Energy shifts in time dependent perturbation theory

[Malamala]

Hello! I saw in many papers people talking about the effects of a time dependent perturbation (usually an oscillating E or B field) on the energy levels of an atom or molecule (for now let's assume this is a 2 level system). Taking about energy makes sense when the hamiltonian is time independent. But here it is not. Moreover, this shift (e.g. AC Stark Shift) it's a constant (which depends on the magnitude and frequency of the field), even if the field itself is time varying. Given that this is usually talked about in the context of perturbation theory, I assume that at a point we do an approximation related to the relative frequencies of the field and of the atom (the resonance frequency), but I am not sure how to proceed. Can someone help me a bit in understanding this? Here is the paper that I am reading that made me ask this question. Thank you!

 

[BigJDubs]

The paper you are reading is talking about a technique called the AC Stark effect, which is used to modify the energy levels of an atom or molecule in the presence of an oscillating electric or magnetic field. The AC Stark effect is based on perturbation theory and involves finding the energy shifts due to the external field. To do this, we must calculate the expectation value of the perturbative Hamiltonian for the system in the presence of the field. The perturbative Hamiltonian contains terms that depend on the frequency of the external field and the resonance frequency of the atom or molecule. If the field frequency is close to the resonance frequency of the atom or molecule, then the energy shift is significant. In order to calculate the energy shift, we need to solve the Schrodinger equation with the perturbative Hamiltonian. This is usually done using a perturbative expansion, where we expand the energy shifts in terms of the strength of the external field and the frequency of the field. We then use the energy shifts to modify the energy levels of the atom or molecule. Hope this helps!