Capture and release of quantum vortices using mechanical devices in low-temperature superfluids

TL;DR

This paper develops a theoretical and numerical framework using the GP-W equations to understand how nanowires detect quantum vortices in superfluid helium, matching experimental data and revealing vortex-induced frequency shifts.

Contribution

It introduces a combined numerical and analytical approach to model vortex detection via nanowires in superfluids, including the derivation of the dispersion relation with vortex effects.

Findings

Numerical simulations match experimental vortex detection signals.

The vortex causes a measurable frequency gap in wire oscillations.

Analytical dispersion relation confirms the vortex-induced frequency shift.

Abstract

We show that the Gross-Pitaevskii equation coupled with the wave equation for a wire (GP-W) provides a natural theoretical framework for understanding recent experiments employing a nanowire to detect a single quantum vortex in superfluid $^4 {\rm He}$. We uncover the complete spatiotemporal evolution of such wire-based vortex detection via direct numerical simulations of the GP-W system. Furthermore, by computing the spatiotemporal spectrum, we obtain the vortex-capture-induced change in the oscillation frequency of the wire. We quantify this frequency shift by plotting the wire's oscillation frequency versus time and obtain results that closely match experimental observations. In addition, we provide analytical support for our numerical results by deriving the dispersion relation for the oscillating wire, with and without a trapped vortex. We show that the Magnus force opens a gap in the wire dispersion relation. The size of the gap becomes the characteristic frequency of the wire when a vortex is trapped.