PHYS598MAP Spring 2005 Blog

1. Earnshaw's and Wing's theorem. The upshot is that we cannot trap charged particles using static electric fields, and we can only trap atoms with negative magnetic moments in magnetic traps. Wing's theorem is also a cool example of what you can do with vector calculus.

2. Quadrupole traps. You can trap atoms using quadrupole traps, but the hole of death will limit the density. The hole of death comes from non-adiabatic Marjorana transitions.

3. The adiabatic theorem. This is deep thing, man. It tells us that any transformation of a Hamiltonian is adiabatic if it is slow enough compared with "internal" timescales. There is also a specific statement of the adiabatic theorem for quantum mechanical systems, which relates the fractional rate of change of the Hamiltonian to the characteristic energy gap in the system.

4. Majorana transitions. These happen for a magnetic dipole in a field which changes direction, and cause trouble near the middle of a quadrupole trap. Near the center of a quadrupole trap, the Larmor frequency is small, and non-adiabatic spin-flip transitions become more likely.

5. TOP traps. This is a quadrupole trap with an additional rotating bias field. The hole death gets moved away from the atoms in this kind of trap.

6. Ioffe-Pritchard traps. These are a complicated mess of coils, which confine atoms using magnetic forces. They use static fields, and nominally have a bias field with a fixed direction.

Whew! See you Thursday!

Brian