PHYS598MAP Spring 2005 Blog

1. Visual simulations of the Bloch vector and Rabi oscillations. Play with them - you might learn something!

2. If you look at Rabi oscillations over an ensemble that has atoms with different Larmor frequencies or pulse areas, then you need to average what you see over that ensemble. Examples are finite transit times in a beam experiment, or the effects of an inhomogeneous field.

3. Ramsey experiments, which are confusing to just about everyone. You can play with the VPython files to get a feeling for how the lineshape comes about. You should be able to understand the lineshape for small detunings when the free precession time is long by using the Bloch vector picture. The key ideas:

   • Use a single rotating frame, at the drive frequency.

   • The first pi/2 pulse rotates the Bloch vector almost into the x-y plane.

   • During the free precession time, the Bloch vector precesses with an angular frequency equal to the detuning.

   • The second pi/2 pulse rotates the Bloch vector somewhere, with a projection onto the z-axis not equal to 1. One fact: the azimuthal angle in the plane before the second pulse is roughly equal to delta*t. Second fact: that angle is fixed with respect to the effective torque vector. If the effective torque vector is almost in the x-y plane, then the angle between the plane and the Bloch vector after the second pi/2 pulse is just delta*t. Then do some geometry!

Cheers,

Brian