We investigate vortex shedding from a moving penetrable obstacle in a highly oblate Bose-Einstein condensate. The penetrable obstacle is formed by a repulsive Gaussian laser beam that has the potential barrier height lower than the chemical potential of the condensate. The moving obstacle periodically generates vortex dipoles and the vortex shedding frequency
fv linearly increases with the obstacle velocity
v as ${f}_{v}=a(v\ensuremath{-}{v}_{c})$, where
vc is a critical velocity. Based on the periodic shedding behavior, we demonstrate deterministic generation of a single vortex dipole by applying a short linear sweep of a laser beam. This method will allow further controlled vortex experiments such as dipole-dipole collisions.
We present measurements of the critical velocity for vortex shedding in a highly oblate Bose-Einstein condensate with a moving repulsive Gaussian laser beam. As a function of the barrier height
V0, the critical velocity
vc shows a dip structure having a minimum at ${V}_{0}\ensuremath{\approx}\ensuremath{\mu}$, where $\ensuremath{\mu}$ is the chemical potential of the condensate. At fixed ${V}_{0}\ensuremath{\approx}7\ensuremath{\mu}$, we observe that the ratio of
vc to the speed of sound
cs monotonically increases for decreasing $\ensuremath{\sigma}/\ensuremath{\xi}$, where $\ensuremath{\sigma}$ is the beam width and $\ensuremath{\xi}$ is the condensate healing length. We explain our results with the density reduction effect of the soft boundary of the Gaussian obstacle, based on the local Landau criterion for superfluidity. The measured value of
vc/cs with our stiffest obstacle is about 0.4, which is in good agreement with theoretical predictions for a two-dimensional superflow past a circular cylinder.
When a superfluid flows past an obstacle, quantized vortices can be created in the wake above a certain critical velocity. In the experiment by Kwon et al. [Phys. Rev. A 91, 053615 (2015)], the critical velocity
vc was measured for atomic Bose-Einstein condensates (BECs) using a moving repulsive Gaussian potential, and
vc was minimized when the potential height
V0 of the obstacle was close to the condensate chemical potential $\ensuremath{\mu}$. Here we numerically investigate the evolution of the critical vortex shedding in a two-dimensional BEC with increasing
V0 and show that the minimum
vc at the critical strength ${V}_{0c}\ensuremath{\approx}\ensuremath{\mu}$ results from the local density reduction and vortex-pinning effect of the repulsive obstacle. The spatial distribution of the superflow around the moving obstacle just below
vc is examined. The particle density at the tip of the obstacle decreases as
V0 increases to
Vc0, and at the critical strength, a vortex dipole is suddenly formed and dragged by the moving obstacle, indicating the onset of vortex pinning. The minimum
vc exhibits power-law scaling with the obstacle size $\ensuremath{\sigma}$ as ${v}_{c}\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}\ensuremath{\gamma}}$ with $\ensuremath{\gamma}\ensuremath{\approx}1/2$.
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.
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.
Vortex Shedding from a Microsphere Oscillating in Superfluid
4He at mK Temperatures and from a Laser Beam Moving in a Bose–Einstein Condensate
Abstract Turbulent drag of an oscillating microsphere that is levitating in superfluid
4 4 He at mK temperatures, is unstable slightly above a critical velocity amplitude
vc v c . The lifetime
τ τ of the turbulent state is determined by the number n of vortices shed per half-period. It is found that this number is identical to the superfluid Reynolds number. The possibility of moving a levitating sphere through superfluid
3 3 He at microkelvin temperatures is considered. A laser beam moving through a Bose–Einstein condensate (BEC) (as observed by other authors) also produces vortices in the BEC. In particular, in either case, a linear dependence of the shedding frequency
fv f v on
Δv=v−vc Δ v = v - v c is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above
vc v c for the onset of turbulent flow:
fv=aΔv f v = a Δ v , where the coefficient a is proportional to the oscillation frequency
ω ω above some characteristic frequency
ωk ω k and assumes a finite value for steady motion
ω→0 ω → 0 . A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.