Chemistry Reference
In-Depth Information
an insulating domain appears at the center of the trap (if the density there is
close to commensurate). Increasing
U
further reduces the correlation length
[system (c)] because the system moves away from the transition. Systems
(d)-(f) show how the second shell forms when the density is increased.
The corresponding momentum distributions are shown in Figure 15. The
superfluid sample (a) shows a single narrow peak at zero momentum.
(The broadening of the
-function contribution of the condensate expected
in a superfluid arises from the harmonic confining potential.) When a domain
of the insulating phase appears, the momentum distribution develops a
pronounced fine structure [clearly visible in systems (b) and (c)]. System (e)
is similar to (a) except for the large momentum tail due to the insulating shell.
d
n
n
k
φ
k
k
φ
k
(a)
(b)
2
2
0
0
ka
ka
1
2
3
1
2
3
n
n
k
φ
k
k
φ
k
(c)
(d)
2
2
0
0
ka
ka
1
2
3
1
2
3
n
n
k
φ
k
k
φ
k
(e)
(f)
2
2
0
0
ka
ka
1
2
3
1
2
3
Figure 15
Superfluid-insulator transition in an optical lattice: Single-particle momen-
tum distribution. Panels (a)-(f) correspond to the systems shown in Figure 14. (Taken
with permission from Ref. 111.)
