Mapping trapped atomic gas with spin-orbit coupling to quantum Rabi-like model

We construct a connection of the ultracold atomic system in a harmonic trap with Raman-induced spin-orbit coupling to the quantum Rabi-like model. By mapping the trapped atomic system to a Rabi-like model, we can get the exact solution of the Rabi-like model following the methods to solve the quantum Rabi model. The existence of such a mapping implies that we can study the basic model in quantum optics by using trapped atomic gases with spin-orbit coupling.