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arXiv:cond-mat/0107090 · Physical review. B, Condensed matter

Depinning of a superfluid vortex inside a circular defect

José A. Freire

Published May 1, 2000• 0 citations
arXivHTMLPDF

Abstract

In this work we study the process of depinning of a quantum of circulation trapped inside a disk by an applied two-dimensional superflow. We use the Gross-Pitaevskii model to describe the neutral superfluid. The collective coordinate dynamics is derived directly from the condensate equation of motion, the nonlinear Schr\"odinger equation, and it is used to obtain an expression for the critical velocity as a function of the defect radius. This expression is compared with a numerical result obtained from the time-independent nonlinear Schr\"odinger equation. Below the critical velocity, we obtain the dependence of the semiclassical nucleation rate with the flow velocity at infinity. Above the critical velocity, the classical vortex depinning is illustrated with a numerical simulation of the time-dependent nonlinear Schr\"odinger equation.

DOI
10.1103/physrevb.61.11656

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In this work we study the process of depinning of a quantum of circulation trapped inside a disk by an applied two-dimensional superflow. We use the Gross-Pitaevskii model to describe the neutral superfluid. The collective coordinate dynamics is derived directly from the condensate equation of motion, the nonlinear Schr"odinger equation, and it is used to obtain an expression for the critical velocity as a function of the defect radius. This expression is compared with a numerical result obtained from the time-independent nonlinear Schr"odinger equation. Below the critical velocity, we obtain the dependence of the semiclassical nucleation rate with the flow velocity at infinity. Above the critical velocity, the classical vortex depinning is illustrated with a numerical simulation of the time-dependent nonlinear Schr"odinger equation.
Abstract 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.
We report on numerical solutions of the Gross-Pitaevskii equation for two-dimensional flow of a superfluid condensate through a small orifice. Above a critical velocity of about 30%30\%30% of the speed of sound, cavitation occurs in the throat of the orifice. The cavitating bubbles form the cores of singly quantized vortices which detach from the boundary and are convected downstream.
The Bose condensate model is used to elucidate the motion of the electron bubble in superfluids. An asymptotic expansion is developed for steady subcritical flow. Numerical integration of the coupled nonlinear Schrödinger equations, that describe the evolution of the wavefunctions of the Bose condensate and the impurity, is used to study the nucleation and capture of vortex rings. Because an electron bubble is made oblate by its motion relative to the condensate, the critical velocity for the vortex nucleation is reduced by about 20%, in agreement with experiments.
In this thesis, we analytically and numerically study two different scenarios of vortex dynamics in a two-dimensional superfluid. The first system we explore is an expanding cluster of like-sign vortices, which recently suggested it could explain observations in a superfluid optomechanics experiment. We employ a recent theoretical model that approximates large collections of vortices as a fluid and present an analytic solution for its dynamics. Analysis suggests that as a cluster expands due to thermal friction, it forms a Rankine vortex (i.e., a top-hat distribution) that expands self-similarly in time regardless of initial vorticity distribution. Numerical simulations of point vortices confirm this universal expanding regime and further demonstrates vortex lattice formation that goes beyond the vortex fluid theory. We analyse correlations that emerge in the resulting lattices and observe decaying disorder as the cluster expands. Furthermore, we analyse experimental data from a quasi-two-dimensional 87Rb Bose-Einstein condensate, which supports the vortex fluid theory’s predictions.The second scenario considers the dynamics of a scattering event where a single quantum vortex interacts with a uniform, circular pinning potential in a steady two-dimensional superfluid flow. We first develop an approximate hydrodynamical model to understand the interaction between the vortex and the pinning potential in the conservative regime and find it is in good agreement with the mean-field Gross-Pitaevskii equation in the low-velocity limit. We further solve the Gross-Pitaevskii equation for higher background velocities to study how the vortex moves around pinning sites, interacts with it, and ultimately becomes pinned. We uncover four different regimes of vortex pinning, each marked with a characteristic emission of sound energy. Finally, we study how vortices become unpinned from a pinning site, revealing large vortex dipoles form to stabilise the system.Our work in this thesis takes significant steps towards advancing knowledge of both the collective dynamics of vortices and their individual interaction with defects upon surface substrates. Our numerical and analytical results opens up new avenues of exploration be it further understanding dissipation mechanisms in two-dimensional superfluids, or elucidating the nature of vortex pinning in systems such as neutron stars.
We simulate the motion of a massive object through a dilute Bose-Einstein condensate by numerical solution of the Gross-Pitaevskii equation coupled to an equation of motion for the object. Under a constant applied force, the object accelerates up to a maximum velocity where a vortex ring is formed which slows the object down. If the applied force is less than a critical value, the object becomes trapped within the vortex core. We show that the motion follows the time-independent solutions, and use these solutions to predict the conditions required for vortex detachment.