Entanglement control in two interacting qubits coupled to a radiation field

The interaction between a quantum system and a bosonic field has been one of the central problems in physics. It manifests itself in many different systems of interest such as atoms, ions, molecules and quantum dots coupled to radiation fields in cavity QED, which all are of special interest for quantum information processing. The coupling between a two-level quantum system and a bosonic field is best described by the Rabi model (1936), which is not analytically solvable. Latter, the Jaynes-cummings model (JCM)(1963) presented a solution using the rotated wave approximation. Since then, most of the investigations have focused on the coupling between multiple quantum systems at one hand and radiation fields at the other hand, ignoring the possible coupling between the quantum systems themselves. We consider two interacting two-level quantum systems (qubits) coupled to a single-mode quantized field, where we present an analytic solution for the problem. We show the impact of the coupling between the two quantum systems on the different properties of the composite system, such as the entanglement and the collapse-revival phenomenon. The interplay between the qubit-qubit coupling and the qubit-radiation coupling is investigated thoroughly.