Equatorial Waves in Rotating Bubble-Trapped Superfluids

TL;DR

This paper predicts that rapidly rotating bubble-shaped Bose-Einstein condensates can support equatorial wave modes analogous to Earth's oceanic and atmospheric waves, revealing topological properties of superfluid hydrodynamics.

Contribution

It introduces a topological hydrodynamic framework for rotating BECs in spherical traps, predicting specific equatorial wave modes supported by superfluids.

Findings

Kelvin, Yanai, and Poincaré modes are supported

Rossby mode is not supported

Topologically nontrivial Hamiltonian describes oscillations

Abstract

As the Earth rotates, the Coriolis force causes several oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we show that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Based on a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation by a Schr\"odinger-like eigenvalue problem. The obtained non-Hermitian Hamiltonian is topologically nontrivial. Furthermore, we solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincar\'e equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.