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

Presence of harmonic trap yields much richer system than
a uniform interacting Bose gas [5]
• trap gives new energy scale ω 0 and new length scale
d 0 = √ /Mω 0
• assume repulsive interactions with a s > 0
• trap leads to new dimensionless parameter Na s /d 0
• typical value of ratio of lengths: a s /d 0 ∼ 10 −3
• but Na s /d 0 is large for typical N ∼ 10 6
• in strong repulsive limit (Na s /d 0 ≫ 1), condensate
expands to mean radius R 0 ≫ d 0
• neglect radial gradient of Ψ when R 0 ≫ d 0
• GP equation then simplifies and gives local density
4πa s 2
M
|Ψ(r,z)|2 = µ − V tr (r,z)
[called Thomas-Fermi (TF) limit]
• harmonic trap produces quadratic density variation
with condensate dimensions R 2 j = 2µ/(Mω2 j )
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