Measurement of Turbulence in Superfluid 3He-B

The experimental investigation of superfluid turbulence in 3He-B is generally not possible with the techniques which have been developed for 4He-II. We describe a new method by which a transient burst of turbulent vortex expansion can be generated in 3He-B. It is based on the injection of a few vortex loops into rotating vortex-free flow. The time-dependent evolution of the quantized vorticity is then monitored with NMR spectroscopy. Using these techniques the transition between regular (i.e. vortex number conserving) and turbulent vortex dynamics can be recorded at T ~ 0.6 Tc and a number of other characteristics of turbulence can be followed down to a temperature of T ~ 0.4 Tc.Comment: 31 pages, 10 figure

Onset of turbulence in superfluid 3He-B and its dependence on vortex injection in applied flow

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.Comment: To be published in the proceedings of the 24th International Conference on Low Temperature Physics - LT24, in Conference Proceedings of the American Institute of Physic

Vortex Multiplication in Applied Flow: the Precursor to Superfluid Turbulence

The dynamics of quantized vortices in rotating $^3$He-B is investigated in the low density (single-vortex) regime as a function of temperature. An abrupt transition is observed at $0.5 T_{\rm c}$. Above this temperature the number of vortex lines remains constant, as they evolve to their equilibrium positions. Below this temperature the number of vortices increases linearly in time until the vortex density has grown sufficiently for turbulence to switch on. On the basis of numerical calculations we suggest a mechanism responsible for vortex formation at low temperatures and identify the mutual friction parameter which governs its abrupt temperature dependence.Comment: 5 pages, 4 figures; version submitted to Phys. Rev. Let

Classical and quantum regimes of the superfluid turbulence

We argue that turbulence in superfluids is governed by two dimensionless parameters. One of them is the intrinsic parameter q which characterizes the friction forces acting on a vortex moving with respect to the heat bath, with 1/q playing the same role as the Reynolds number Re=UR/\nu in classical hydrodynamics. It marks the transition between the "laminar" and turbulent regimes of vortex dynamics. The developed turbulence described by Kolmogorov cascade occurs when Re >> 1 in classical hydrodynamics, and q << 1 in the superfluid hydrodynamics. Another parameter of the superfluid turbulence is the superfluid Reynolds number Re_s=UR/\kappa, which contains the circulation quantum \kappa characterizing quantized vorticity in superfluids. This parameter may regulate the crossover or transition between two classes of superfluid turbulence: (i) the classical regime of Kolmogorov cascade where vortices are locally polarized and the quantization of vorticity is not important; and (ii) the quantum Vinen turbulence whose properties are determined by the quantization of vorticity. The phase diagram of the dynamical vortex states is suggested.Comment: 12 pages, 1 figure, version accepted in JETP Letter

Structure of surface vortex sheet between two rotating 3He superfluids

We study a two-phase sample of superfluid 3He where vorticity exists in one phase (3He-A) but cannot penetrate across the interfacial boundary to a second coherent phase (3He-B). We calculate the bending of the vorticity into a surface vortex sheet on the interface and solve the internal structure of this new type of vortex sheet. The compression of the vorticity from three to two dimensions enforces a structure which is made up of half-quantum units, independently of the structure of the source vorticity in the bulk. These results are consistent with our NMR measurements.Comment: 4 pages, 4 figure

System size scaling of topological defect creation in a second-order dynamical quantum phase transition

We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for large N, we find that the net defect number variance in convex volumina scales like the surface area of the sample for short-range correlations. This behaviour follows generally from spatial and internal symmetries. Conversely, if spatial isotropy is broken, e.g., by a lattice, and in addition long-range periodic correlations develop in the broken-symmetry phase, we get the rather counterintuitive result that the scaling strongly depends on the dimension being even or odd: For even dimensions, the net defect number variance scales like the surface area squared, with a prefactor oscillating with the system size, while for odd dimensions, it essentially vanishes.Comment: 20 pages of IOP style, 6 figures; as published in New Journal of Physic

Superconducting Nb-film LC resonator

Sputtered Nb thin-film LC resonators for low frequencies at 0.5 MHz have been fabricated and tested in the temperature range 0.05--1 K in magnetic fields up to 30 mT. Their Q value increases towards decreasing temperature as sqrt(T) and reaches 10^3 at 0.05 K. As a function of magnetic field Q is unstable and displays variations up to 50%, which are reproducible from one field sweep to the next. These instabilities are attributed to dielectric losses in the plasma deposited SiO_2 insulation layer, since the thin-film coil alone reaches a Q > 10^5 at 0.05 K.Comment: 6 pages, 7 figures, submitted to Review of Scientific Instrument

Transition to superfluid turbulence governed by an intrinsic parameter

Hydrodynamic flow in both classical and quantum fluids can be either laminar or turbulent. To describe the latter, vortices in turbulent flow are modelled with stable vortex filaments. While this is an idealization in classical fluids, vortices are real topologically stable quantized objects in superfluids. Thus superfluid turbulence is thought to hold the key to new understanding on turbulence in general. The fermion superfluid 3He offers further possibilities owing to a large variation in its hydrodynamic characteristics over the experimentally accessible temperatures. While studying the hydrodynamics of the B phase of superfluid 3He, we discovered a sharp transition at 0.60Tc between two regimes, with regular behaviour at high-temperatures and turbulence at low-temperatures. Unlike in classical fluids, this transition is insensitive to velocity and occurs at a temperature where the dissipative vortex damping drops below a critical limit. This discovery resolves the conflict between existing high- and low-temperature measurements in 3He-B: At high temperatures in rotating flow a vortex loop injected into superflow has been observed to expand monotonically to a single rectilinear vortex line, while at very low temperatures a tangled network of quantized vortex lines can be generated in a quiescent bath with a vibrating wire. The solution of this conflict reveals a new intrinsic criterion for the existence of superfluid turbulence.Comment: Revtex file; 5 pages, 2 figure