Analytical study of the splitting process of a multiply-quantized vortex in a Bose-Einstein condensate and collaboration of the zero and complex modes

K. Kobayashi, Y. Nakamura, Makoto Mine, Yoshiya Yamanaka

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3 Citations (Scopus)

Abstract

We study the dynamics of a trapped Bose-Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross-Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov-de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.

Original languageEnglish
Pages (from-to)2359-2371
Number of pages13
JournalAnnals of Physics
Volume324
Issue number11
DOIs
Publication statusPublished - 2009 Nov

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Bose-Einstein condensates
vortices
completeness
condensates
conservation
synchronism
eigenvalues
perturbation theory
interactions

Keywords

  • 03.75.Kk
  • 03.75.Lm
  • 05.30.Jp
  • Bose-Einstein condensation
  • Dynamical instability
  • Quantized vortex
  • Zero mode

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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abstract = "We study the dynamics of a trapped Bose-Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross-Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov-de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.",
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T1 - Analytical study of the splitting process of a multiply-quantized vortex in a Bose-Einstein condensate and collaboration of the zero and complex modes

AU - Kobayashi, K.

AU - Nakamura, Y.

AU - Mine, Makoto

AU - Yamanaka, Yoshiya

PY - 2009/11

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N2 - We study the dynamics of a trapped Bose-Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross-Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov-de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.

AB - We study the dynamics of a trapped Bose-Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross-Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov-de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.

KW - 03.75.Kk

KW - 03.75.Lm

KW - 05.30.Jp

KW - Bose-Einstein condensation

KW - Dynamical instability

KW - Quantized vortex

KW - Zero mode

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