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

m f inal = −2 m f inal = −1 m f inal = 0 m f inal = 1 m f inal = 2
m initial = −1 -3/2 -1 -1/2 0 1/2
minitial = 0 -1 -1/2 0 1/2 1
minitial = 1 -1/2 0 1/2 1 3/2
Table 6.1: Calculation of γm f ,mi in Sodium for the |F = 1〉 → |F′ = 2〉-Raman transition
section 2.4 we already used the relation between the transition dipole matrix element
and the lifetime of the respective transition. Knowing the lifetime of the 3 2 P3/2 and the
3 2 P1/2 excited state we can calculate the dipole matrix elements using [10]
|〈J ′ ||er||J〉| =
1
τJ ′ J
3πɛ0λ 3
(2π) 3
The dipole matrix elements for the D2- and D1-line are
and
respectively.
(2J ′ + 1). (6.1)
|〈J = 1/2||µ||J = 3/2〉| = 4.22 · 10 −29 Cm (6.2)
|〈J = 1/2||µ||J = 1/2〉| = 2.11 · 10 −29 Cm (6.3)
6.3 Effective Raman-Rabi frequencies and final state probabil-
ity
In a multi-level atom the effective Raman-Rabi frequency is given by
β f i = −
I
〈 f |µE2|I〉〈I|µE1|i〉
, (6.4)
2 2 ∆I
where we have to sum over all possible paths for a transition, see section 5.4.1.
In this section we will assume without loss of generality that the two electric
fields are { ˆy, ˆz} linearly polarized or E1 = E1 ˆy, E2 = E2 ˆz. The magnetic field is taken to
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