Persistent asymptotic entangled states in an interacting asymmetric Tavis-Cummings model

The rapid advancement in the field of quantum information processing sparked great interest in developing what are believed to be new promising qubits made of artificial atoms as well as customized natural ones. Those qubits enjoy mutual interaction with other qubits of the same type or different one in what is known as the hybrid quantum systems. In this work, an asymmetrical generalized version of the famous Tavis-Cummings model is used to prototype the behavior of such hybrid systems. The problem is explored in its full generality by analytically solving the model while upholding realistic conditions, namely two mutually interacting non-identical qubits coupled off-resonance to a radiation field, with non-linearity in both the cavity medium and the qubit-field interaction. The work focuses on studying the entanglement dynamics of the system and its asymptotic behavior, with special emphasis on entanglement sudden death (ESD) and birth (ESB). The system is found to exhibit typical death-revival pattern, which asymptotically approaches a pseudo-steady state that is considerably sensitive to the degree of asymmetry between the qubits, the initial state, and other system parameters. We show that for certain initial entangled states, the system parameters can be tuned to provide maximized persistent terminal entanglement values that are steady and free of any collapse-revival patterns or ESD. In contrary, the disentangled initial states asymptotically attain scattered entanglement maxima that lack any systematic behavior. This terminal entanglement behavior can be attained more rapidly by strengthening the mutual interaction between the qubits, a process that is now experimentally accessible with contemporary artificial qubit systems. These results pave the road for preparing strongly entangled qubits in long-life steady states that are crucially needed for performing efficient quantum information algorithms. These systems can be realized using typical qubits such as quantum dots, trapped ions, superconductors, and Rydberg atoms, in either cavity or circuit QED structures.