Francesco Piazza, Lee A. Collins, Augusto Smerzi
We compare the theoretical prediction obtained with the Gross-Pitaevskii equation with recent experimental results of (A. Ramanathan, \emph{et al.}, Phys. Rev. Lett {\bf 106}, 130401 (2011)) for the instability of the superfluid flow of a toroidal Bose-Einstein condensate in presence of a tunable weak link. The superflow with one unit of angular momentum becomes unstable at a critical strength of the link (implemented using a repulsive optical barrier), and decays through the mechanism of phase slippage performed by vortex-antivortex pairs. We find out the Gross-Pitaevskii prediction to be in agreement with the measured values of the critical barrier height. At the critical point the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, $v_{\rm barr}=c_{\rm l}$. The Feynman critical velocity $v_{\rm f}$ is instead much lower than the observed critical velocity, since we in general have $v_{\rm f}=\epsilon\ c_{\rm l}$ where $\epsilon$ is a small parameter of the model. Given the failure of the Feynman criterion, the question remains open whether the superfluid instability is energetical or dynamical.
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http://arxiv.org/abs/1208.0734
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