Here we present supplementary online video material concerning the following publication:
Noel Cuadra,1, ∗ Alberto Villois,2,3 Thomas Gasenzer,1,4,5 and Davide Proment2,3,5
1Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
2School of Engineering, Mathematics and Physics, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, United Kingdom
3Centre for Photonics and Quantum Science, University of East Anglia, Norwich Research Park, Norwich, NR4 7TJ, United Kingdom
4Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
5ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung, Planckstrasse 1, 64291 Darmstadt, Germany
The nonlinear excitations underlying the onset of rotation in a dilute Bose–Einstein condensate confined to a thin spherical shell are studied. These excitations correspond to solitary waves rotating about the sphere at constant angular speed: at low speeds they appear as dipoles of singly quantized vortices with opposite circulation, while at higher speeds they evolve into vortex-free Jones–Roberts solitons. With further increase of the angular speed, these excitations hybridize with equatorially confined modes whose azimuthal wave number is set by the sphere radius measured in units of the healing length. The propagation speed of these modes is shown to play the role of a Landau critical velocity, thereby setting the upper limiting angular speed of the entire Jones–Roberts family.
This page allows downloading videos. If you have an appropriate plugin installed, clicking on the download links streams the video in your browser window.
The video shows the temporal evolution according to Eq. (2) using, as initial condition, the solitary wave depicted in Fig.1(b-c).
Download Wolfram Mathematica Notebooks:
• RankinePoleVortex.nb: Wolfram Mathematica notebook showing the details of the calculations of angular momentum and kinetic energy of a fluid possessing the Rankine polar vortex solution discussed in Appendix E.
• LandauAngularSpeed.nb: Wolfram Mathematica notebook showing the details of the calculations of the Landau critical value lLandau and lim R → ∞ discussed in Appendix F.
