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Measurements

The geometry dependent stability of a single trapped dipolar BEC has been experimen-

tally investigated in our group [35]. In the experiment, a cylindrically symmetric trap is

used, with the symmetry axis oriented along the polarization direction

of the dipoles.

The trap geometry is then conveniently described by the trap ratio

/ω

, with

and

the trap frequency in the

-direction and in the radial directions, respectively.

Figure 5.5(a) shows the measured stability diagram: the stable and the unstable regions

for the dBEC are separated by the critical scattering length

crit

, measured as a function

of the trap ratio

. We see that the stability of the dipolar BEC crucially depends on

the trap ratio, since the external trapping potential mainly deﬁnes the shape of the

condensate. Using a prolate trap (

λ <

1), the condensate is experimentally found to

be unstable at a positive critical scattering length

crit

= (15

' a

. Then, for

increasing trap ratios, the critical scattering length decreases. For the most oblate trap

geometry in the experiment, with

= 10, a purely dipolar BEC with

crit

0 is obtained.

The measurements basically reproduce the expected results from our simple geometri-

cal picture. However, the expected regime of the dipolar stabilization has not been reached.

bi-concave

density

(a)

-10

-20

-30

-2a

(b)

(d)

(c)

(e)

0.1

10 10

-2

-1

0.1 1 10 10

Fig. 5.5, Stability diagram of a single trapped dipolar BEC:

(a) Experimental

values (green dots) for the critical scattering length

crit

as a function of the trap

ratio

. The blue line shows the results for

crit

(

) obtained from variational

calculations for a mean trap frequency

¯ω

= 2

π ·

700

and

= 20

000

atoms. The grey line is obtained in the limit

N → ∞

and the red line marks

the stability threshold for a purely contact interacting BEC using the same

parameters. Full numerical simulations of the GPE [37] (green line) reveal a

bi-concave BEC-density close to

crit

for oblate traps. (b)-(e) Energy landscape

(

, l

) in the variational calculations. Lines of equal energy are plotted for

= 10 and

= (18

, −

32)

as indicated by the black dots in (a).

The widths (

, l

) are given in units of the mean harmonic oscillator length

¯a

~/(m¯ω). Figure taken from [113].

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