Bose 2.2 User Manual download pdf (Page 91)

the images, taken after the expansion from the lattice, we observe the interference pattern

of the condensate and, in addition, a thermal cloud in the background (see Fig. 5.8(a)).

To extract the atom number in the condensate, we ﬁrst integrate the recorded 2D

0 2 4 6 8 10

absorption image integrated along z

optical density

y (in pixels)

(a) (b)

Fig. 5.8, Data acquisition and evaluation:

(a) 2D density distribution of the atomic

cloud after time-of-ﬂight, recorded by absorption imaging (lattice depth

lat

, ﬁnal scattering length

= 20

). The ﬁeld of view is (50

50)

pixels

(307

307)

. Red (blue) colors indicate high (low) density. (b) Density

proﬁle in the

-direction (black crosses) obtained by integrating the 2D density

distribution along

. We extract the BEC atom number from a bi-modal ﬁt

(red line). Before performing the full ﬁt, we ﬁt the thermal cloud (blue line)

to the wings of the density proﬁle, i.e. we disregard the region between the

magenta horizontal bars.

density distribution along the

-direction. Then, we perform a one-dimensional bi-modal

ﬁt, accounting for the presence of the condensate and the thermal cloud as shown in

Fig. 5.8(b). The 1D ﬁtting function for the BEC is obtained by integrating the 3D density

of a single condensate (see Eq. (2.22)) over the x- and y-direction with the result [197]

BEC,1D

(y, t) =

15 N

BEC

16 R

(t)

max

1 −

(t)

, 0

. (5.5)

where

BEC

is the atom number in the condensate and

(

) is the radius of the BEC

after an expansion of time t. The thermal cloud has the following Gaussian shape,

th,1D

(y, t) =

√

2π l

(t, T )

exp

−

(t, T )

, (5.6)

with

the number of thermal atoms and

(

t, T

) the width of the thermal cloud,

determined by the expansion time

and the temperature

of the sample. We brieﬂy

explain the ﬁtting procedure in Fig. 5.8 while more technical details are given in Ref. [122,

Ch. A.2.]. By using the 1D ﬁtting method, we obtain a reliable evaluation of the BEC

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