# Energy levels shifts in a time-varying electric field

• A
• BillKet
In summary, the conversation discusses the effects of a laser on resonance with a transition between two levels with different parities. The laser frequency corresponds to the energy difference between these levels and can cause a shift in the effective location of the levels. This shift is dependent on the Rabi frequency of the laser and can be observed when measuring the transition from either level to the same energy state.

#### 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!

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