When detuning doesn't equal 0, meaning frequency of light doesn't equal the frequency of the atom oscillating (when dealing with 2 level systems), we see there are light shifts as a result. In the large detuning limit, we can split this into two cases; delta>0 (blue detuning) and delta<0 (red detuning). When this happens, the rotation axis is no longer simply |X> but has a |Z> component. I am trying to figure out how to visualize this on the Bloch Sphere, as in, whether blue detuning will cause the rotation axis to shift towards |+Z> (the excited state) or |-Z> (the ground state), and same for red-detuning. Please help!
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