Quantized superfluid vortex dynamics on cylindrical surfaces and planar annuli

Abstract

Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being $\pm \hslash /(2MR)$, with $M$ the mass of the superfluid particles and $R$ the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function $\chi ({\mathbf{r}}_{12})$, and it crosses over from logarithmic to linear when the intervortex separation ${\mathbf{r}}_{12}$ becomes larger than the cylinder radius. An Appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second Appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.

16 pages, 7 figures; published version, with thoroughly revised Appendices

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Cited by in corpus (24)

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• Vortex Mass in a Superfluid
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• Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution
• Superfluid vortex dynamics on a spherical film
• Layering transitions in superfluid helium adsorbed on a carbon nanotube mechanical resonator
• Emergent periodic and quasiperiodic lattices on surfaces of synthetic Hall tori and synthetic Hall cylinders
• Superfluid vortex dynamics on a torus and other toroidal surfaces of revolution
• Analysis of a trapped Bose-Einstein condensate in terms of position, momentum, and angular-momentum variance
• Massive superfluid vortices and vortex necklaces on a planar annulus
• Superfluid Vortex Dynamics on Planar Sectors and Cones
• Spontaneous dipolar Bose-Einstein condensation on the surface of a cylinder
• Suppression of the superfluid Kelvin-Helmholtz instability due to massive vortex cores, friction and confinement
• Dynamical mechanisms of vortex pinning in superfluid thin films
• Condensates in annuli: Dimensionality of the variance
• Quantum Vortices in Curved Geometries
• Artificial magnetic field for synthetic quantum matter without dynamical modulation
• Vortex and soliton dynamics in particle-hole symmetric superfluids
• Superfluid vortex multipoles and soliton stripes on a torus
• Expansion dynamics of a cylindrical-shell-shaped strongly dipolar condensate
• Dynamics and transport of Bose-Einstein condensates in bent potentials
• Conformal maps and superfluid vortex dynamics on curved and bounded surfaces: the case of an elliptical boundary