Description
We use the Gross–Pitaevskii equation to study the evolution of Bogoliubov excitations in a Bose–Einstein condensate with arbitrary one- and two-dimensional geometries. By numerically solving the time-dependent equation in experimentally relevant trapping potentials, we analyze how boundary conditions and density inhomogeneities modify the excitation spectrum and nonlinear mode dynamics. In a two-dimensional ring trap, where the azimuthal mode number is quantized to integer values, we find that azimuthal modulation of both the trap depth and the ring geometry enhances the lifetime and frequency of an imprinted azimuthal mode, thus improving the Q factor by orders of magnitude.
Experimentally, we have previously observed long lifetime phonon modes in a two-dimensional Helmholtz resonator geometry [1, 2], demonstrating strong agreement with an acoustic LC resonator model. Extending this framework to a ring geometry, we observe a similar frequency dependence on geometric parameters, consistent with an inductive–capacitive description of compressible superfluid flow. By additionally introducing controlled azimuthal density modulation, we analyse the mode frequency in terms of a weak periodic perturbation.
Using an undamped Gross–Pitaevskii model, we identify the dominant mechanism underlying the lifetime improvement as a reduction in nonlinear mode coupling. In particular, geometric and density modulation suppress four-wave mixing processes by reducing spatial overlap of the target mode with other azimuthal and radial modes. The resulting increase in resonator Q factor has direct implications for atomtronic applications of trapped BECs including high-precision rotation sensing in toroidal Bose–Einstein condensates [3] and cold atom phononic circuitry where long-lived modes can reduce error rates [4].
References
[1] G. Gauthier et al., Phys. Rev. Lett. 123, 260402 (2019)
[2] S. Eckel et al., Phys. Rev. A 93, 063619 (2016)
[3] C. W. Woffinden et al. SciPost Phys. 15, 128 (2023)
[4] Li, A. et al. Phys. Rev. A 94, 023626 (2016)
| I am the presenting author | Yes |
|---|