arXiv:2412.07368 · Physical Review A

Critical velocity for wake vortex generation behind a plate in a superflow

Haruya Kokubo, Hiromitsu Takeuchi, Kenichi Kasamatsu

Published Apr 18, 2025• 6 citations

Abstract

We study theoretically the critical velocity ${U}_{c}$ 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 $L$. In the limit of large $L$, 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 $L$ 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.

DOI: 10.1103/physreva.111.043314

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arXiv:2412.07368 · Physical Review A

Critical velocity for wake vortex generation behind a plate in a superflow

Haruya Kokubo, Hiromitsu Takeuchi, Kenichi Kasamatsu

Published Apr 18, 2025• 6 citations

arXiv HTML PDF

Abstract

We study theoretically the critical velocity

{U}_{c}

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

L

. In the limit of large

L

, 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

L

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.

DOI: 10.1103/physreva.111.043314

Related papers

Critical Velocity for Quantized Vortex Formation in a Superfluid with a Plate-Shaped Obstacle

Haruya Kokubo, Hiromitsu Takeuchi, Kenichi Kasamatsu

Abstract We theoretically investigate the dependence of the critical velocity for quantum vortex formulation on the size L of a plate-shaped obstacle moving in a uniform Bose-Einstein condenste in quasi-two-dimensions.Numerical simulations of the Gross-Pitaevskii equation reveal that the critical velocity vc is proportional to L-1/2 when L is much larger than the healing length. The power law behavior is quantitatively explained by the potential flow theory of classical hydrodynamics for the large L limit.Abstract We theoretically investigate the dependence of the critical velocity for quantum vortex formulation on the size L of a plate-shaped obstacle moving in a uniform Bose-Einstein condenste in quasi-two-dimensions.Numerical simulations of the Gross-Pitaevskii equation reveal that the critical velocity vc is proportional to L-1/2 when L is much larger than the healing length. The power law behavior is quantitatively explained by the potential flow theory of classical hydrodynamics for the large L limit.

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

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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 ${v}_{c}$ 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 $\ensuremath{\gamma}\ensuremath{\approx}1/2$.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 $\ensuremath{\gamma}\ensuremath{\approx}1/2$.

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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 ${V}_{0}$ , 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.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.

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Vortex Depinning in a Two-Dimensional Superfluid

I-Kang Liu, Srivatsa B. Prasad, Andrew William Baggaley +2 more

© The Author(s) 2024. We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.© The Author(s) 2024. We employ the Gross–Pitaevskii theory to model a quantized vortex depinning from a small obstacle in a two-dimensional superfluid due to an imposed background superfluid flow. We find that, when the flow’s velocity exceeds a critical value, the vortex drifts orthogonally to the flow before subsequently moving parallel to it away from the pinning site. The motion of the vortex around the pinning site is also accompanied by an emission of a spiral-shaped sound pulse. Through simulations, we present a phase diagram of the critical flow velocity for vortex depinning together with an empirical formula that illustrates how the critical velocity increases with the height and width of the pinning site. By employing a variety of choices of initial and boundary conditions, we are able to obtain lower and upper bounds on the critical velocity and demonstrate the robustness of these results.

Jun 1, 20240 citations

We study theoretically the critical velocity

{U}_{c}

L

. In the limit of large

L

, 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

L

{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 $\ensuremath{\gamma}\ensuremath{\approx}1/2$.

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.