It's well established that an optical tweezer and optical lattices can trap atoms. The typical explanation for this is that the AC stark shift creates a position-dependent energy which can be interpreted as a potential that the atom moves in.
I've seen a derivation of the Born-Oppenheimer approximation, which explains that you can find the vibrational energy levels of molecules in the following way: (1) Find the groundstate of the electronic wavefunction as a function of the distance between the two nuclei (2) interpret this groundstate energy as a potential that the nuclei move in, and find a wavefunction for the nuclei given that potential. A similar justification can explain why atoms are trapped in a system where their groundstate energy depends on position.
But it's not so clear to me why the quasienergies created by the AC stark shift behave the same way energy levels do in static quantum mechanics. The AC stark shift is justified by the Floquet theorem, which says that in a time-periodic potential there are "quasienergies" (which are defined only modulo the frequency of the potential, which seems like it might be an issue when we talk about "minimizing the quasienergy"). Why are these quasienergies equivalent to energies in the sense that atoms are attracted to regions where the quasienergy is lower?
