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arXiv:1502.03542 · Physical Review A

Critical velocity for vortex shedding in a Bose-Einstein condensate

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

Published May 15, 2015• 80 citations
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Abstract

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 ${V}_{0}$, the critical velocity ${v}_{c}$ 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 ${v}_{c}$ to the speed of sound ${c}_{s}$ 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 ${v}_{c}/{c}_{s}$ 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.

DOI
10.1103/physreva.91.053615

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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 V0\ensuremath≈\ensuremathμ{V}_{0}\ensuremath{\approx}\ensuremath{\mu}V0​\ensuremath≈\ensuremathμ, where \ensuremathμ\ensuremath{\mu}\ensuremathμ is the chemical potential of the condensate. At fixed V0\ensuremath≈7\ensuremathμ{V}_{0}\ensuremath{\approx}7\ensuremath{\mu}V0​\ensuremath≈7\ensuremathμ, we observe that the ratio of vc{v}_{c}vc​ to the speed of sound cs{c}_{s}cs​ monotonically increases for decreasing \ensuremathσ/\ensuremathξ\ensuremath{\sigma}/\ensuremath{\xi}\ensuremathσ/\ensuremathξ, where \ensuremathσ\ensuremath{\sigma}\ensuremathσ is the beam width and \ensuremathξ\ensuremath{\xi}\ensuremathξ 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.
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 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 ${f}_{v}=a(v\ensuremath{-}{v}_{c})$, 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.
This thesis examines the manifestation of the critical velocity for superfluidity in dilute gas Bose-Einstein condensates (BECs). Superfluidity is a macroscopic quantum phenomenon characterised by unique properties such as frictionless flow, high thermal conductivity and the presence of quantised vortices. Our study focuses on what is arguably the most well-known attribute: the ability for an object to move through a superfluid without experiencing a drag force when travelling below a threshold critical velocity.The Landau criterion for superfluidity predicts the critical velocity in a BEC is equal to the speed of sound, and this conclusion is supported by a large body of theoretical work. However, a number of experiments have observed lower critical velocities than theory predicts. In the first part of this thesis, we numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept a repulsive obstacle, formed by a optical dipole potential, through the long axis of a condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of v _ 0:3 mm s
We numerically model experiments on the superfluid critical velocity of an elongated, harmonically trapped Bose-Einstein condensate as reported by [P. Engels and C. Atherton, Phys. Rev. Lett. 99, 160405 (2007)]. These experiments swept an obstacle formed by an optical dipole potential through the long axis of the condensate at constant velocity. Their results found an increase in the resulting density fluctuations of the condensate above an obstacle velocity of v≈0.3v\approx 0.3v≈0.3 mm/s, suggestive of a superfluid critical velocity substantially less than the average speed of sound. However, our analysis shows that the that the experimental observations of Engels and Atherton are in fact consistent with a superfluid critical velocity equal to the local speed of sound. We construct a model of energy transfer to the system based on the local density approximation to explain the experimental observations, and propose and simulate experiments that sweep potentials through harmonically trapped condensates at a constant fraction of the local speed of sound. We find that this leads to a sudden onset of excitations above a critical fraction, in agreement with the Landau criterion for superfluidity.
We study theoretically the critical velocity Uc{U}_{c}Uc​ for quantum vortex generation by a thin plate-shaped obstacle moving through a uniform two-dimensional Bose-Einstein condensate. Our results based on the Gross-Pitaevskii theory reveal that the critical velocity monotonically decreases with increasing the plate size LLL. In the limit of large LLL, the critical velocity is asymptotic to ${L}^{\ensuremath{-}1/2}$ predicted by the potential flow theory for an incompressible ideal fluid with a phenomenological length correction. As LLL decreases, however, the incompressible analysis breaks down quantitatively. By performing a perturbative analysis to incorporate compressibility into the potential flow theory, we successfully reproduced the numerical results analytically over a wide parameter range.