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Physical Review Letters

Vortex sheet in rotating superfluid A3

Ülo Parts, E. V. Thuneberg, Григорий Ефимович Воловик, Jaakko Henrik KOIVUNIEMI, V. M. H. Ruutu, Marko T. Heinilä, J. M. Karimäki, M. Krusius

Published Jun 13, 1994• 137 citations
Publisher

Abstract

A new state of rotating superfluid $^{3}\mathit{A}$ has been found. Instead of quantized vortex lines, it consists of a continuous vortex sheet. The sheet has as a backbone a topologically stable domain wall called soliton, to which the vorticity is bound. The sheet folds to equidistant layers that fill uniformly the rotating container. The new state can easily be created experimentally in spite of its higher energy. Its identification is deduced from nuclear magnetic resonance.

DOI
10.1103/physrevlett.72.3839

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A new state of rotating superfluid 3A^{3}\mathit{A}3A has been found. Instead of quantized vortex lines, it consists of a continuous vortex sheet. The sheet has as a backbone a topologically stable domain wall called soliton, to which the vorticity is bound. The sheet folds to equidistant layers that fill uniformly the rotating container. The new state can easily be created experimentally in spite of its higher energy. Its identification is deduced from nuclear magnetic resonance.
We have observed spin-mass vortices (SMV) in superfluid 3B^{3}\mathit{B}3B. The SMV is a combined topological object made up of a vortex line with mass current and a disclination line with spin current. It is also a termination line of a planar defect, the so-called \ensuremath{\theta} soliton. The SMVs are bound either as pairs or to the container wall by the soliton. They are nucleated when a rotating 3He^{3}\mathrm{He}3He sample cools slowly through the A\ensuremath{\rightarrow}B phase transition. The identification of the SMV is based on the NMR signatures of the soliton.
This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.
We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.
Insight in the dynamics of quantized vortex lines has been obtained by performing NMR measurements in uniformly rotating superfluid 3B^{3}\mathit{B}3B. Compared to superfluid 4He^{4}\mathrm{He}4He, in 3B^{3}\mathit{B}3B the viscosity of the normal component is three orders of magnitude larger and the pinning of vortices is weaker. The collective modes governing the hydrodynamic response of an array of vortex lines are highly overdamped. Two distinct modes are identified: (1) a relatively fast mutual-friction-resisted mode, which controls the redistribution of the vortex density on a time scale of a few seconds, and (2) an exponentially relaxing slow mode with a time constant of a few minutes, which governs asymptotically the approach to equilibrium at nearly constant vortex density. Measurement of the fast motion allows us to extract the dissipative mutual friction. The slow mode is dominated by the elastic tension along the vortex line and by weak pinning at the top and bottom surfaces of the rotating container. With increasing vortex density the surface pinning becomes a collective process, in which coherently moving groups of vortices are pinned in unison. Collective pinning is a result of the shear elasticity related to the crystalline order of the vortex lattice. Our measurements on the slow mode indicate that the crystalline correlation extends over many lattice spacings.
We have used torsional oscillators, containing disk-shaped slabs of superfluid (3)He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating. Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity Ω(0) is left behind after stopping rotation. The bias toward a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation. When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation relative to that of l. A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when the angular velocity, Ω, is parallel to l.
In He-3 superfluids quantized vorticity can take many different forms: It can appear as distributed periodic textures, as sheets, or as lines. In the anisotropic He-3A phase in most cases the amplitude of the order parameter remains constant throughout the vortex structure and only its orientation changes in space. In the quasi-isotropic He-3B phase vortex lines have a hard core where the order parameter has reduced, but finite amplitude. The different structures have been firmly identified, based on both measurement and calculation. What parallels can be drawn from this information to the new unconventional superconductors or Bose-Einstein condensates?