Bose 2.2 User Manual download pdf (Page 108)

for short holding times

hold

≤

from an exponential ﬁt

to the remnant fraction,

as shown in Fig. 6.5(a). We note that the choice of the exponential ﬁtting function is not

related to any physical model, but describes well the data in the considered time interval

and thus enables to quantify the time scale of the collapse dynamics. The resulting loss

0.0 0.2 0.4 0.6

remnant fraction

0.0

0.2

0.4

U = 0

U = 6.3

U = 8.2

(a) (b)

stability threshold

0 2 4 6 8 10 12 14

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Fig. 6.5, Loss rate in collapse dynamics:

(a) Evolution of the remnant fraction (see

text for deﬁnition) for diﬀerent ﬁnal lattice depths

, from which the loss rate is

extracted by ﬁtting an exponential function (solid lines). (b) Loss rate extracted

from the diﬀerent datasets, versus ﬁnal lattice depth

. The vertical dashed

line marks the stability threshold obtained from numerical calculations.

rate, shown in Fig. 6.5(b), is crucially depending on whether the ﬁnal lattice depth

chosen above or below the stability threshold. For values of

above the stability threshold

(located at around 7

) the loss rate is smaller than 0

−1

. This indicates that there

is basically no in-trap evolution of the system, as expected. When crossing the calculated

stability threshold, the loss rate suddenly increases. If we completely ramp down the

lattice potential, the loss rate increases further to about 2

−1

. The remnant fraction

thus reduces by around 60% when holding the atoms for 0

in the trap. Therefore, in

the case

= 0

, our measurements agree well with the observed atom number decay in

a single dBEC [36] (see section 6.1). Measuring a smaller loss rate at larger lattice depths

(but below the stability threshold), we infer that the presence of a lattice slows down the

collapse dynamics of the system.

While the loss rate measurements provide an estimate for the time scale of the collapse

dynamics, they cannot clearly distinguish whether the atom losses occur in-trap or during

the TOF. In contrast, numerical simulations can reveal the real-time dynamics of the

collapsing system. Therefore, they are a valuable tool to investigate the collapse dynamics

of a dipolar BEC, as we show in the following section 6.2.3.

We ﬁt the measured remnant fraction by a function

(

) =

exp [−Lt]

, with

and the loss rate

being the ﬁtting parameters.

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