Rapidly rotating Bose-Einstein condensatesâ Alexander Fetter ...

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• ENS group observed small vortex arrays of up to 11 vortices (arranged in two concentric rings) • like patterns predicted and seen in superfluid 4 He [16] 16
• MIT group has prepared considerably larger rotating condensates in less elongated trap • they have observed triangular vortex lattices with up to 130 vortices [17] • like Abrikosov lattice of quantized flux lines (which are charged vortices) in type-II superconductors • JILA group has now made large rotating condensates with several hundred vortices and angular velocity Ω/ω ⊥ ≈ 0.995 [18] • these rapidly rotating systems open many exciting new possibilities (discussed below) 17
Page 1 and 2: Rapidly rotating Bose-Einstein cond
Page 3 and 4: • assume an energy functional ⎡
Page 5 and 6: • general property: circulation a
Page 7 and 8: One vortex line in trapped BEC Firs
Page 9 and 10: Energy of rotating TF condensate wi
Page 11 and 12: curve (a) is ∆E ′ (r 0 , Ω) fo
Page 13 and 14: 2 Experimental creation/detection o
Page 15: École Normale Supérieure (ENS) in
Page 19 and 20: As Ω increases, the mean vortex de
Page 21 and 22: For Ω along z, can complete square
Page 23 and 24: • TF formulas for condensate radi
Page 25 and 26: • variation with respect to u yie
Page 27 and 28: Tkachenko oscillations of the vorte
Page 29 and 30: • rough agreement with JILA exper
Page 31 and 32: General two-dimensional energy func
Page 33 and 34: • assume that the GP wave functio
Page 35 and 36: Take this LLL trial function seriou
Page 37 and 38: • if vortex lattice is exactly un
Page 39 and 40: • in either scenario, BEC and the
Page 41 and 42: What is physics of this phase trans
Page 43 and 44: References [1] F. Dalfovo, S. Giorg
Page 45: [27] I. Coddington, P. Engels, V. S

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