Question about anapole moment measurement

[BillKet]

Hello! My questions is about this paper, aiming to measure the anapole moment in a molecule. In their derivation, starting from equation (1), they assume that the frequency of the field felt by molecules $\omega$ is much bigger than the energy splitting $\Delta$. That basically implies that the electric field frequency is very far detuned, which allows them to use perturbation theory in their derivation. Is that a limitation of the experiment, or does it offer any advantage? If $\omega$ was close to $\Delta$, would that influence the experimental result i.e. would that prevent us from extracting W (of course in that case one would need to solve the S.E. numerically). Also, I see that all they need is a time varying electric field. Given that anyway the frequency of the field is very far detuned, can they use, for example an RF/microwave source whose electric field can act as the field needed in this experiment, without having to build the whole setup needed to shape the potential? Thank you!

 

[BigJDubs]

The assumption that the frequency of the electric field $\omega$ is much bigger than the energy splitting $\Delta$ is not a limitation of the experiment, but rather offers an advantage. This assumption allows the researchers to use perturbation theory in their derivation, which simplifies the calculations and makes the experiment more feasible. If the frequency of the electric field was close to the energy splitting, then the researchers would have to solve the Schrödinger equation numerically, which would be much more difficult. It is possible to use an RF/microwave source for the electric field needed in this experiment, without having to build the whole setup needed to shape the potential. However, it is important to note that the frequency of the RF/microwave source should be far detuned from the energy splitting $\Delta$ in order to ensure that the perturbative analysis is valid.