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arXiv:1508.00958 · Physical Review A

Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate

Woo Jin Kwon, Sang Won Seo, Yong-il Shin

Published Sep 15, 2015• 80 citations
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Abstract

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 ${f}_{v}$ linearly increases with the obstacle velocity $v$ as ${f}_{v}=a(v\ensuremath{-}{v}_{c})$, where ${v}_{c}$ 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.

DOI
10.1103/physreva.92.033613

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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{f}_{v}fv​ linearly increases with the obstacle velocity vvv as fv=a(v\ensuremath−vc){f}_{v}=a(v\ensuremath{-}{v}_{c})fv​=a(v\ensuremath−vc​), where vc{v}_{c}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.
Abstract We experimentally investigate the periodic vortex shedding dynamics in a highly oblate Bose–Einstein condensate using a moving penetrable Gaussian obstacle. The shedding frequency f v is measured as a function of the obstacle velocity v and characterized by a linear relationship of f v = a(v − v c) with v c being the critical velocity. The proportionality constant a is linearly decreased with a decrease in the obstacle strength, whereas v c approaches the speed of sound. When the obstacle size increases, both a and v c are decreased. We discuss a possible association of a with the Strouhal number in the context of universal shedding dynamics of a superfluid. The critical vortex shedding is further investigated for an oscillating obstacle and found to be consistent with the measured f v. When the obstacle’s maximum velocity exceeds v c but its oscillation amplitude is not large enough to create a vortex dipole, we observe that vortices are generated in the low-density boundary region of the trapped condensate, which is attributed to the phonon emission from the oscillating obstacle.
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{V}_{0}V0​, the critical velocity vc{v}_{c}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{v}_{c}vc​ to the speed of sound cs{c}_{s}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{v}_{c}/{c}_{s}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.
While quantized vortices and vortex lattices in Bose-Einstein condensates (BECs) have received much recent attention, the formation and dynamics of vortex dipoles have been nearly unexplored in experimental BECs. Vortex dipoles consist of a pair of vortices of opposite circulation moving under the influence of each other, and may be considered as metastable topological structures that carry linear momentum in a fluid. In this talk, a collaborative experimental and numerical study of the formation, dynamics, and lifetimes of vortex dipoles in BECs will be presented. In our work [1], single vortex dipoles were deterministically nucleated by causing highly oblate, harmonically trapped BECs to move past a repulsive obstacle above a supercritical flow velocity. Our measured critical velocity for vortex dipole shedding, and the subsequent dipole dynamics, are in good agreement with new numerical simulations. We find that vortex dipoles can survive for many seconds in the BEC without selfannihilation, and that multiply charged vortex dipoles can be formed with high enough flow velocities. References: 1. T.W. Neely, E.C. Samson, A.S. Bradley, M.J. Davis, and B.P. Anderson, preprint available at http://arxiv.org/abs/0912.3773.
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{v}_{c}vc​ was measured for atomic Bose-Einstein condensates (BECs) using a moving repulsive Gaussian potential, and vc{v}_{c}vc​ was minimized when the potential height V0{V}_{0}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{V}_{0}V0​ and show that the minimum vc{v}_{c}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{v}_{c}vc​ is examined. The particle density at the tip of the obstacle decreases as V0{V}_{0}V0​ increases to Vc0{V}_{c0}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{v}_{c}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 propose methods to generate and manipulate vortex dipoles in an atomic Bose-Einstein condensate using Gaussian beams of red-or blue-detuned laser.Vortex dipoles with controlled velocities are shown to be created and launched by a red-detuned beam and by two blue-detuned beams.Critical beam velocities for the vortex nucleation are investigated.The launched vortex dipoles can be trapped, curved, accelerated, and decelerated by using Gaussian laser beams.Collisions between vortex dipoles are demonstrated.
We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilute-gas Bose-Einstein condensates (BECs). We nucleate pairs of vortices of opposite charge (vortex dipoles) by forcing superfluid flow around a repulsive Gaussian obstacle within the BEC. By controlling the flow velocity we determine the critical velocity for the nucleation of a single vortex dipole, with excellent agreement between experimental and numerical results. We present measurements of vortex dipole dynamics, finding that the vortex cores of opposite charge can exist for many seconds and that annihilation is inhibited in our trap geometry. For sufficiently rapid flow velocities, clusters of like-charge vortices aggregate into long-lived multiply charged dipolar flow structures.