Anomalous minimization for critical velocity of superflow along a step potential

TL;DR

This paper introduces a simplified model to analyze the critical velocity of superflow along a step potential in a Bose-Einstein condensate, revealing a critical point where the velocity minimizes and scales with system size.

Contribution

The study provides a semi-classical analysis linking the critical velocity to a local phase transition and explains experimental power-law scaling.

Findings

Critical velocity minimizes and drops to zero when potential height equals chemical potential.

Critical velocity scales with system size as approximately L_x^{-0.963}.

The model explains the experimentally observed power-law behavior of critical velocity.

Abstract

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 $v_\mathrm{c}$ obeys a power-law scaling with the system size $L_x$ as $v_\mathrm{c}\propto L_x^{-0.963}$. This criticality provides an explanation of the power-law scaling of the minimum critical velocity observed in the experiment.