Energy levels shifts in a time-varying electric field

[BillKet]

Hello! I have 2 levels of the same parity with energies $E_1 < E_2$, and another level of opposite parity a distance $E$ from the $E_2$. I also have that $E_2 - E_1 << E$. I have a laser on resonance (I am trying to scan along the resonance and find it) with the transition from $E_2$ to the other level (so the laser frequency corresponds to $E$). Does this mean that while I am scanning the transition of interest, the laser will also couple $E_1$ with the other level and hence shift the effective location of the 2 levels? Basically by this effect, the opposite parity level will be shifted by $\frac{\Omega^2}{4(E_2-E_1)}$, where $\Omega$ is the Rabi frequency of the laser. So the frequency I am measuring in practice will be shifted. Similarly, if I measure the transition from $E_1$ to $E$, I will have the exactly same shift, but in opposite direction. Is this right or am I missunderstanding my system? Thank you!

 

[Twigg]

Your analysis looks right to me, in the limit of $\Omega << E_2 - E_1$.