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

B.3 Dipole matrix elements for Sodium
The hyperfine dipole matrix elements for the Sodium D1 and D2 line are calculated
using the Wigner-Eckart Theorem, see appendix A.
F’=3
F’=2
F’=1
mF = −2 mF = −1 mF = 0 mF = 1 mF = 2
1
60
1
24
1
40
1
20
1
4
1
80
1
10
1
4
1
240
1
6
1
24
Table B.2: Sodium D2-line hyperfine dipole transition matrix elements for σ + transitions
(F = 2mF → F ′ m ′
F = mF + 1) in multiples of 〈J = 1
2 ||µ2 ||J ′ = 3
2 〉
F’=3 −
F’=2 −
F’=1
mF = −2 mF = −1 mF = 0 mF = 1 mF = 2
1
12
1
12
2
15
1
48
1
80
−
−
−
3
20
0
1
60
2
15
1
48
1
80
−
−
1
2
1
12
1
12
Table B.3: Sodium D2-line hyperfine dipole transition matrix elements for π transitions
(F = 2mF → F ′ m ′
F = mF) in multiples of 〈J = 1
2 ||µ2 ||J ′ = 3
2 〉
F’=3
mF = −2 mF = −1 mF = 0 mF = 1 mF = 2
1
2
F’=2 −
F’=1
1
6
1
24
1
10
− 1
4
1
240
1
20
− 1
4
1
80
1
60
1
24
1
40
Table B.4: Sodium D2-line hyperfine dipole transition matrix elements for σ− transitions
(F = 2mF → F ′ m ′
F = mF − 1) in multiples of 〈J = 1
2 ||µ2 ||J ′ = 3
2 〉
59
−