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February 10, 2005

Class review — 2/10

Hey Class,

Remember to check the blog for comments on the homework.

Pre-flights for Tuesday and the lecture notes from today will be ready by tomorrow (Friday) night.

Here's what we talked about today:

  1. RF Paul traps. Classical motion of ions in a Paul trap is described by the Matheiu equations, which have exact solutions. An approximate solution can be put together using the "pseudopotential" approximation, where the slow, secular motion is separated from the fast micromotion at the RF frequency. Paul traps have regions of stable motion determined by the charge-to-mass ratio and the DC and RF voltages.

  2. We started on 2-state systems! We'll use spin-1/2 language, where we always imagine a static magnetic field present along the z-direction.

  3. Larmor precession. If a spin-1/2 particle is not prepared in an eigenstate, then the spin precesses around the magnetic field. Spin precession just means that áSxñ and áSyñ oscillate out of phase.

  4. Mixing of states when we apply a static, transverse field. The new eigenstates rotate as the ratio of the transverse (B^) to z-field (B0) is varied. The energy of the two states also varies in a hyperbolic fashion as the ratio B^/B0changes.

  5. Landau-Zener transitions. Note that the formula I showed today is only valid when B0 is changed with B^ fixed (that's the case that Zener considers in his paper). The beautiful two-state picture (with a transverse field) contains all of the Landau-Zener transition and Majorana physics in it.

See you next week!

Brian

Posted by Brian at February 10, 2005 08:06 PM

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