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arXiv:2210.04403 · Physical Review A

Minimum critical velocity of a Gaussian obstacle in a Bose-Einstein condensate

Haneul Kwak, Jong Heum Jung, Yong-il Shin

Published Feb 15, 2023• 16 citations
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Abstract

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 ${v}_{c}$ was measured for atomic Bose-Einstein condensates (BECs) using a moving repulsive Gaussian potential, and ${v}_{c}$ was minimized when the potential height ${V}_{0}$ 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 ${V}_{0}$ and show that the minimum ${v}_{c}$ 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 ${v}_{c}$ is examined. The particle density at the tip of the obstacle decreases as ${V}_{0}$ increases to ${V}_{c0}$, 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 ${v}_{c}$ exhibits power-law scaling with the obstacle size $\ensuremath{\sigma}$ as ${v}_{c}\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}\ensuremath{\gamma}}$ with $\ensuremath{\gamma}\ensuremath{\approx}1/2$.

DOI
10.1103/physreva.107.023310

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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 \ensuremathμ\ensuremath{\mu}\ensuremathμ. 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 V0c\ensuremath≈\ensuremathμ{V}_{0c}\ensuremath{\approx}\ensuremath{\mu}V0c​\ensuremath≈\ensuremathμ 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 \ensuremathσ\ensuremath{\sigma}\ensuremathσ as vc\ensuremath∼\ensuremathσ\ensuremath−\ensuremathγ{v}_{c}\ensuremath{\sim}{\ensuremath{\sigma}}^{\ensuremath{-}\ensuremath{\gamma}}vc​\ensuremath∼\ensuremathσ\ensuremath−\ensuremathγ with \ensuremathγ\ensuremath≈1/2\ensuremath{\gamma}\ensuremath{\approx}1/2\ensuremathγ\ensuremath≈1/2.
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.
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.
To reveal a microscopic mechanism for the anomalous minimization and dependence of the superfluid critical velocity on a moving obstacle potential in a atomic Bose-Einstein condensate [\href{https://link.aps.org/doi/10.1103/PhysRevA.91.053615}{Phys.~Rev.~A \textbf{91}, 053615 (2015)}], we introduce a considerably simplified model of superflow along a step potential. The energy spectrum and wave functions of the lowest-energy excitations in this system are well described by the semi-classical analysis based on the Bogoliubov theory. We found that the critical velocity is minimized and becomes zero when the potential height equals the hydrostatic chemical potential, which corresponds to the critical point of the local condensation phase transition inside the step potential. In a finite-size system, the critical velocity vcv_\mathrm{c}vc​ obeys a power-law scaling with the system size LxL_xLx​ as vc∝Lx−0.963v_\mathrm{c}\propto L_x^{-0.963}vc​∝Lx−0.963​. This criticality provides an explanation of the power-law scaling of the minimum critical velocity observed in the experiment.
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 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.
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.