Can the Jaynes-Cummings model serve as photon induced particle hopping?

If you have an electron in a cavity and it has a ground state and an excited state which are somehow localized in either site of the cavity, does this mean that you can describe this situation as photon induced hopping? If you would then create a lattice of cavities all pointed in the x-direction could you then describe this system with a Hubbard model where the hoppings in the x-direction involve photon emission?