Critical Velocity for Quantized Vortex Formation in a Superfluid with a Plate-Shaped Obstacle

We theoretically investigate the dependence of the critical velocity for quantum vortex formation on the size L of a plate-shaped obstacle moving in a uniform Bose–Einstein condensate in quasi-two-dimensions. Numerical simulations of the Gross–Pitaevskii equation reveal that the critical velocity \(v_c\) $v_c$ is proportional to \(L^{-1/2}\) $L^{-1/2}$ when L is much larger than the healing length. The power-law behavior is quantitatively explained by the potential flow theory of classical hydrodynamics for the large L limit.