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arXiv:1009.1574 · Journal of Physics Condensed Matter

Theoretical confirmation of Feynman’s hypothesis on the creation of circular vortices in Bose–Einstein condensates: III

E. Infeld, A. Senatorski, Andrzej A. Skorupski

Published Nov 26, 2010• 1 citation

Abstract

In two preceding papers (Infeld and Senatorski 2003 J. Phys.: Condens. Matter 15 5865, Senatorski and Infeld 2004 J. Phys.: Condens. Matter 16 6589) the authors confirmed Feynman's hypothesis on how circular vortices can be created from oppositely polarized pairs of linear vortices (first paper), and then gave examples of the creation of several different circular vortices from one linear pair (second paper). Here, in part III, we give two classes of examples of how the vortices can interact. The first confirms the intuition that the reconnection processes which join two interacting vortex lines into one, and thus increase the degree of entanglement of the vortex system, practically do not occur. The second shows that new circular vortices can also be created from pairs of oppositely polarized coaxial circular vortices. This seems to contradict the results for such pairs given in Koplik and Levine (1996 Phys. Rev. Lett. 76 4745).

DOI: 10.1088/0953-8984/22/50/505601

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In two preceding papers (Infeld and Senatorski 2003 J. Phys.: Condens. Matter 15 5865, Senatorski and Infeld 2004 J. Phys.: Condens. Matter 16 6589) the authors confirmed Feynman's hypothesis on how circular vortices can be created from oppositely polarized pairs of linear vortices (first paper), and then gave examples of the creation of several different circular vortices from one linear pair (second paper). Here, in part III, we give two classes of examples of how the vortices can interact. The first confirms the intuition that the reconnection processes which join two interacting vortex lines into one, and thus increase the degree of entanglement of the vortex system, practically do not occur. The second shows that new circular vortices can also be created from pairs of oppositely polarized coaxial circular vortices. This seems to contradict the results for such pairs given in Koplik and Levine (1996 Phys. Rev. Lett. 76 4745).

The recent creation of pure Bose–Einstein condensates in alkali metals and also of vortices supported by them has increased interest in these phenomena. In particular, changes observed in the topology of these vortices is a partially unsolved problem. Here we confirm Feynman’s hypothesis on how circular vortices can be created from oppositely polarized pairs of linear vortices. This is done by following the transformation numerically. The circular vortices so obtained satisfy known constraining relations between radii and velocities.

We study the formation of vortices in a Bose-Einstein condensate (BEC) that has been prepared by allowing isolated and independent condensed fragments to merge together. We focus on the experimental setup of Scherer et al. [Phys. Rev. Lett. 98, 110402 (2007)], where three BECs are created in a magnetic trap that is segmented into three regions by a repulsive optical potential; the BECs merge together as the optical potential is removed. First, we study the two-dimensional case; in particular, we examine the effects of the relative phases of the different fragments and the removal rate of the optical potential on the vortex formation. We find that many vortices are created by instant removal of the optical potential regardless of relative phases, and that fewer vortices are created if the intensity of the optical potential is gradually ramped down and the condensed fragments gradually merge. In all cases, self-annihilation of vortices of opposite charge is observed. We also find that for sufficiently long barrier ramp times, the initial relative phases between the fragments leave a clear imprint on the resulting topological configuration. Finally, we study the three-dimensional system and the formation of vortex lines and vortex rings due to the merger of the BEC fragments; our results illustrate how the relevant vorticity is manifested for appropriate phase differences, as well as how it may be masked by the planar projections observed experimentally.

The vortex-vortex interaction in two-component Bose-Einstein condensates is shown to present characteristic effects not possible in single-component condensates. In particular, vortices in different components undergo separate, but concentric, orbits for both the same and opposite circulation. In addition, contrary to the well-known behavior in single-component condensates, vortices with the same circulation created in the less dense component merge in the presence of dissipation, allowing for the creation of metastable vortices with more than one quantum of circulation.

When two vortices in superfluid helium-4 get close enough together, their cores are very likely to "reconnect". That is, the vortices collide, coalesce, and re-emerge as two new vortices, with the head of one of the original vortices joined to the tail of the other one and vice versa (figure 1). Vortex reconnection has long been assumed to be possible in this exotic liquid, despite the absence of any firm theoretical basis. But now Joel Koplik of the City College of New York and Herbert Levine of the University of California, San Diego, have unravelled the microscopic details of this interesting topology-changing process through numerical simulations of the relevant nonlinear Schrödinger equation (Phys. Rev. Lett. (1993) 71 1375).