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

as the final state probability.
5.4 Raman transition in a multi-level atom
In general the selection rule ∆mF = 0, ±1, ±2 applies for a Raman transition. Never-
theless in alkali-atoms transitions from one hyperfine ground state into the other with
∆m = ±2 are forbidden. This is easily understood by looking at the two-photon process
in tensor notation and recalling that all alkali-atoms occupy a ground state with J = 1/2.
By combining two one-photon processes we can generally create three different
tensor operators. The scalar operator E1E∗ vanishes for perpendicular polarized light
2
beams. The vector operator E1 × E∗ causes Raman transitions with ∆m = 0, ±1, see
2
fig. 5.5. An outer product operator E1 ⊗ E∗ of rank 2 cannot be formed for atoms in
2
a J = 1/2 ground state [30]. Therefore transitions with ∆m = ±2 do not occur. By
explicitly calculating the multiple paths between the initial and the final state the same
result arises due to destructive interference.
Figure 5.5: Possible Raman transitions between two hyperfine states with J = 1/2.
For simplicity we assume all atoms to start in the |F = 1, m = 0〉 state. The detuning
of 1.772GHz belongs to the Sodium ground state 2 S1/2. The splitting of the magnetic
sublevels is according to the anomalous Zeeman-effect.
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