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

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 full a Lagrangian, is spontaneously broken, while massive NG modes appear when a modified symmetry is spontaneously broken.

13 pages, 12 figures, final version published in Phys. Rev. A

References in corpus (11)

• Nonrelativistic conformal field theories
• Counting rule for Nambu-Goldstone modes in nonrelativistic systems
• A relativistic non-relativistic Goldstone theorem: gapped Goldstones at finite charge density
• Kelvin Waves of Quantized Vortex Lines in Trapped Bose-Einstein Condensates
• Quasi-Nambu-Goldstone Modes in Bose-Einstein Condensates
• Counting rule of Nambu-Goldstone modes for internal and spacetime symmetries: Bogoliubov theory approach
• Nambu-Goldstone Modes Propagating along Topological Defects: Kelvin and Ripple Modes from Small to Large Systems
• Higher Derivative Corrections to Manifestly Supersymmetric Nonlinear Realizations
• On Nambu's Fermion-Boson Relations for Superfluid ${}^3$He-B
• Quasi-Nambu-Goldstone modes in nonrelativistic systems
• Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current