Abstract
Ultracold quantum gases are highly controllable and thus capable of simulating difficult quantum many-body problems ranging from condensed matter physics to astrophysics. Although experimental realizations have so far been restricted to flat geometries, recently also curved quantum systems, with the prospect of exploring tunable geometries, have been produced in microgravity facilities as ground-based experiments are technically limited. Here, we analyze bubble-trapped condensates, in which the atoms are confined on the surface of a thin spherically symmetric shell by means of external magnetic fields. A thermally induced proliferation of vorticity yields a vanishing of superfluidity. We describe the occurrence of this topological transition by conceptually extending the theory of Berezinskii, Kosterlitz, and Thouless for infinite uniform systems to such finite-size systems. Unexpectedly, we find universal scaling relations for the mean critical temperature and the finite width of the superfluid transition. Furthermore, we elucidate how they could be experimentally observed in finite-temperature hydrodynamic excitations.
Highlights
The physical understanding of nature, since the birth of modern science, relies on the reduction of a complex system to a properly idealized model that allows a mathematical description
It is possible to engineer different physical systems in such a way that they are described by the same laws: The study of each system will offer important information on the others
All these results are obtained with advanced techniques for the description of curved Bose-Einstein condensates and contribute to the fundamental understanding of BKT and vortex physics, a paradigmatic topic in statistical physics, condensed matter physics, and biology [30–32]
Summary
The physical understanding of nature, since the birth of modern science, relies on the reduction of a complex system to a properly idealized model that allows a mathematical description. Considering two-dimensional curved gases in regimes of quantum degeneracy, it is quite natural to ask whether the delicate interplay of curvature, geometry, and interactions allows for the superfluid properties to emerge [12] It is unclear whether and how the Berezinskii-Kosterlitz-Thouless (BKT) transition [13–15] of the superfluid density occurs in curved closed shells and whether its driving mechanism is the thermally driven unbinding of vortex-antivortex excitations for these finite-size systems. For the experimentally relevant parameters in which the finite-size effects are sizable, we calculate the frequencies of the hydrodynamic excitations of the superfluid, which represent the main experimental probe of BKT physics [28,29] All these results are obtained with advanced techniques for the description of curved Bose-Einstein condensates and contribute to the fundamental understanding of BKT and vortex physics, a paradigmatic topic in statistical physics, condensed matter physics, and biology [30–32]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
