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5.3.1 Measurement procedure

Before describing the details of the experimental procedure, let us consider the principle

of the stability measurement. We ﬁrst have to ﬁnd an observable that is suited to identify

the critical scattering length. From the discussion of the stability of a single trapped

condensate, we know that above the stability threshold a stable BEC exists, with its radii

determined e.g. by variational calculations. When reaching the critical scattering length,

the condensate will suddenly shrink and collapse [36], following the largest gradient in

the energy landscape presented in Fig. 5.5(d). With the contraction of the condensate

comes a dramatic increase in density, which in turn leads to strongly enhanced losses of

atoms [195]. Hence, the idea of the measurement is the following: we load the BEC into

the lattice in the stable regime and then approach the critical scattering length while

measuring the number of atoms in the BEC. If the ramp in scattering length is suﬃciently

slow, the system remains in the stable state until we reach the critical scattering length

that is identiﬁed by a sudden drop in the BEC atom number [35].

B-field

lattice

forced evaporation

TOF

ODT1

crit

Time

1.3 s

4.5 s

lat

absorption

image

6 ms

2 ms

second

ramp

first

ramp

20 ms10 ms 8 ms

5ms

hold

BEC

(a)

(b)

evap

lattice

ramp

shutter

open

Fig. 5.6, Experimental sequence for stability measurements in the 1D lattice:

(a) Time evolution of the power of the lattice laser beam (orange) and the

horizontal beam of the optical dipole trap (“ODT1”, blue). (b) Evolution of the

magnetic ﬁeld strength (green) deﬁning the scattering length via the Feshbach

resonance. The red dashed line illustrates the stability threshold, given by

crit

= a(B

crit

To perform the stability measurements as described above, we have chosen the exper-

imental sequence shown in Fig. 5.6. We show the time evolution of the most relevant

parameters: the power in the lattice laser beam (deﬁning the lattice depth), the power in

the horizontal beam of the optical dipole trap (“ODT1”, producing a conﬁnement in the

radial direction of the lattice), and the magnetic ﬁeld strength which deﬁnes the scattering

length close to the Feshbach resonance.

Once we have created a thermal cloud of atoms in the crossed ODT, we perform forced

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