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, Muneto Nitta

Research output: Contribution to journalArticle

1 Citation (Scopus)

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)APNYA60003-491610.1016/j.aop.2014.12.009]. 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.

Original languageEnglish
Article number023626
JournalPhysical Review A
Volume96
Issue number2
DOIs
Publication statusPublished - 2017 Aug 29

Fingerprint

ripples
symmetry
traps
Bose-Einstein condensates
condensates
Bogoliubov theory
harmonics
breathing
kinetic energy
trapping
vortices
oscillations
composite materials

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes. / Takahashi, Daisuke A.; Ohashi, Keisuke; Fujimori, Toshiaki; Nitta, Muneto.

In: Physical Review A, Vol. 96, No. 2, 023626, 29.08.2017.

Research output: Contribution to journalArticle

@article{e2a422c6076649afa7a5f626e3e85add,
title = "Two-dimensional Schr{\"o}dinger 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 Schr{\"o}dinger symmetry, that is, the Schr{\"o}dinger 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{\"o}dinger 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{\"o}dinger 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)APNYA60003-491610.1016/j.aop.2014.12.009]. 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.",
author = "Takahashi, {Daisuke A.} and Keisuke Ohashi and Toshiaki Fujimori and Muneto Nitta",
year = "2017",
month = "8",
day = "29",
doi = "10.1103/PhysRevA.96.023626",
language = "English",
volume = "96",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "2",

}

TY - JOUR

T1 - Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes

AU - Takahashi, Daisuke A.

AU - Ohashi, Keisuke

AU - Fujimori, Toshiaki

AU - Nitta, Muneto

PY - 2017/8/29

Y1 - 2017/8/29

N2 - 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)APNYA60003-491610.1016/j.aop.2014.12.009]. 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.

AB - 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)APNYA60003-491610.1016/j.aop.2014.12.009]. 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.

UR - http://www.scopus.com/inward/record.url?scp=85028654950&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028654950&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.96.023626

DO - 10.1103/PhysRevA.96.023626

M3 - Article

AN - SCOPUS:85028654950

VL - 96

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

M1 - 023626

ER -