Analytic solution for entangled two-qubit in a cavity field
Mahmoud Abdel‐Aty, A.‐S. F. Obada · Journal of Mathematical Physics · 2004
An exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (ions or atoms) within a perfect cavity for the case of multiphoton transition and in the presence of both the Stark shift and phase shift is obtained. Employing this solution, the significant features of the entanglement when a second qubit is allowed to interact with cavity mode and becomes entangled with the first qubit are investigated in the context of the measure defined by negative eigenvalues for the partial transposition of the density operator. The effects of Stark shift, distance between the two qubits, and an instantaneous phase shift experienced by the second qubit on the entanglement and probability amplitudes are indicated. It has been shown that the entanglement as well as the intensity are markedly affected by different parameters when the nonlinear two-photon process is involved. Moreover, the quasiprobability distribution function is investigated before and after the sudden phase shift experienced by the second qubit. We believe that this may throw some light on the question of the entanglement of multi-qubit systems.