Observation of von Kármán Vortex Street in an Atomic Superfluid Gas

We report on the experimental observation of vortex cluster shedding from a moving obstacle in an oblate atomic Bose-Einstein condensate. At low obstacle velocities $v$ above a critical value, vortex clusters consisting of two like-sign vortices are generated to form a regular configuration like a von Kármán street, and as $v$ is increased, the shedding pattern becomes irregular with many different kinds of vortex clusters. In particular, we observe that the Stouhal number associated with the shedding frequency exhibits saturation behavior with increasing $v$. The regular-to-turbulent transition of the vortex cluster shedding reveals remarkable similarities between a superfluid and a classical viscous fluid. Our work opens a new direction for experimental investigations of the superfluid Reynolds number characterizing universal superfluid hydrodynamics.

Figure 1

(a) Schematic of the experiment. An impenetrable obstacle, formed by focusing a repulsive Gaussian laser beam, moves at velocity $v$ in a highly oblate Bose-Einstein condensate (BEC). Evolution of vortex shedding: (b) no excitations for $v<v_c$, (c) von Kármán street of clusters of two like-sign quantum vortices for small $v>v_c$ [14, 15, 16], and (d) turbulent shedding of diversely clustered vortices for $v\gg v_c$. Red and blue circles represent vortices with clockwise and counterclockwise circulations, respectively.

Figure 2

Quantum vortex shedding from a moving optical obstacle in a highly oblate BEC. (a) Images of BECs for various obstacle velocities $v$, taken after 36 ms time of flight [18]. Because of vortex core expansion, a vortex cluster appears with a large density-depleted hole, whose area depends on the cluster charge $\kappa$, i.e., the number of vortices in the cluster. (b) Normalized histograms of the cluster hole area. Each histogram was obtained from over 100 image data as in (a). The dashed lines indicate the transition positions for the charge number $\kappa$, which are determined from the multiple peak structure of the histograms.

Figure 3

Regular-to-turbulent transition of the quantum vortex shedding. (a) Total vortex number $N_v$ (solid red diamonds), individual ($\kappa =1$) vortex number $N_1$ (open red diamonds), (b) the number of emitted vortex clusters, $N_c$, and (c) the fractional populations $P_{\kappa }$ of charge-$\kappa$ clusters as functions of $v$. The vertical solid line denotes the critical velocity $v_c$ and the two dashed lines mark the transitions from (I) an individual vortex shedding regime to (II) a $\kappa =2$ cluster shedding regime and (III) an irregular shedding regime. The error bars indicate the standard deviation of measurements.

Figure 4

Vortex shedding from a smaller obstacle with $\sigma /\xi \approx 18$ and $V_0/\mu \approx 3.2$. (a) Regular shedding pattern comprised of six $\kappa =2$ vortex clusters was observed at $v=1.62\mathrm{mm}/\mathrm{s}$. Its appearance frequency was lower than 5%. (b) Typical irregular shedding pattern at the same experimental condition. The critical velocity was measured to be $v_c=1.2\mathrm{mm}/\mathrm{s}$ for the obstacle.