Bogoliubov theory and Lee-Huang-Yang corrections in spin-1 and spin-2 Bose-Einstein condensates in the presence of the quadratic Zeeman effect

Shun Uchino, Michikazu Kobayashi, Masahito Ueda

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Abstract

We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, pressure, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.

Original languageEnglish
Article number063632
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume81
Issue number6
DOIs
Publication statusPublished - 2010 Jun 25
Externally publishedYes

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Bogoliubov theory
Zeeman effect
Bose-Einstein condensates
acoustic velocity
depletion
generators
ground state
symmetry

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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AU - Kobayashi, Michikazu

AU - Ueda, Masahito

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AB - We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates (BECs) in the presence of a quadratic Zeeman effect, and derive the Lee-Huang-Yang (LHY) corrections to the ground-state energy, pressure, sound velocity, and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs that can be realized experimentally. We also examine the stability of each phase against quantum fluctuations and the quadratic Zeeman effect. Furthermore, we discuss a relationship between the number of symmetry generators that are spontaneously broken and that of Nambu-Goldstone (NG) modes. It is found that in the spin-2 nematic phase there are special Bogoliubov modes that have gapless linear dispersion relations but do not belong to the NG modes.

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