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arXiv:1702.00040 · Physical Review A

Internal structure and stability of vortices in a dipolar spinor Bose-Einstein condensate

Magnus O. Borgh, Justin Lovegrove, Janne Ruostekoski

Published May 1, 2017• 19 citations
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Abstract

Effects of diplolar interactions on the structure of vortices are studied theoretically for spinor Bose-Einstein condensates of Cr atoms, where experimentally observable non-Abelian vortices, thanks to a ground-state order parameter that exhibits a hexagonal point-group symmetry, are predicted.
DOI
10.1103/physreva.95.053601

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•Sep 1, 2013•0 citations
We study the influence of dipole–dipole interaction on the formation of vortices in a rotating dipolar Bose–Einstein condensate (BEC) of 52 Cr and 164 Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross–Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices, while a repulsive contact interaction increases the stability of the vortices. Furthermore, an ordered vortex lattice of a relatively large number of vortices is found in a strongly dipolar BEC.
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We study the ground states of rotating atomic Bose-Einstein condensates with dipolar interactions. We present the results of numerical studies on a periodic geometry which show vortex lattice ground states of various symmetries: triangular and square vortex lattices, ``stripe crystal,'' and ``bubble crystal.'' We present the phase diagram (for systems with a large number of vortices) as a function of the ratio of dipolar to contact interactions and of the chemical potential. We discuss the experimental requirements for observing transitions between vortex lattice ground states via dipolar interactions. We finally investigate the stability of mean-field supersolid phases of a quasi-two-dimensional nonrotating Bose gas with dipolar interactions.
This thesis is concerned with the structure and stability of vortices in spin-1 atomic Bose-Einstein Condensates (BECs) in rotating, optical traps. We numerically study these vortex structures using a classical mean-field theory which allows atomic interactions to change the local expectation value of the atomic spin. Initially applying a model in which the atoms interact only via scattering which does not conserve an initial longitudinal magnetisation, we identify the energetically stable configurations of singular and nonsingular vortices via propagation in imaginary time in a rotating frame of reference. We find that the cores of singular vortices fill with atoms in the spinor BEC and show that this can be understood in terms of an energetic hierarchy of length scales. By refining the numerical model to explicitly conserve longitudinal magnetisation, we show that the conservation of a strong magnetisation can lead to a mixing of the two phases of the ground-state manifold (polar and ferromagnetic), which are characterised by the expectation value of the spin. This occurs as a result of the introduction of a new characteristic length scale determined by the longitudinal magnetisation. A surprising consequence is the stability of a ferromagnetic coreless vortex in the polar interaction regime, which otherwise is energetically unstable. We construct analytic spinor wavefunctions which parametrise the interpolation between the polar and ferromagnetic phases, exhibiting different vortex topologies in the respective phases. Finally by identifying stationary states of the system, we show how nonlocal dipoledipole interactions between atoms introduces an additional length scale determined by the strength of the dipolar interaction. The energetic hierarchy of length scales then determines whether the dipolar interactions have a significant effect on the stationary vortex structures. In particular we show how a BEC with polar interactions adopts the properties of a ferromagnetic condensate when the dipolar interactions dominate.