Confused about AC Stark effect

Can someone explain to me in an intuitive way (or a nice mathematical demonstration) or point me towards some accessible papers about the AC Stark effect (Autler-Townes effect)? I am mainly confused by how can one start from a 2 level system (consider a 2 level system for simplicity) add a time dependent potential to the Hamiltonian and end up with a 4 level system (here is a picture at the end of the paper with what I mean)? I am pretty sure I am missing something but I can’t figure out what. Thank you!