Copyright by Kirsten Viering 2006 - Raizen Lab - The University of ...

In the absence of a magnetic field, all sublevels are equally populated. In a
magnetic trap only the atoms with F=1 M=-1 will be trapped. In this case eq. 6.7
reduces to
P f (r, θ, δ, τ) = sin 2 √
3
(
4 τ β00 sin θ) · sinc 2 ( (δ + 3/2 µB dB/dr · r/) τ
)
2
+sin 2 √
3
(
4 τ β00 cos θ) · sinc 2 ( (δ + µB dB/dr · r/) τ
)
2
+sin 2 ( 1
√ τ β00 sin θ) · sinc
2 4 2 ( (δ + 1/2 µB dB/dr · r/) τ
). (6.9)
2
A plot of the final state probability as a function of the positionr is shown in fig. 6.5. The
optimal pulse duration changes to 345.0µs and the population transfer reaches 100%,
since the resonance frequency of the transition from the M=-1 level is dependant on the
magnetic field. Therefore only atoms in the resonant Raman region can be transferred.
Figure 6.5: Dependance of the final state probability of the position. O belongs to the
point of 0 magnetic field. The Raman detuning δ equals 0, the magnetic field gradient
is 150G/cm. The angle θ equals 0, i.e. the magnetic field points along the z-axis (atom
and lab frame coincide). All atoms start in the F=1 M=-1 state.
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