Von Kármán vortex street in dipole BEC induced by a circular moving potential

Abstract

The dynamical behaviors of a dipole Bose-Einstein condensate (BEC), which is stirred by a circular moving Gaussian potential, are numerically investigated by using the mean-field theory. In this work, the atom is assumed to polarize along the<i> z</i>-axis. Firstly, the stationary state of the system is obtained by solving the quasi-two-dimensional Gross-Pitaevskki equation numerically under periodic boundary conditions. And then, taking the obtained ground state as the initial condition, the dynamic evolution of the dipole BEC system is studied by the time-splitting Fourier spectrum method. Four types of emissions, namely, the stable laminar flow, vortex dipole, Bénard–von Kármán (BvK) vortex street and irregular turbulence, are observed in the wake when the velocity and size of the Gaussian potential change gradually. When the velocity of the Gaussian potential reaches the critical velocity of vortex excitation, vortex pairs with opposite circulations alternately fall off from the surface of the Gaussian potential. Owing to the interaction between the vortex dipoles, the dipoles rotate around their own centers. Finally, a ring structure will be formed and exist in the wake stably for a long time. With the increase of the velocity of Gaussian potential, the period of dipoles shedding is also shortened. For the appropriate velocity and size of the Gaussian potential, the vortex pairs with the same circulations will periodically fall off from the Gaussian potential and stably distributed on the inner and outer rings, forming BvK vortex street. Our caculation reveals that the conditions for forming BvK vortex street when the dipole BEC is stirred with a circular moving potential are very restricted. When the velocity or size of the Gaussian potential continues to increase, the phenomenon of the periodic vortex pairs shedding in the wake of the Gaussian potential will disappear, and the shedding pattern of the dipole BEC becomes irregular. Using experimental parameters, the parameter ranges of different dipole interactions are obtained through numerical calculation. The influences of dipole interactions, velocity and size of the Gaussian potential on different emission are discussed. In the end, the physical mechanisms of different emissions are analyzed by calculating the drag force acting on Gaussian potential.