Quantum Analogs of Classical Wakes in Bose-Einstein Condensates

We show that an elliptical obstacle moving through a Bose-Einstein condensate generates wakes of quantum vortices which resemble those of classical viscous flow past a cylinder or sphere. The role of ellipticity is to facilitate the interaction of the vortices nucleated by the obstacle. Initial steady symmetric wakes lose their symmetry and form clusters of like-signed vortices, in analogy to the classical B\'enard-von K\'arm\'an vortex street. Our findings, demonstrated numerically in both two and three dimensions, confirm the intuition that a sufficiently large number of quanta of circulation reproduce classical physics.