Rapidly rotating Bose-Einstein condensatesâ Alexander Fetter ...

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Plot ∆E ′ (r 0 , Ω) as function of ζ 0 for various fixed Ω [9], where ζ 0 = r 0 /R 0 is scaled displacement from center 10
curve (a) is ∆E ′ (r 0 , Ω) for Ω = 0 • ∆E ′ (r 0 , 0) decreases monotonically with increasing ζ 0 • curvature is negative at ζ 0 = 0 • for no dissipation, fixed energy means constant ζ 0 • only allowed motion is uniform precession at fixed r 0 • angular velocity is given by variational Lagrangian method [10, 11, 3] ˙φ0 ∝ −∂E(r 0 )/∂r 0 • precession arises from nonuniform trap potential (not image vortex) and nonuniform condensate density • in presence of weak dissipation, vortex moves to lower energy and slowly spirals outward 11
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: Energy of rotating TF condensate wi
Page 13 and 14: 2 Experimental creation/detection o
Page 15 and 16: École Normale Supérieure (ENS) in
Page 17 and 18: • MIT group has prepared consider
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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