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Physica B Condensed Matter

Gap anisotropy, vortex cluster, and nucleation of vortices in rotating 3He-B

Y. Kondo, J. S. Korhonen, Ülo Parts, M. Krusius, Olli V. Lounasmaa, A. D. Gongadze

Published May 1, 1992• 24 citations
Publisher
DOI
10.1016/0921-4526(92)90183-s

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For a Bose-Einstein condensate placed in a rotating trap, we study the simplified energy of a vortex line derived by Aftalion and Riviere [Phys. Rev. A 64, 043611 (2001)] in order to determine the shape of the vortex line according to the rotational velocity and the elongation of the condensate. The energy reflects the competition between the length of the vortex, which needs to be minimized taking into account the anisotropy of the trap, and the rotation term, which pushes the vortex along the z axis. We prove that if the condensate has the shape of a pancake, the vortex stays straight along the z axis, while in the case of a cigar, the vortex is bent. We study the local stability of the straight vortex and find an estimate for the critical angular speed at which bent vortices are nucleated. When vortices are nucleated, we prove that they must have some finite length.
In this thesis, we perform investigations into the behaviour of finite-temperature degenerate Bose gases using a classical-field formalism, focussing in particular on the dynamics of quantum vortices in these systems. We demonstrate that the coherence of the classical field can be characterised by its temporal correlations, and discuss how the phase-symmetry-broken averages familiar from mean-field theories emerge from the field trajectories. We show that a finite-temperature condensate containing a precessing vortex in a cylindrically symmetric trap can be realised as an ergodic equilibrium of the classical-field theory, and demonstrate the identification of the rotationally symmetry-broken condensate orbital and core-filling thermal component from the field correlations. We then consider the nonequilibrium dynamics that result when such a precessing-vortex configuration is subjected to a static trap anisotropy which arrests its rotation, and observe novel coupled relaxation dynamics of the condensed and noncondensed components of the field. Finally, we consider the nucleation of vortices in an initially zero-temperature quasi-two-dimensional condensate stirred by a rotating trap anisotropy. We quantify the emergence of a rotating thermal component of the field, which drives the nucleation of vortices from condensate-surface oscillations, and study the relaxation and rotational equilibration of the initially turbulent collection of vortices. We find that thermal fluctuations of the field prevent the vortices from settling into a rigid crystalline lattice in this reduced dimensionality, and that true condensation in the field is completely destroyed by the disordered motion of vortices. We show, however, that the temporal correlations of the field distinguish the quasi-coherent vortex-liquid phase in the trap centre from the truly thermal material in its periphery.
A method to produce a spin-dependent rotating potential using near-resonant circularly polarized laser beams is proposed. It is shown that half-quantum vortices are nucleated in a spinor Bose-Einstein condensate (BEC) with an antiferromagnetic interaction. In contrast to the vortex nucleation in a scalar BEC, the spin-vortex nucleation occurs at a low rotation frequency ($\ensuremath{\simeq}0.1{\ensuremath{\omega}}_{\ensuremath{\perp}}$ with ${\ensuremath{\omega}}_{\ensuremath{\perp}}$ being the radial trap frequency) in a short nucleation time $\ensuremath{\simeq}50\phantom{\rule{0.3em}{0ex}}\mathrm{ms}$ without dissipation. A method for nondestructive measurement of half-quantum vortices is discussed.