibrating wires.
Linear defects are generic in continuous media. In quantum systems they appear as topological line defects which are associated with a circulating persistent current. In relativistic quantum field theories they are known as cosmic strings, in superconductors as quantized flux lines, and in superfluids and low-density Bose-Einstein condensates as quantized vortex lines. A conventional quantized vortex line consists of a central core around which the phase of the order parameter winds by 27(pi)n, while within the core the order parameter vanishes or is depleted from the bulk value. Usually vortices are singly quantized (that is, have n = 1). But it has been theoretically predicted that, in superfluid 3He-A, vortex lines are possible that have n = 2 and continuous structure, so that the orientation of the multicomponent order parameter changes smoothly throughout the vortex while the amplitude remains constant. Here we report direct proof, based on high-resolution nuclear magnetic resonance measurements, that the most common vortex line in 3He-A has n = 2. One vortex line after another is observed to form in a regular periodic process, similar to a phase-slip in the Josephson effect.
Coherent condensates appear as emergent phenomena in many systems 1-8 , sharing the characteristic feature of an energy gap separating the lowest excitations from the condensate ground state. This implies that a scattering object, moving through the system with high enough velocity for the excitation spectrum in the scatter frame to become gapless, can create excitations at no energy cost, initiating the breakdown of the condensate 1,9-13 . This limit is the well-known Landau velocity 9 . While, for the neutral Fermionic superfluid 3 He-B in the T=0 limit, flow around an oscillating body displays a very clear critical velocity for the onset of dissipation 12,13 , here we show that for uniform linear motion there is no discontinuity whatsoever in the dissipation as the Landau critical velocity is passed and exceeded. Since the Landau velocity is such a pillar of our understanding of superfluidity, this is a considerable surprise, with implications for the understanding of the dissipative effects of moving objects in all coherent condensate systems.The Landau critical velocity marks the minimum velocity at which an object moving through a condensate can generate excitations with zero energy cost 9 . In the frame of the object, moving at velocity v relative to the fluid, excitations of momentum p are shifted, by Galilean transformation, from energy E to (E -v.p). Superfluid 3 He has a BCS dispersion curve 1 with energy minima, E = Δ at momenta ±p F . Therefore excitation generation should begin as soon as one energy minimum reaches zero, i.e. when the velocity reaches the Landau critical value,We can investigate v L in condensates in two limiting regimes, i.e. for the motion of microscopic objects (e.g. ions) or for that of macroscopic objects. For ions, the critical velocity has been observed 10 in superfluid 4 He at the expected value of ≈ 45 m s -1 , and 3 confirmed in superfluid 3 He-B at 28 bar as consistent with the expected ≈ 71 mm s -1 value 11 . For macroscopic objects, the onset of extra dissipation at v L in superfluid 4 He cannot be observed since damping from vorticity becomes prohibitive at much lower velocities. However, while macroscopic objects can be readily accelerated at the lowest temperatures to the much lower critical velocities in superfluid 3 He, the experimental picture is somewhat misleading.In superfluid 3 He, oscillating macroscopic objects do indeed show a sudden increase in damping 12 , but at a velocity of only ≈ v L /3, arising from the emission of quasiparticle excitations from the pumping of surface excitation driven by the reciprocating motion 13 .Although this mechanism does not involve bulk pair breaking, it has created the impression that a Landau critical velocity has indeed been confirmed in 3 He, which is not the case.What should we expect for uniform motion? The textbook prediction suggests that at v L all details of the process become irrelevant. Condensate breakdown becomes inevitable; the constituent Cooper pairs separate; and the properties rapidly approaching those of...
A high precision torsional oscillator has been used to study 3He films of thickness from 100 to 350 nm, in the temperature range 5
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