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The Area Theorem

Let be the angle which the Bloch vector makes with the -w axis. At resonance, is related to the Rabi frequency by the simple differential equation [8]

It is a simple matter to generalize this equation to a frequency off of resonance by replacing the Rabi frequency by the generalized Rabi frequency

The most general solution to this differential equation would therefore be

where . This equation is often referred to as the area theorem because it relates the area under the generalized Rabi frequency curve to the angle through which the Bloch vector rotates.

Andy Antonelli
Wed May 17 14:34:24 EDT 1995