Rapidly rotating Bose-Einstein condensates∗ Alexander Fetter ...

1 Physics of one vortex line in harmonic trap
Assume general axisymmetric trap potential
V tr (r) = V tr (r, z) = 1 2 M ( ω 2 ⊥r 2 + ω 2 zz 2)
Basic idea (Bogoliubov): for weak interparticle potentials,
nearly all particles remain in condensate for T ≪ T c
• for ideal gas at T = 0, all particles are in condensate.
• hence treat occupation of non-condensate as small
• dilute: s-wave scattering length a s ≪ interparticle
spacing n −1/3
• equivalently, require na 3 s ≪ 1
• assume self-consistent condensate wave function Ψ(r)
• gives nonuniform condensate density n(r) = |Ψ(r)| 2
• for T ≪ T c , normalization requires N = ∫ dV |Ψ(r)| 2
2