Experiments to Control Atom Number and Phase-Space Density in ...

= E0
1 −n2 √2 exp
σ0
± iE0
√2 exp
2(1+δ 2 )
ik
2f (x′2 +y ′2 )
(1+iδ)
ˆy ′
ik
exp
2f (x′2 +y ′2
) ˆx ′
Defining I = k|Etot| 2 and I0 = k|Einc| 2 leads to
|E0|
I0 = k
2 2 |E0|
+ = k|E0|
2 2
2
|E0|
I = k
2
2 exp
1 −n 2σ0 1+δ 2
+ |E0| 2
2
and thus
I
I0
= 1
2 exp
1 −n 2σ0 1+δ 2
+ 1
2
1
=
2 exp
∗ −nσ
1+δ 2
(7.26)
(7.27)
(7.28)
+ 1
. (7.29)
2
The effective scattering cross section σ ∗ is only half of σ0. In addition, only half
the light interacts with the atoms. The temperature of the MOT and the compressed
MOT is measured using the setup shown in 7.38, where this calculation applies.
For imaging atoms trapped in the CO2 laser a few changes to the optical setup
shown in figure 7.38 are necessary. First, the f = 50 mm lens is removed, changing the
magnification to be roughly 1:4. Because of the lower atom number and the increased
magnification the signal-to-noise ratio is reduced as compared to imaging of the MOT.
Instead of using a polarizing beam splitter cube to combine the MOT and the imaging
beam, a mirror mounted on a motorized flipper is added to the setup. It is then possible
to use linearly polarized light for imaging the atoms. The intensity in the image plane
is then given by [109]
I
I0
1 −n 2 = exp
σ0
1+δ 2
. (7.30)
The disadvantage of this setup is that atoms cannot be imaged in the MOT, because
the time the flipper requires exceeds the storage time of the atoms.
Lithium atoms expand faster than other alkali atoms. This means that especially
at MOT temperatures the atoms can move a significant distance even during the imaging
exposure time. The imaging pulse duration is therefore restricted to between 10 µs and
20 µs to minimize this effect.
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