Instabilities of vortices in a binary mixture of trapped Bose-Einstein condensates: role of collective excitations with positive and negative energies

Dmitry V. Skryabin

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Abstract

Correspondence between frequency and energy spectra and biorthogonality conditions for the excitations of Bose-Einstein condensates described by the Gross-Pitaevskii model have been derived self-consistently using general properties arising from the Hamiltonian structure of the model. It has been demonstrated that frequency resonances of the excitations with positive and negative energies can lead to their mutual annihilation and appearance of the collective modes with complex frequencies and zero energies. Conditions for the avoided crossing of energy levels have also been discussed. General theory has been verified both numerically and analytically in the weak interaction limit considering an example of vortices in a binary mixture of condensates. Growth of excitations with complex frequencies leads to spiraling of the unit and double vortices out of the condensate center to its periphery and to splitting of the double- and higher order vortices to the unit-order vortices.
Original languageEnglish
Number of pages14
JournalPhysical Review A
Volume63
Issue number1
DOIs
Publication statusPublished - 7 Dec 2000

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Bose-Einstein condensates
binary mixtures
vortices
excitation
condensates
energy
energy spectra
energy levels

Keywords

  • energy
  • Bose-Einstein condensates
  • excitations
  • vortices
  • positive energies
  • negative energies

Cite this

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title = "Instabilities of vortices in a binary mixture of trapped Bose-Einstein condensates: role of collective excitations with positive and negative energies",
abstract = "Correspondence between frequency and energy spectra and biorthogonality conditions for the excitations of Bose-Einstein condensates described by the Gross-Pitaevskii model have been derived self-consistently using general properties arising from the Hamiltonian structure of the model. It has been demonstrated that frequency resonances of the excitations with positive and negative energies can lead to their mutual annihilation and appearance of the collective modes with complex frequencies and zero energies. Conditions for the avoided crossing of energy levels have also been discussed. General theory has been verified both numerically and analytically in the weak interaction limit considering an example of vortices in a binary mixture of condensates. Growth of excitations with complex frequencies leads to spiraling of the unit and double vortices out of the condensate center to its periphery and to splitting of the double- and higher order vortices to the unit-order vortices.",
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T1 - Instabilities of vortices in a binary mixture of trapped Bose-Einstein condensates

T2 - role of collective excitations with positive and negative energies

AU - Skryabin, Dmitry V.

PY - 2000/12/7

Y1 - 2000/12/7

N2 - Correspondence between frequency and energy spectra and biorthogonality conditions for the excitations of Bose-Einstein condensates described by the Gross-Pitaevskii model have been derived self-consistently using general properties arising from the Hamiltonian structure of the model. It has been demonstrated that frequency resonances of the excitations with positive and negative energies can lead to their mutual annihilation and appearance of the collective modes with complex frequencies and zero energies. Conditions for the avoided crossing of energy levels have also been discussed. General theory has been verified both numerically and analytically in the weak interaction limit considering an example of vortices in a binary mixture of condensates. Growth of excitations with complex frequencies leads to spiraling of the unit and double vortices out of the condensate center to its periphery and to splitting of the double- and higher order vortices to the unit-order vortices.

AB - Correspondence between frequency and energy spectra and biorthogonality conditions for the excitations of Bose-Einstein condensates described by the Gross-Pitaevskii model have been derived self-consistently using general properties arising from the Hamiltonian structure of the model. It has been demonstrated that frequency resonances of the excitations with positive and negative energies can lead to their mutual annihilation and appearance of the collective modes with complex frequencies and zero energies. Conditions for the avoided crossing of energy levels have also been discussed. General theory has been verified both numerically and analytically in the weak interaction limit considering an example of vortices in a binary mixture of condensates. Growth of excitations with complex frequencies leads to spiraling of the unit and double vortices out of the condensate center to its periphery and to splitting of the double- and higher order vortices to the unit-order vortices.

KW - energy

KW - Bose-Einstein condensates

KW - excitations

KW - vortices

KW - positive energies

KW - negative energies

U2 - 10.1103/PhysRevA.63.013602

DO - 10.1103/PhysRevA.63.013602

M3 - Article

VL - 63

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

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