2017/06/30 by Daisuke Takahashi, Daisuke A. Takahashi, Keisuke Ohashi +2
Physics and Astronomy · #Breather #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Dispersion relation #Geometry #Harmonic oscillator #Mechanics #Physics #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Rotational symmetry #Strong Light-Matter Interactions #Symmetry (geometry) #Symmetry breaking #cond-mat.quant-gas #hep-th
paper · pdf · doi:10.1103/physreva.96.023626
published as Phys. Rev. A 96, 023626 (2017) · 13 pages, 12 figures, final version published in Phys. Rev. A
openalex publication_date 2017/08/29 · arxiv created 2017/08/31 · arxiv updated 2017/09/04 · openalex created_date 2017/09/15 · openalex updated_date 2026/08/05
Bose-Einstein condensates (BECs) confined in a two-dimensional (2D) harmonic trap are known to possess a hidden 2D Schr"odinger symmetry, that is, the Schr"odinger symmetry modified by a trapping potential. Spontaneous breaking of this symmetry gives rise to a breathing motion of the BEC, whose oscillation frequency is robustly determined by the strength of the harmonic trap. In this paper, we demonstrate that the concept of the 2D Schr"odinger symmetry can be applied to predict the nature of three-dimensional (3D) collective modes propagating along a condensate confined in an elongated trap. We find three kinds of collective modes whose existence is robustly ensured by the Schr"odinger symmetry, which are physically interpreted as one breather mode and two Kelvin-ripple complex modes, i.e., composite modes in which the vortex core and the condensate surface oscillate interactively. We provide analytical expressions for the dispersion relations (energy-momentum relation) of these modes using the Bogoliubov theory [D. A. Takahashi and M. Nitta, Ann. Phys. 354, 101 (2015)]. Furthermore, we point out that these modes can be interpreted as ``quasi-massive-Nambu-Goldstone (NG) modes'', that is, they have the properties of both quasi-NG and massive NG modes: quasi-NG modes appear when a symmetry of a part of a Lagrangian, which is not a symmetry of a full Lagrangian, is spontaneously broken, while massive NG modes appear when a modified symmetry is spontaneously broken.