Bose 2.2 User Manual download pdf (Page 110)

0.45 ms

0.85 ms 1.25 ms

1.45 ms

1.85 ms

t = 0

0.15 ms

0.40 ms 0.60 ms

1.25 ms

1.45 ms

t = 0

time t (ms)

0.0 0.5

1.0 1.5

in-trap

TOF

U = 12.6

U = 0

U = 3.2

U = 6.3

U = 8.2

(a)

(b) (c)

Fig. 6.6, Real-time simulations of the collapsing dBEC:

(a) Time evolution of the

system for a ﬁnal lattice depth

= 12

(ﬁrst row) and

= 0

(second

row). Note that the snapshots in the two sequences are taken at diﬀerent times

, with the time origin set at the end of the lattice ramp. At the time

= 0

the TOF is started, i.e. the trapping potentials are suddenly switched oﬀ. (b)

Momentum distribution of the system in the ballistic regime, corresponding to

the spatial density distribution in the far ﬁeld of the TOF (for

= 12

only the zero-momentum component is shown). (c) Evolution of the atom

numbers N for diﬀerent ﬁnal lattice depths U (speciﬁed in the ﬁgure).

modulation vanishes due to the absence of the lattice potential, as shown in the

second row of the images in Fig. 6.6(a). The condensate then shrinks and shows

strong atom losses while it is still trapped in the harmonic potential. The decay of

the BEC atom number slows down at around

= 0

and after the release from

the trap (at

= 0

) we do not observe any atom losses anymore. The simulations

therefore conﬁrm our hypothesis that, for

= 0

, the collapse is initiated in the

trap. In addition, the simulations show a loss of about 60% of the atoms within the

ﬁrst 0

of the in-trap holding time, which is close to our experimental results.

During the TOF, the cloud explodes mainly radially. Its shape in the far ﬁeld of

the TOF (see Fig. 6.6(b)) is similar to the one observed in the experiment for the

longest applied holding time.

(ii)

Considering the stable in-trap conﬁgurations

= 12

and

= 8

, the

evolution of the atom number, shown in Fig. 6.6(c), clearly supports the hypothesis

of the TOF-triggered collapse: while there are almost no in-trap atom losses, we

observe a sudden drop in the atom number only some time after switching oﬀ the

trapping potentials. For

= 12

the drop occurs at

t '

, where we also

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