Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes

Daisuke A. Takahashi, Keisuke Ohashi, Toshiaki Fujimori, and Muneto Nitta
Phys. Rev. A 96, 023626 – Published 29 August 2017

Abstract

Bose-Einstein condensates (BECs) confined in a two-dimensional (2D) harmonic trap are known to possess a hidden 2D Schrödinger symmetry, that is, the Schrödinger 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 Schrödinger 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 Schrödinger 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.

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  • Received 30 June 2017

DOI:https://doi.org/10.1103/PhysRevA.96.023626

©2017 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsNonlinear DynamicsParticles & Fields

Authors & Affiliations

Daisuke A. Takahashi1,*, Keisuke Ohashi1, Toshiaki Fujimori1, and Muneto Nitta1,2

  • 1Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan
  • 2Department of Physics, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan

  • *daisuke.takahashi@keio.jp

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Vol. 96, Iss. 2 — August 2017

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