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

(a)
(b)
scattering length a
0
Energy E
0
bound state
B 0
continuum
magnetic eld B
magnetic eld B
Figure 2.12: Scattering length and molecular state energy near a magnetic Feshbach
resonance. (a) The scattering length varies with the magnetic field strength, if the
magnetic moments of the entrance and closed channels differ. (b) The hyperfine coupling
between the entrance and closed channel leads to an avoided crossing between the free
atomic state and the bound molecular state.
Because Feshbach resonances allow tuning of the s-wave scattering length, they
are a very useful tool during evaporative cooling of cold atomic clouds, see chapter
2.10. Evaporative cooling using two different spin states in 6 Li is typically done using
states |1〉 and |2〉, see figure 2.10. For these states a Feshbach resonance with a width
of ∆ ≈ −300 G is located at 834 G [30]. The broad width of this resonance makes
it particularly useful [32]. The scattering length of these states as a function of the
magnetic field B can be found in [32–34].
2.6 Interaction of Atoms with Light
One of the most powerful methods to trap, cool, and manipulate the internal
quantum states of atoms is through interaction with light. One can roughly distinguish
between two regimes that will be treated separately in this discussion: the interaction
with near-resonant light, which leads to a strong scattering force, and the far-detuned
regime, which leads to an AC Stark shift or an optical dipole force. Both regimes are
16