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

7.2 Bogoliubov bands and Bogoliubov Bloch amplitudes 91
as s →∞. The normalization (7.8) can then only be ensured if uq and vq grow to infinity in
this limit.
d|bjql| 2 ,d|cjql| 2
6
4
2
0
6
4
2
0
6
4
2
0
j =1, ¯hq =0.1qB
−2 −1 0 1 2
j =1, ¯hq =0.5qB
−2 −1 0 1 2
j =1, ¯hq =0.9qB
−2 −1 0 1 2
6
4
2
0
6
4
2
0
6
4
2
0
j =2, ¯hq =0.1qB
−2 −1 0 1 2
j =2, ¯hq =0.5qB
−2 −1 0 1 2
j =2, ¯hq =0.9qB
−2 −1 0 1 2
l l
Figure 7.5: Square modulus of the Fourier coefficients bjql (white bars) and cjql (black bars)
of ũjq(z) and ˜vjq(z) respectively as defined in (7.17,7.18) for the lowest Bogoliubov band
(j =1, left column) and the first excited Bogoliubov band (j =2, right column) at q =
0.1qB, 0.5qB, 0.9qB as obtained from the numerical solution of Eqs.(7.14,7.15) with gn =
0.5ER and lattice depth s =5.