Manipulating entanglement sudden death in two coupled two-level atoms interacting off-resonance with a radiation field: an exact treatment

We study a model of two coupled two-level atoms (qubits) interacting off-resonance (at non-zero detuning) with a single mode radiation field. This system is of special interest in the field of quantum information processing (QIP) and can be realized in electron spin states in quantum dots or Rydberg atoms in optical cavities and superconducting qubits in linear resonators. We present an exact analytical solution for the time evolution of the system starting from any initial state. Utilizing this solution, we show how the entanglement sudden death (ESD), which represents a major threat to QIP, can be efficiently controlled by tuning atom-atom coupling and non-zero detuning. We demonstrate that while one of these two system parameters may not separately affect the ESD, combining the two can be very effective, as in the case of an initial correlated Bell state. However in other cases, such as a W-like initial state, they may have a competing impacts on ESD. Moreover, their combined effect can be used to create ESD in the system as in the case of an anti-correlated initial Bell state. A clear synchronization between the population inversion collapse-revival pattern and the entanglement dynamics is observed at all system parameter combinations. Nevertheless, only for initial states that may evolve to ESD, the population inversion revival oscillations, where exchange of energy between the atoms and the field takes place, temporally coincide with the entanglement revival peaks, whereas the population collapse periods match the ESD intervals. The variation of the radiation field intensity has a clear impact on the duration of the ESD at any combination of the other system parameters.