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arXiv:1602.05303 · The European Physical Journal B

Effect of non-local interactions on the vortex solution in Bose-Einstein Condensates

Abhijit Pendse, A. Bhattacharyay

Published Dec 1, 2017• 5 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2017-80213-6

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We consider a Gross-Pitaevskii(GP) model of a Bose-Einstein Condensate(BEC). We study a single vortex line in the presence of non-local s-wave interactions. We show that the width of such a vortex is a microscopic length scale of the order of s-wave scattering length and is independent of the healing length. This analysis fixes the problem of arbitrariness in the selection of the width of vortices which is so far approximately considered to be the healing length ξ0\xi_{0}ξ0​ despite not being selected explicitly. We present a variational method to construct analytical solution for vortices of any quantum of circulation from the core to any finite extent. Using our analysis we predict hydrogen BEC to produce the thinnest vortex line.
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.
We study the vortex nucleation in a finite Bose-Einstein condensate. Using a set of non-local and chiral boundary conditions to solve the Schro¨\ddot{o}o¨dinger equation of non-interacting bosons in a rotating trap, we obtain a quantitative expression for the characteristic angular velocity for vortex nucleation in a condensate which is found to be 35% of the transverse harmonic trapping frequency.