PHYS598MAP Spring 2005 Blog

Today we learned all about the fun Zeeman effect, which is just how anything with a magnetic moment interacts with a static magnetic field.

The real story that we care about is for alkali atoms in magnetic fields. Some good things to keep in mind:

1. In the low field limit, the Zeeman effect is treated as a pertubation to the hyperfine Hamiltonian. The energy shift is m₀g_Fm_FB. Note that g_F has a different sign for states with different F! That means that sometimes the m>0 states increase in energy with increasing magnetic fields, and sometimes the m<0 states increase in energy with increasing magnetic fields. This happens because the hyperfine interaction mixes together states with different magnetic moments (which is always dominated by the electron magnetic moment).

2. Always remember how the stretched states shift with field. These states have a fixed magnetic moment, which is, to a good approximation, the electron magnetic moment.

3. At high fields, the states group by their m_J quantum numbers. In this limit, the hyperfine interaction is treated as a pertubation to the Zeeman Hamiltonian. The hyperfine interaction breaks the degeneracy between states with the same m_J.

4. At intermediate fields, we have to solve the problem exactly. For the ground state this is not too hard — see the homework! The magnetic moment of the hyperfine states depends on field, which is because the makeup of the states in the |m_I,m_S> basis is changing!

   
   

We also started talking about traps today. We learned that nature foils our ability to trap both neutral and charged atoms. But, experimentalists are clever, and we trap all kinds of atoms anyway! We'll learn more next class.

Cheers,

Brian