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

β0−1 = −
I
= − 1 √ 2
= − 1 √ 2
〈F = 2, m = 0|µE2|I〉〈I|µE1|F = 1, m = −1〉
E1E2
2 2
2 2 ∆I
〈F = 2, m = 0|µ2|I〉〈I|µ1|F = 1, m = −1〉
I
2 2 ∆I
E1E2 1
( 〈F = 2, m = 0|µ2|F = 1, m = 0〉〈F = 1, m = 0|µ1|F = 1, m = −1〉
22 ∆3/2
+ 1
〈F = 2, m = 0|µ2|F = 2, m = 0〉〈F = 2, m = 0|µ1|F = 1, m = −1〉
∆3/2
+ 1
〈F = 2, m = 0|µ2|F = 1, m = 0〉〈F = 1, m = 0|µ1|F = 1, m = −1〉
∆1/2
+ 1
∆1/2
〈F = 2, m = 0|µ2|F = 2, m = 0〉〈F = 2, m = 0|µ1|F = 1, m = −1〉)
1
60
5
48 · (4.22 · 10−29 Cm) 2 + 1
1
48 · (4.22 · 10−29 Cm) 2
= − 1 E1E2 1
√ ( 0
2 22 ∆3/2
∆3/2
+ 1
1
−
∆1/2 6
1
24 · (2.11 · 10−29Cm) 2 + 1
0 −
∆1/2
1
24 · (2.11 · 10−29Cm) 2 )
= − 1 E1E2
√
2 22 · 1.09 · 10−73C 2 m 2 . (6.5)
The detunings ∆1/2 and ∆3/2 are the detunings of a Verdi laser beam (532nm) from
the D1- and D2-line respectively. The detunings due to the hyperfine splitting of the
excited states are negligible. We should keep in mind that E1 and E2 cannot be chosen
independantly. The theoretical description for the final state probability is only valid
if the relative light shifts between the two ground states vanishes. In Sodium we will
introduce an undesired AC-Stark shift if E1 E2.
It is sufficient to calculate one Raman-Rabi frequency explicitly, the others can
be calculated using the Wigner-Eckart Theorem, e.g.
β00 = 〈F = 2, m = 0|µ|F = 1, m = 0〉 = (−1) 2
=
2 √
30 β0−1 = 2 β0−1
15
2 1 1
〈F = 2||µ||F = 1〉
0 0 0
(6.6)
The values for the effective Raman-Rabi frequencies are listed in tab. 6.2 as multiples
of β00.
43