Energy and angular momentum balance in wall-bounded quantum turbulence at very low temperatures.

A superfluid in the absence of a viscous normal component should be the best realization of an ideal inviscid Euler fluid. As expressed by d'Alembert's famous paradox, an ideal fluid does not drag on bodies past which it flows, or in other words it does not exchange momentum with them. In addition, the flow of an ideal fluid does not dissipate kinetic energy. Here we study experimentally whether these properties apply to the flow of superfluid (3)He-B in a rotating cylinder at low temperatures. It is found that ideal behaviour is broken by quantum turbulence, which leads to substantial energy dissipation, as was also observed earlier. Remarkably, the angular momentum exchange between the superfluid and its container approaches nearly ideal behaviour, as the drag almost disappears in the zero-temperature limit. Here the mismatch between energy and angular momentum transfer results in a new physical situation, with severe implications on the flow dynamics.

Self-trapping of magnon Bose-Einstein condensates in the ground state and on excited levels: from harmonic to box confinement.

Long-lived coherent spin precession of (3)He-B at low temperatures around 0.2T(c) is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.

Superfluid vortex front at T→0: decoupling from the reference frame.

Steady-state turbulent motion is created in superfluid (3)He-B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of (3)He-B and replaces vortex-free flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2T(c) during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e., the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.

Stability and dissipation of laminar vortex flow in superfluid 3He-B.

A central question in the dynamics of vortex lines in superfluids is dissipation on approaching the zero temperature limit T→0. From both NMR measurements and vortex filament calculations, we find that vortex flow remains laminar up to large Reynolds numbers Re{α}∼10(3) in a cylinder filled with 3He-B. This is different from viscous fluids and superfluid 4He, where the corresponding responses are turbulent. In 3He-B, laminar vortex flow is possible in the bulk volume even in the presence of sizable perturbations from axial symmetry to below 0.2Tc. The laminar flow displays no excess dissipation beyond mutual friction, which vanishes in the T→0 limit, in contrast with turbulent vortex motion where dissipation has been earlier measured to approach a large T-independent value at T≲0.2Tc.

Quantum turbulence in a propagating superfluid vortex front.

We present experimental, numerical, and theoretical studies of a vortex front propagating into a region of vortex-free flow of rotating superfluid 3He-B. We show that the nature of the front changes from laminar through quasiclassical turbulent to quantum turbulent with decreasing temperature. Our experiment provides the first direct measurement of the dissipation rate in turbulent vortex dynamics of 3He-B and demonstrates that the dissipation becomes mutual-friction independent with decreasing temperature, and it is strongly suppressed when the Kelvin-wave cascade on vortex lines is predicted to be involved in the turbulent energy transfer to smaller length scales.

Twisted vortex state.

We study a twisted vortex bundle where quantized vortices form helices circling around the axis of the bundle in a "force-free" configuration. Such a state is created by injecting vortices into a rotating vortex-free superfluid. Using continuum theory we determine the structure and the relaxation of the twisted state. This is confirmed by numerical calculations. We also present experimental evidence of the twisted vortex state in superfluid 3He-B.

Vortex multiplication in applied flow: A precursor to superfluid turbulence.

A surface-mediated process is identified in 3He-B which generates vortices at a roughly constant rate. It precedes a faster form of turbulence where intervortex interactions dominate. This precursor becomes observable when vortex loops are introduced in low-velocity rotating flow at sufficiently low mutual friction dissipation at temperatures below 0.5Tc. Our measurements indicate that the formation of new loops is associated with a single vortex interacting in the applied flow with the sample boundary. Numerical calculations show that the single-vortex instability arises when a helical Kelvin wave expands from a reconnection kink at the wall and then intersects again with the wall.

An intrinsic velocity-independent criterion for superfluid turbulence.

Hydrodynamic flow in classical and quantum fluids can be either laminar or turbulent. Vorticity in turbulent flow is often modelled with vortex filaments. While this represents an idealization in classical fluids, vortices are topologically stable quantized objects in superfluids. Superfluid turbulence is therefore thought to be important for the understanding of turbulence more generally. The fermionic 3He superfluids are attractive systems to study because their characteristics vary widely over the experimentally accessible temperature regime. Here we report nuclear magnetic resonance measurements and numerical simulations indicating the existence of sharp transition to turbulence in the B phase of superfluid 3He. Above 0.60T(c) (where T(c) is the transition temperature for superfluidity) the hydrodynamics are regular, while below this temperature we see turbulent behaviour. The transition is insensitive to the fluid velocity, in striking contrast to current textbook knowledge of turbulence. Rather, it is controlled by an intrinsic parameter of the superfluid: the mutual friction between the normal and superfluid components of the flow, which causes damping of the vortex motion.

Structure of the 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 1 / 2-quantum units, independently of the structure of the source vorticity in the bulk. These results are consistent with our NMR measurements.

Shear flow and Kelvin-Helmholtz instability in superfluids.

The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid 3He is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consistent with the classic Kelvin-Helmholtz theory when modified for two-fluid hydrodynamics.

Transitions from vortex lines to sheets: interplay of topology and dynamics in an anisotropic superfluid.

In isotropic macroscopic quantum systems vortex lines can be formed while in anisotropic systems also vortex sheets are possible. Based on measurements of superfluid 3He-A, we present the principles which select between these two competing forms of quantized vorticity: sheets displace lines if the frequency of the external drive exceeds a critical limit. The resulting topologically stable state consists of multiple vortex sheets and has much faster dynamics than the state with vortex lines.

Composite defect extends analogy between cosmology and 3He

Spin-mass vortices have been observed to form in rotating superfluid 3He-B, following the absorption of a thermal neutron and a rapid transition from the normal to the superfluid state. The spin-mass vortex is a composite defect which consists of a planar soliton (wall) which terminates on a linear core (string). This observation fits well within the framework of a cosmological scenario for defect formation, known as the Kibble-Zurek mechanism. It suggests that in the early Universe analogous cosmological defects might have formed.

Double-quantum vortex in superfluid 3He-A

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.