Experiments with Supersonic Beams as a Source of Cold Atoms

3 P2
E
Figure 4.2: This graph gives an example of the Zeeman shift of the mJ sub-levels of
a 3 P2 state. Since J = 2 there are 5 sublevels (mJ = −2, −1, 0, 1, 2). The g-factor for
this state is gJ = 3
2 which means that the negative mJ levels lose energy in the field
and are high field seekers, while the positive mJ levels gain energy and are low field
seekers.
Using the g-factors gL =1andgS ≈ 2, and the relationship J · B = BJz allows
the Hamiltonian to be simplified to
HB = μBB
1+
m J =2
m J =1
m J =0
m J =-1
m J =-2
J(J +1)−L(L +1)+S(S +1)
Jz = μBgJBJz, (4.11)
2J(J +1)
where gJ is the Landé g-factor. This Hamiltonian shifts the energy of the mJ sub-
levels by
B
ΔE = μBmJgJB. (4.12)
This shift is illustrated in figure 4.2. Particles which gain potential energy in the
magnetic field are called low-field-seeking, since magnetic field gradients will exert
a force pushing them away from regions of high field. Particles that lose potential
energy in the field will feel the opposite force and are referred to as high-field-seeking.
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