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

Hence TF wave function depends explicitly on Ω through
the altered radial trap frequency ω⊥ 2 → ω2 ⊥ − )
Ω2
|Ψ(r, z)| 2 = n(0)
(1 − r2
− z2
Rz
2
where
R 2 ⊥ =
2µ
M(ω 2 ⊥ − Ω2 )
R 2 ⊥
and R 2 z = 2µ
Mω 2 z
• for pure harmonic trap, must have Ω < ω ⊥ to retain
radial confinement
• normalization ∫ dV |Ψ| 2 = N shows that
( ) 2/5
µ(Ω)
µ(0) = 1 − Ω2
ω⊥
2
in three dimensions
• central density given by n(0) = µ(Ω)/g
• n(0) decreases with increasing Ω because of reduced
radial confinement
22