If we have a 2 level system and I send a laser on resonance, when working in the dressed atom description, each level gets split by $\pm\Omega$ i.e. the Rabi frequency of the laser. Now if we send a second, probe laser, that laser will see a Mollow triplet due to this splitting. However, if we have only the first laser, and use it to search for the resonance of the transition we won't see a triplet, just a peak at the resonance i.e. the laser doesn't induce an AC stark shift on itself (please correct me if this is wrong). Now let's assume we have 3 levels g, e1 and e2 and only one laser which we use to scan the g$\rightarrow$e1 transition. If it was not for e2, we would be in the above case. But if e2 is present will that change the location of the g$\rightarrow$e1 transition i.e. will the laser induce an AC Stark shift on itself, through the e2 energy level? And if so, how would I calculate that shift (I assume as a function of the laser Rabi frequency and the detuning of the laser from the e1$\rightarrow$e2)? Thank you!
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