Single-Photon Atomic Cooling - Raizen Lab - The University of ...

gF = −1/2 using the approximate expressions for this value and for gJ derived
above. In the low field limit, the magnetic sublevels will shift in energy in
response to an external magnetic field according to
∆EZE = µBgFmFB. (2.33)
Recall that because F = 1, mF can take on the values of −1, 0, and 1.
This splitting is shown in Fig. 2.3 and is the basis for magnetically trapping
neutral atoms, the topic of the next section. Note that because the value of gF
in negative in this state, the sublevel with mF = −1 increases in energy with
increasing magnetic field while the sublevel with mF = 1 decreases in energy.
The sublevel with mF = 0 is unaffected to first order by the presence of the
external magnetic field.
5 2 S 1/2 (F=1)
E
Figure 2.3: Zeeman spitting of the F = 1 hyperfine manifold. Because F = 1,
mF can take on the values −1, 0, and 1. The value of gF in this state is −1/2
so the magnetic sublevel with mF = −1 increases in energy with increasing
magnetic field while the sublevel with mF = 1 decreases in energy. The energy
of the mF = 0 sublevel is unaffected to first order.
39
m F =-1
m F =0
m F =1
B