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

8.1 Dynamic structure factor 105
The excitation strength to the lowest Bogoliubov band - Numerical results
The study of the excitation strength to the lowest Bogoliubov band Z1(p) requires the evaluation
of (8.8) with the solutions u1q(z), v1q(z) and ϕ(z) for a given lattice depth s and
interaction parameter gn/ER. Numeric results are depicted in Figs.8.3 and 8.4 for s =5, 10
and gn =0ER, 0.02ER and gn =0.5ER.
In general, we find the following characteristics:
• Z1(p) features an overall decay for increasing |p|. This is due to the fact that the
momentum components of the created excitations are smaller at large momenta.
• Provided that gn/ER = 0, Z1(p) exhibits characteristic oscillations: Z1(p) is suppressed
in the vicinities of p = l2π/d where the excitations contributing to the strength have
phonon character and is exactly zero at p = l2π/d (l integer) where the energy of the
contributing excitation vanishes.
• Increasing gn/ER at fixed s or increasing s at fixed gn/ER = 0leads to an overall
decrease of Z1(p).
Z1(p)/Ntot
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
−6 −4 −2 0 2 4 6
p/qB
Figure 8.3: Excitation strength to the lowest Bogoliubov band Z1(p) (8.8) at lattice depth
s =5for gn =0.5ER (solid line), gn =0.02ER (dashed line) and gn =0(dash-dotted line).