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

5 Behavior for Ω → ω ⊥
What happens beyond the “mean-field quantum Hall”
regime is still subject to vigorous debate
Predict quantum phase transition from coherent BEC
states to various correlated many-body states
• define the ratio ν ≡ N/N v = the number of atoms
per vortex
• because of similarities to a two-dimensional electron
gas in a strong magnetic field, ν is called the “filling
fraction” [33, 34]
• current experiments [18] have N ∼ 10 5 and N v ∼
several hundred, so ν ∼ a few hundred
• numerical studies [34] for small number of vortices
(N v 8) and variable N indicate that the coherent
GP state is favored for ν 6 − 8
• softening of Tkachenko spectrum for rapid rotation
can induce melting of vortex lattice at similar filling
fraction ν [35, 36]
38