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I have a general question on how to work with quantization axis. Here is the setup:

I am looking at a single two-level atom placed at the origin $(0, 0, 0)$, which is unperturbed in the sense that no magnetic field is applied to it.

I now send in a coherent EM-field, resonant with the transition of the atom. With a right-handed coordinate system in mind, the field is linearly polarized along $y$ and propagagtes along $+x$.

Since there is no magnetic field applied, I am allowed to choose the quantization as I wish.

  1. The easiest choice is to choose the $y$-axis directly such that the EM-field drives the $\pi$-transition of the atom.
  2. If I had chosen the $z$-axis instead, then the EM-field would drive $\sigma$-transitions instead. Since no magnetic field is applied, they are equal to the $\pi$-transition, so we get exactly the same signal as we should.
  3. Now say I had instead chosen to put my quantization axis along in the $(y, z)$-plane with an angle $A$ relative the $y$-axis. Is it valid to to decompose the quantization axis into a $\cos(A)$ part (driving the $\pi$-transition) and a $\sin(A)$ part (driving the $\sigma$-transitions)?
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