Bose 2.2 User Manual download pdf (Page 61)

of ultra-cold gases in optical lattices:

lat

the lattice wave number, (4.3a)

lat

2md

lat

the recoil energy, and (4.3b)

s =

lat

the dimensionless lattice depth. (4.3c)

4.1.2 Experimental Realization of the 1D Lattice

The optical lattice along the

-direction is produced by an ytterbium ﬁber laser

with a

maximum output power

= 20

, operating at a wavelength

= 1064

. In contrast

to the ODT laser, the lattice laser has a single output frequency at a narrow linewidth

∆

ν '

kHz

. The long coherence length

∆

ν ∼

allows for the creation

of a standing-wave intensity pattern by interfering a single laser beam with itself in

an “almost back-reﬂected” geometry, as illustrated in Fig. 4.2. The angle

between

the ﬁrst and the back-reﬂected beam in our setup

= 9

◦

, resulting in a

lattice spacing

lat

= (533

. We have chosen the waists of the two lattice

laser beams

lat,1

lat,2

to be larger than the waist of the ODT1 laser beam

(

ODT1

= 30

). Therefore, the radial conﬁnement of the lattice is typically much smaller

than the conﬁnement by the underlying ODT. This conﬁnement has to be taken into

account, however, when applying deep lattice potentials as we show in section 5.3.1.

We tune the power of the lattice laser beam via an AOM

that uses a sheer-mode

acoustic wave. Such device shows a reduced beam movement during intensity ramps when

compared to standard AOMs, and thus ensures a stable operation of the lattice potential

in the experiment.

4.2 The Non-Interacting BEC in a 1D Lattice

In this part of the chapter, we neglect all inter-atomic interactions to derive some basic

properties of a BEC in a 1D lattice. The resulting formalism is closely related to the

description of the quasi-free electron gas inside a crystal, found in many solid state physics

textbooks [171–173]. We furthermore ﬁnd an analogy to light diﬀraction from a phase

grating when discussing the diﬀraction of a BEC from the optical lattice, a technique that

we use to calibrate the depth of the optical lattice potential.

IPG: ‘YLR-20-1064-LP-SF´.

Measuring the angle between the symmetry axis of the lattice and the

-axis of the vacuum chamber,

we found only a small tilt of 1

◦

[122, Ch.4.3]. This tilt is not expected to have any signiﬁcant

impact on our experiments.

AA Opto-Electronic:MTS80, rise-time: T = 1 s for our beam diameter d = 1 mm

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