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

TL;DR

This study numerically investigates the critical velocity for vortex creation in a Bose-Einstein condensate when flowing past a Gaussian obstacle, revealing how obstacle strength and size influence vortex dynamics and pinning effects.

Contribution

It provides a detailed numerical analysis of the minimum critical velocity and vortex pinning phenomena in BECs with Gaussian obstacles, extending experimental insights.

Findings

Minimum critical velocity occurs near obstacle strength equal to chemical potential.

Vortex dipole formation indicates vortex pinning at critical obstacle strength.

Critical velocity scales with obstacle size as v_c ~ σ^(-1/2).

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 $\mu$. 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 $V_{0c}\approx \mu$ 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 $\sigma$ as $v_c\sim \sigma^{-\gamma}$ with $\gamma\approx 1/2$.