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

Quantitative description of rotating TF condensate
Kinetic energy of condensate involves
2 ∫ ∫
dV |∇Ψ| 2 = dV 1 2M
2 Mv2 |Ψ| 2
} {{ }
superflow energy
∫
dV (∇|Ψ|) 2
}
2M
{{ }
density variation
+ 2
where Ψ = exp(iS)|Ψ| and v = ∇S/M is flow velocity
• generalized TF approximation: retain the energy of
superflow but ignore the energy from density variation
• this approximation will fail eventually when vortex
lattice becomes dense and cores start to overlap
• in rotating frame, generalized TF energy functional is
∫
E ′ [Ψ] = dV [( 1
2 Mv2 + V tr − MΩ · r × v ) |Ψ| 2
+ 1 2 g|Ψ|4]
• here, v is flow velocity generated by all the vortices
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