Experiments to Control Atom Number and Phase-Space Density in ...

The total magnetic moment of an atom is given by the sum of its electronic and
nuclear moments,
µ = µB(gJ J +gI I), (2.13)
where µB is the Bohr magneton, J and I are the electronic angular momentum and
nuclear spin, and gJ and gI are the electronic and nuclear magnetic g-factors. The
Hamiltonian describing the interaction between the atomic magnetic moment µ and the
external magnetic field B is given by [22, 23, 25]
H = −µ· B. (2.14)
This Hamiltonian can be diagonalized in the hyperfine basis |F,mF〉. Each of the hyper-
fine levels F consists of 2F +1 magnetic sublevels (mF), corresponding to the different
projections of the total atomic angular momentum along the quantization axis given by
the direction of the magnetic field. The associated energy shift of the state |F,mF〉 is
given by
where
F(F +1)−I(I +1)+J(J +1)
gF = gJ
+gI
2F(F +1)
∆E = µBgFmF|B|, (2.15)
F(F +1)+I(I +1)−J(J +1)
. (2.16)
2F(F +1)
Table 2.3 summarizes the values of gI and gJ for the transitions important to this
dissertation for both rubidium and lithium.
Rubidium
gI -0.0009951414(10)
gJ(5 2 S1/2) 2.00233113(20)
gJ(5 2 P1/2) 2/3
gJ(5 2 P3/2) 1.3362(13)
Table 2.3: g-factors for rubidium and lithium
Lithium
gI -0.0004476540
gJ(22S1/2) 2.00233113(20)
gJ(22P1/2) 0.6668
gJ(22P3/2) 1.335
Figure 2.8 shows the anomalous Zeeman splitting of the ground state of 87 Rb. The
magnetic field strengths used during the course of the rubidium single-photon cooling
experiment remain in the anomalous Zeeman regime. This figure shows that it is possible
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