Bose 2.2 User Manual download pdf (Page 89)

evaporation by continuously lowering the power of the ODT laser beams

. Before reaching

degeneracy, we switch on the strong magnetic ﬁeld to a strength

evap

= 602

, well

above the Feshbach resonance (FR) located at

= 589

. At the scattering length

(

evap

) = 90

, we ﬁnish the evaporation and create the BEC in a trap with frequencies

x,y,z

= 2π · (440 ± 14, 330 ± 10, 290 ± 10) Hz.

We then linearly decrease the magnetic ﬁeld to

lat

, to approach the FR with

(

lat

) = 60

. As a next step, we load the BEC into the lattice by increasing the power

of the lattice laser

in an s-shaped ramp to a variable value which deﬁnes the lattice depth

lat

. While doing so, the lattice introduces an additional transverse (radial) conﬁnement.

In order to keep the radial (

x, y

) trap frequencies constant during the ramp (and to avoid

excitations in the BEC), we decrease the power in the ODT1 laser beam in an inverted

s-shaped ramp

In a second linear ramp of the magnetic ﬁeld strength to the ﬁnal value

, we then

bring the system close to the stability threshold, deﬁned by the critical scattering length

crit

(

crit

). We hold the condensate in this conﬁguration for

hold

= 2

, such that

the system can equilibrate. After this holding time, we switch oﬀ all trapping potentials

to perform a 6

time-of-ﬂight and ﬁnally take an absorption image of the expanded cloud.

Loading of the BEC into the lattice

To probe the stability of the condensate in the lattice, we have to prepare the system in its

ground-state, i.e. in the lowest energy band of the lattice. This implies that any excitation

to higher bands has to be avoided during the loading of the lattice potential. We thus

obtain a criterion for the speed of the lattice ramp [170]. In general, the adiabaticity

criterion is given by [196]

dU/dt 

(∆

)

with ∆

the spacing between the ﬁrst

and the second excited band and with

(

) the time-dependent lattice depth during the

ramp. At the center of the Brillouin zone, i.e. at quasi-momentum

= 0, the energy gap

∆

= 4

is independent of the lattice depth, such that the adiabaticity criterion for

the lattice ramp in our experimental sequence is given by



16 E

. (5.3)

For our parameters (, the lattice must be ramped up much slower than 0

/ s

to fulﬁll

the criterion given by Eq.

(5.3)

. Experimentally, we ramp up the lattice using an s-shaped

During the sequence, we not only lower the power of the horizontal ODT beam, but we also decrease

the light level of the vertical beam (“ODT2”). After reaching the BEC, the power in ODT2 is not

changed anymore until it is switched oﬀ to perform the time-of-ﬂight.

The lattice laser beam is switched on during the production process of the BEC to heat the optical

components in the beam path. During this time the beam is blocked by a shutter in front of the vacuum

chamber. With this technique, we minimize the movement of the focus of the laser beam during the

lattice ramp that is induced by thermal eﬀects in the lenses.

For our trap frequencies, and for the given parameters of the lattice laser beams (waists

lat,1

lat,2

), we can provide constant radial trap frequencies up to a lattice depth of around 200

. This is

suﬃcient for all our experiments.

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Bose 2.2 User Manual Page 89

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