Dicke state generation via selective interactions in a Dicke-Stark model

We propose a method to create selective interactions with Dicke-Stark model by means of a time-dependent perturbation theory. By choosing the proper rotating framework, we find that the time oscillating terms depend on the number of atomic excitations and the number of photonic excitations. Consequently, the Rabi oscillation between selective states can be realized by properly choosing the frequency of the two-level system. The second order selective interactions can also be studied with this method. Then various states, such as Dicke states, superposition of Dicke states and GHZ states, can be created by means of such selective interactions. The numerical results show that high fidelity Dicke states and Greenberger-Horne-Zeilinger states can be created by choosing the proper frequency of the two-level system and controlling the evolution time.