Analytic solution for entangled two-qubit in a cavity field A.-S. F. Obada 1 and M. Abdel-Aty 2, 3 1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt. 2 M at hemat ics Depart ment , Facult y of Science, Sout h Valley University, 82524 Sohag, Egypt . An exact solution of the time-dependent master equation that describes the evolution of two two-level qubits (or atoms) within a perfect cavity for the case of multi-photon 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, is 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 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. 1 Overview Investigations into the emerging science of quantum information has led to the widespread belief that entanglement in states shared between two systems can be used as a resource in nonclassical applications [1-3]. The theory of quantum entanglement has occupied a central place in modern research because of its promise of enormous utility in quantum computing, cryptography, etc [4-8]. A major thrust of current research is to find a quantitative measure of entanglement for general states. One of the most intriguing problems of quantum mechanics is the interpretation of the measurement process (for an overview of fundamental problems in quantum measurement, see for example Ref. [9-11]). The reason for this central role of the measurement process is the absence of fundamental, elements of reality, that would simultaneously characterize both the 3 Present address: Institut fur Mathematik und ihre Didaktik, Universitat Flensburg, Flensburg, Germany. (E-mail: abdelaty@uni-flensburg.de) 1