Superfluid toroidal currents in atomic condensates

TL;DR

This paper investigates the dynamics and excitation spectrum of superfluid toroidal condensates, revealing how currents and geometry influence energy levels, and proposes an experimental approach to study these phenomena.

Contribution

It provides a detailed calculation of the Bogoliubov spectrum for toroidal condensates and explores the effects of currents and geometry on excitations, introducing a new experimental method.

Findings

Energy levels form narrow bands during geometry transition.

Toroidal currents split co-rotating and counter-rotating modes.

Radial dipole excitations are the lowest energy dissipation modes.

Abstract

The dynamics of toroidal condensates in the presence of condensate flow and dipole perturbation have been investigated. The Bogoliubov spectrum of condensate is calculated for an oblate torus using a discrete-variable representation and a spectral method to high accuracy. The transition from spheroidal to toroidal geometry of the trap displaces the energy levels into narrow bands. The lowest-order acoustic modes are quantized with the dispersion relation $\omega \sim |m| \omega_s $ with $m=0,\pm 1,\pm 2, ...$. A condensate with toroidal current $\kappa$ splits the $|m|$ co-rotating and counter-rotating pair by the amount: $\Delta E \approx 2 |m|\hbar^2 \kappa < r^{-2}>$. Radial dipole excitations are the lowest energy dissipation modes. For highly occupied condensates the nonlinearity creates an asymmetric mix of dipole circulation and nonlinear shifts in the spectrum of excitations so that the center of mass circulates around the axis of symmetry of the trap. We outline an experimental method to study these excitations.