Bose-Einstein Condensates in Rotating Traps and Optical ... - BEC

12 Vortex nucleation
Here, we have used expression (2.6) with ε =0for the energy in the laboratory frame and
(2.8) for the angular momentum in an axi-symmetric trap.
Some interesting features emerge from Eq. (2.10). First we observe that the occurrence of
a vortex at d =0is energetically favorable for angular velocities satisfying the condition
Ω ≥ Ωv(µ) = Ev(d =0,ε=0,µ)
. (2.11)
N¯h
This is the well known criterion for the so called thermodynamic stability of the vortex. If
it is satisfied the energy Ev(d/R⊥, Ω,µ) exhibits a global minimum at d = 0 where the
vortex states carries angular momentum ¯h per particle. In contrast the vortex solution at
d =0is energetically unstable if Ω ≤ 3Ωv(µ)/5, while it is metastable (local minimum) if
3Ωv(µ)/5 ≤ Ω ≤ Ωv(µ) [49, 27].
It is worth noticing that in the TF-limit one should have Ωv(µ)/ω⊥