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arXiv:0907.3077 · Physical Review A

Core sizes and dynamical instabilities of giant vortices in dilute Bose-Einstein condensates

Pekko Kuopanportti, Emil Lundh, Jukka A. M. Huhtamäki, Ville Pietilä, Mikko Möttönen

Published Feb 5, 2010• 28 citations
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Abstract

Motivated by a recent demonstration of cyclic addition of quantized vorticity into a Bose-Einstein condensate, the vortex pump, we study dynamical instabilities and core sizes of giant vortices. The core size is found to increase roughly as a square-root function of the quantum number of the vortex, whereas the strength of the dynamical instability either saturates to a fairly low value or increases extremely slowly for large quantum numbers. Our studies suggest that giant vortices of very high angular momenta may be achieved by gradually increasing the operation frequency of the vortex pump.

DOI
10.1103/physreva.81.023603

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Motivated by a recent demonstration of cyclic addition of quantized vorticity into a Bose-Einstein condensate, the vortex pump, we study dynamical instabilities and core sizes of giant vortices. The core size is found to increase roughly as a square-root function of the quantum number of the vortex, whereas the strength of the dynamical instability either saturates to a fairly low value or increases extremely slowly for large quantum numbers. Our studies suggest that giant vortices of very high angular momenta may be achieved by gradually increasing the operation frequency of the vortex pump.
We study the splitting of multiply quantized vortices with large quantum numbers in dilute nonrotated Bose-Einstein condensates in the zero-temperature limit. The splitting is observed to result in vortex-free condensate fragments which are separated by vortex sheets. The number of these fragments is found to be equal to the angular-momentum quantum number of the Bogoliubov excitation mode responsible for the splitting, although the formulation of the fragments cannot be described by small-amplitude excitations. Thus, the realization of an isolated giant vortex and the observation of its splitting would provide a means to directly relate the experimental data to discrete theoretical quantities.
We study the formation of large vortex aggregates in a rapidly rotating dilute-gas Bose-Einstein condensate. When we remove atoms from the rotating condensate with a tightly focused, resonant laser, the density can be locally suppressed, while fast circulation of a ring-shaped superflow around the area of suppressed density is maintained. Thus a giant vortex core comprising 7 to 60 phase singularities is formed. The giant core is only metastable, and it will refill with distinguishable single vortices after many rotation cycles. The surprisingly long lifetime of the core can be attributed to the influence of strong Coriolis forces in the condensate. In addition we have been able to follow the precession of off-center giant vortices for more than 20 cycles.
The formation of vortices by topological phase engineering has been realized experimentally to create the first two- and four-quantum vortices in dilute atomic Bose-Einstein condensates. We consider a similar system, but in addition to the Ioffe-Pritchard magnetic trap we employ an additional hexapole field. By controlling cyclically the strengths of these magnetic fields, we show that a fixed amount of vorticity can be added to the condensate in each cycle. In an adiabatic operation of this vortex pump, the appearance of vortices into the condensate is interpreted as the accumulation of a local Berry phase. Our design can be used as an experimentally realizable vortex source for possible vortex-based applications of dilute Bose-Einstein condensates.
Abstract In a harmonically-trapped rotating Bose–Einstein condensate (BEC), a vortex of large angular momentum decays to multiple vortices of unit angular momentum from an energetic consideration. We demonstrate the formation of a robust and dynamically stable giant vortex of large angular momentum in a harmonically trapped rotating BEC with a potential hill at the center, thus forming a Mexican hat like trapping potential. For a small inter-atomic interaction strength, a highly controllable stable giant vortex appears, whose angular momentum slowly increases as the angular frequency of rotation is increased. As the inter-atomic interaction strength is increased beyond a critical value, only vortices of unit angular momentum are formed, unless the strength of the potential hill at the center is also increased: for a stronger potential hill at the center a giant vortex is again formed. The dynamical stability of the giant vortex is demonstrated by real-time propagation numerically. These giant vortices of large angular momentum can be observed and studied experimentally in a highly controlled fashion.
We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalized Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction, approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\ensuremath{\hbar}$, reflecting the reduction of the global superfluidity. The real-time vortex nucleation in a rotating trap is shown to be triggered, as for a standard condensate, by the softening of the quadrupole mode. For large angular velocities, when the distance between vortices becomes comparable to the interdroplet distance, the vortices are arranged into a honeycomb structure, which coexists with the triangular geometry of the supersolid lattice and persists during the free expansion of the atomic cloud.
We show that, in the Thomas-Fermi regime, the cores of vortices in rotating dilute Bose-Einstein condensates adjust in radius as the rotation velocity, Omega, grows, thus precluding a phase transition associated with core overlap at high vortex density. In both a harmonic trap and a rotating hard-walled bucket, the core size approaches a limiting fraction of the intervortex spacing. At large rotation speeds, a system confined in a bucket develops, within Thomas-Fermi, a hole along the rotation axis, and eventually makes a transition to a giant vortex state with all the vorticity contained in the hole.