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##.