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

interaction. The shift in the energy states is then well approximated by
∆E ≈ µBgJmJB (2.17)
The energy level structure of lithium in the Zeeman regime is shown in figure
2.10. Even though the highest three magnetic states (labeled |4〉, |5〉 and |6〉 in figure
2.10) are low-field seeking states, it is unfortunately not possible to evaporatively cool
6 Li atoms confined in a magnetic trap. Scattering events during evaporation causes
spin-flips to anti-trapped states leading trap loss [28].
Energy Shift/ MHz
300
200
100
-100
-200
-300
50 100 150
| F , m F ; m S ,m I ,m L >
|6>: |3/2, 3/2; 1/2, 1, 0>
|5>: |3/2, 1/2; 1/2, 1, 0>
|4>: |3/2, -1/2; 1/2,-1, 0>
B/ Gauss
|3>: |3/2,-3/2;-1/2,-1, 0>
|2>: |1/2,-1/2;-1/2, 0, 0>
|1>: |1/2, 1/2;-1/2, 1, 0>
Figure 2.10: Energy shift of the 6 Li ground state in an external magnetic field. For small
magnetic field strengths the energy level splitting follows the anomalous Zeeman-effect.
Above about 30 Gauss angular momenta decouple and the energy splitting is described
by the normal Zeeman effect.
2.5.2 Magnetic Feshbach Resonance
A Feshbach resonance is a quantum mechanical scattering resonance, which was
first encountered in the context of nuclear physics [29]. In general, a Feshbach resonance
can be induced optically as well as magnetically, however, this discussion is limited to
the magnetic case. A simple model is used to describe the general phenomenon.
Consider two potential curves Vbg and VC, and two atoms colliding with the
small energy E as shown in figure 2.11 [30]. For large atomic separations R the potential
Vbg asymptotically connects to two free atoms. For small energies E the potential Vbg
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