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Physical Review Letters

Combined spin-mass vortex with soliton tail in superfluid B3

Y. Kondo, J. S. Korhonen, M. Krusius, Vladimir V. Dmitriev, E. V. Thuneberg, Григорий Ефимович Воловик

Published Jun 1, 1992• 150 citations
Publisher

Abstract

We have observed spin-mass vortices (SMV) in superfluid $^{3}\mathit{B}$. 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 $^{3}\mathrm{He}$ 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.

DOI
10.1103/physrevlett.68.3331

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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.
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.
The polar phase of ^{3}He, which is topological spin-triplet superfluid with the Dirac nodal line in the spectrum of Bogoliubov quasiparticles, has been recently stabilized in a nanoconfined geometry. We pump magnetic excitations (magnons) into the sample of polar phase and observe how they form a Bose-Einstein condensate, revealed by coherent precession of the magnetization of the sample. Spin superfluidity, which supports this coherence, is associated with the spontaneous breaking of U(1) symmetry by the phase of precession. We observe the corresponding Nambu-Goldstone boson and measure its mass emerging when applied rf field violates the U(1) symmetry explicitly. We suggest that the magnon BEC in the polar phase is a powerful probe for topological objects such as vortices and solitons and topological nodes in the fermionic spectrum.
A numerical solution of the Ginzburg-Landau equations for superfluid 3B^{3}\mathit{B}3B vortices gives the following results: The low-pressure vortex is a new ``double core vortex'' whose rotational symmetry around the vortex axis is broken. The high-pressure vortex is the v vortex. The theory gives a transition between these vortices which is in excellent agreement with experiments.
We observe solitonic vortices in an atomic Bose-Einstein condensate (BEC) after free expansion. Clear signatures of the nature of such defects are the twisted planar density depletion around the vortex line, observed in absorption images, and the double dislocation in the interference pattern obtained through homodyne techniques. Both methods allow us to determine the sign of the quantized circulation. Experimental observations agree with numerical simulations. These solitonic vortices are the decay product of phase defects of the BEC order parameter spontaneously created after a rapid quench across the BEC transition in a cigar-shaped harmonic trap and are shown to have a very long lifetime.
The core of the singly quantized nonaxisymmetric v -vortex in rotating 3 He- B is found to display novel topological structure: it is a bound pair of vortices with half-integer circulation . The topology for flaring-out of vorticity from the real space to the momentum space, due to boojums (nodes) on the Fermi surface, is discussed for both the axisymmetric and nonaxisymmetric v -vortices. This difference in topology may explain the physical nature of the observed first-order vortex-core transition in rotating superfluid 3 He- B .
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.