Bose 2.2 User Manual download pdf (Page 60)

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Fig. 4.1, Interference of two coherent laser beams:

Two crossing laser beams

(propagation direction given by the arrows) produce a regular 1D array of

intensity maxima (darker shading means higher intensity). The spacing

lat

between the intensity maxima is deﬁned by the wavelength of the laser and the

inclusion angle θ between the laser beams (see text).

intensity proﬁle

. Using a focussed laser beam or two incoherent laser beams in a crossed

conﬁguration, we can form a single container for an atomic cloud. In contrast, when

overlapping two coherent laser beams, we observe a periodic array of intensity maxima, as

shown in Fig. 4.1. Close to the crossing point of the two lasers, we obtain a 1D optical

lattice potential V

lat

(z) of the form

lat

(z) = U

lat

· sin



πz

lat



, (4.2)

with

lat

the lattice depth and

lat

the lattice spacing which speciﬁes the distance between

the intensity maxima. For the moment, we neglect any trapping perpendicular to the

lattice direction

, which will be included in section 4.3. The lattice spacing is directly

given by

lat

λ/

cos [θ/2]

), where

is the wavelength of the laser and

is the angle

between the laser beams (see Fig. 4.1). From the lattice depth and the spacing

lat

, we

derive the characteristic lattice parameters which are commonly used for the description

The intensity proﬁle of a Gaussian laser beam that propagates along

is given by

(

) =

(

))

exp



−2ρ

/(w(z))



, with

the intensity at the position (

= 0

, z

= 0 ); the beam

radius

(

) is given by

(

) =

1 + (z/z

)

, with

the waist of the laser beam and

the

Rayleigh length.

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Bose 2.2 User Manual Page 60

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