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I have a question on how to work with quantization axis. The setup I am looking at is a single two-level atom placed at the origin (0, 0, 0), which is not perturbed by any magnetic field.

I now send in a laser 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. All OK here.

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. All OK here too.

3) Now say I had instead chosen to put my quantization axis along in the (y, z)-plane with an angle Ω relative the y-axis.

Am I allowed to decompose the quantization axis into a cos(Ω)-part (driving the pi transition) and a sin(Ω) part (driving the sigma transitions)? Or is this reasoning wrong?

Best,

Niles.

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# QM: Quantization axis

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