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

58 Groundstate of a BEC in an optical lattice
and
N0 = 15 Ntot
, (5.30)
16 lm
with ¯ω =(ωxω2 ⊥ )1/3 , aho = ¯h/m¯ω. The profile (5.24) has the usual parabolic TF-form. The
presence of the lattice is accounted for by the dependence of the effective coupling constant ˜g
on s.
The increase of µ−µgn=0 (see Eq.(5.29)) due to the optical lattice (recall ˜g >g) implies an
increase of the radii Rl (see Eqs.(5.26) and (5.28)) with respect to the absence of the lattice.
It is worth pointing out that the axial size increases in the same manner as the radial size, so
that the aspect ratio R/Z is not affected by the optical lattice: The outermost occupied sites
lm, as given by Eq. (5.27), depend on µ − µgn=0 in the same way as the radius R0 at the
central well (see Eq.(5.28)). The increase in size of the condensate is illustrated in Fig. 5.8
where we plot the radius R0 as a function of s. By tuning the lattice depth to s =20,the
condensate grows by about 20%. Hence, the effect is not dramatic. In chapter 6.2 we will
show that ˜g/g ∼ s1/4 in a deep lattice, implying that R0 and Z increase like ∼ s1/20 .
R0(s)/R0(s=0)
1.25
1.2
1.15
1.1
1.05
1
0 5 10 15 20 25 30
Figure 5.8: The condensate radius R0 (5.28) divided by R0(s =0)as a function of lattice
depth s.
As a consequence of the increasing size of the condensate, the average density at the trap
center drops as a function of lattice depth: To evaluate to what degree this happens, recall
s