Transition temperature for the all-optical formation of [Formula Presented] spinor condensate

W. J. Huang, Shih-Chuan Gou, Y. C. Tsai

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We investigate theoretically the transition temperature of a weakly interacting [Formula Presented] spinor Bose-Einstein condensate (BEC) formed in an optical trap. The Hartree-Fock-Bogoliubov formalism for the spinor BEC is developed based on the mean-field theory for inhomogeneous systems at finite temperatures. The shift of the transition temperature due to finite-size effects and the two-body interaction is obtained simultaneously by analytically solving the coupled eigenvalue equations for quasiparticle excitations and amplitudes under Hartee-Fock-Bogoliubov and other relevant approximations. When applying this to the recent experiment of the all-optical formation of a spinor BEC with a condensate of [Formula Presented] [Formula Presented] atoms [Phys. Rev. Lett. 87, 010404 (2001)], our calculations show that the condensation occurs at a temperature about 177 nK. An analytic result for the shift of the transition temperature in the presence of a weak magnetic field is also derived.

Original languageEnglish
Number of pages1
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number6
Publication statusPublished - 2002 Jan 1

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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