Bénard–von Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with nonlocal Rydberg interactions

The dynamics of a Rashba-type spin–orbit-coupled Bose–Einstein Condensate with nonlocal Rydberg interactions stirred by a moving cylindrical obstacle potential are investigated numerically. The results show that the Bénard–von Kármán vortex street consisting of quantized vortex pairs emerge in both component of Rydberg-dressed Bose–Einstein Condensate for appropriate velocity and width of the moving potential. By tracking two point vortices in a pair of the vortex street, we find that the angular velocity at which two point vortices rotates around their center is inversely proportional to the square of distance between two point vortices. The other typical vortex shedding patterns such as stable laminar flow, vortex dipoles, drifting vortex dipoles, V-shaped vortex pairs and irregular turbulence can also be observed. The parameter regions under different Rydberg interactions for various vortex patterns is obtained by systematic numerical simulations. The influence of the Rydberg interaction strength on the vortex street is studied. The drag force exerted by the wake on the moving potential correspond to different vortex shedding patterns is calculated and analyzed. Finally, an experimental protocol to realize the vortex street in Rydberg-dressed Bose–Einstein Condensate is provided.