Bose 2.2 User Manual download pdf (Page 56)

0 20

60 80 100

(a) (b)

dipolar expansion (TF) TF vs. simulations

simulations

0 20 40 60 80 100

Fig. 3.4, Dipolar expansion:

(a) Ratios

(red dots) and

(blue dots), calcu-

lated for diﬀerent scattering lengths using the TF approximation (parameters:

x,y,z

= 2

π ·

(680

624

270)

tof

= 7

= 20

000). (b) Results of the

calculations for

in the TF approximation (red dots) and using full numer-

ical simulations (green dots). The lines are linear ﬁts to the data from which

we extract the value

oﬀset

(see text). The experimental datapoint (black dot)

is taken at

/jointfilesconvert/317304/bg

in low magnetic ﬁeld, where we obtain smaller uncertainties

on R

/N than in the measurements close to the FR.

simulations are expected to recover more closely the dynamics of the real dipolar BEC

than the calculations within the TF approximation.

Measurements

In a typical calibration measurement, we create a BEC at

B ≈

626

(

B ≈

578

) when

measuring above (below) the FR. Then, we ramp the magnetic ﬁeld to a value closer to

the FR and hold the system for 4

at this value, for it to equilibrate. We then switch

oﬀ the optical dipole trap and perform a 7

TOF before we take an absorption image of

the cloud. Using a bimodal ﬁt (accounting for the BEC and for the remaining thermal

atoms), we extract the condensate radius

and the BEC atom number

. In this way,

we take at least four datapoints for each programmed current

in the Feshbach coils to

reduce the uncertainties on the values R

/N(I

Fitting procedure

The ﬁtting of the data is performed in a two-step process (see appendix A.7 for details):

We ﬁrst ﬁt the scaling parameter

eﬀ

and calculate the scattering length values

exp

(

)

via Eq.

(3.2b)

from the measured values

(

). In a second ﬁtting procedure, the

With the strong Feshbach ﬁeld oriented along

, we cannot provide the maximum absorption cross

section for the imaging light (propagating along

) [36]. We thus record a lower atom number in the

absorption images than actually contained in the BEC. However, this eﬀect is fully accounted for in our

evaluation procedure, by introducing the eﬀective scaling parameter σ

eﬀ

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