New analytical formulas for the concurrence are introduced. A system of initially unentangled two two-level atoms entering a cavity successively and the effect of a nonlinear medium on the properties of their entanglement are studied. It is shown that a good periodical entanglement can be achieved with a weak nonlinear medium and low driving field, while the perfect is reached with high driving field and low or high parameters of nonlinearity.Entanglement between separate quantum systems is a distinctive feature of quantum mechanics 1-3 which has recently attracted much attention. Entanglement usually arises from quantum correlations between separated subsystems which cannot be created by local actions on each subsystem. A bipartite system is said to be entangled in quantum mechanics if its state cannot be expressed as a product of the states of its individual constituents. It is well known that quantum entanglement plays a fundamental role in quantum information processing and quantum computing. 4-6 Great effort has been devoted to quantifying entanglement involving various methods and interesting concepts, 7-27 involving, for example, entanglement of formation, 19,20 entanglement of distillation, 19,20 the relative entropy, 21,22 the robustness of entanglement, 23 and others. Among them the concurrence which is associated with the entanglement of formation. The entanglement of formation has more importance, since it intends to quantify the resources needed to create a given entangled state. Nevertheless, of particular interest is generation of entangled states in two-atom systems, since they can represent two qubits, the building blocks of the quantum gates that are essential to implement quantum protocols in quantum information processing. Entanglement has been widely observed in quantum optical systems such as cavity electrodynamics. A number of experiments have been carried out. Recently, practical and theoretical studies have been performed to quantify 535 Int. J. Quantum Inform. 2007.05:535-552. Downloaded from www.worldscientific.com by UNIVERSIT OF SOUTHERN CALIFORNIA on 03/13/15. For personal use only.

The wave function of a system governed by the time-dependent nonlinear JaynesCummings (JC) model is obtained. We compute analytically the eigenvalues of the reduced field density operator by which the dynamics of the entropy of entanglement of the cavity field are analyzed. The influences of the atomic motion, the field-mode structure and the Kerr-like medium on this phenomenon are illustrated. The population dynamics of an excited atom is also discussed for the same set of parameters. The cavity field is assumed to be initially excited in either a Fock or a coherent states. The cavity excitation in a Fock state generates a class of an entanglement without death with fixed amplitude by adjusting the parameters of the atomic motion as well as the Kerr and the field-mode structure. In case of a coherent cavity, the only phenomenon to be noted is the periodical behavior of the dynamics under study when the atomic motion is considered. Although the Kerr medium affects the strength of the entanglement negatively, the entropy of entanglement loses its zeros where the Kerr is taken into consideration.

Entanglement dynamics of two identical non-interacting atoms (qubits) coupled individually with simultaneous classical and quantum fields are studied. The cavity field is filled with a nonlinear Kerr medium and initially prepared in a coherent state. The atoms are initially set up as a Bell-like pure state (BS). We present an approach for diagonalization of time-dependent nonlinear Hamiltonian of the system exactly. Connection between the change in the degree of entanglement and tomography of field state in phase space are also illustrated and interpreted. We demonstrate the possibility of atom–atom (qubit–qubit) entanglement optimization by suitably choosing initial interaction settings. Overall, we show that both classical driving amplitude and detuning as well as Kerr media and initial atomic states acts as the control parameters for the qubit–qubit entanglement. By adjusting of these parameters, accurately, entanglement can be enhanced noticeably and high degree of steady periodical entanglement can be generated. Moreover, starting with initial atomic BSs in presence of classical driving suppresses coherences randomness and considerably accompanied with (for specific values of detuning) slight decrease in their amplitudes. Furthermore, the addition of cross Kerr term suppresses degree of entanglement noticeably, where entanglement creation and enhancement could just be possible if cross Kerr effect is moved out from interaction. Our present approach promises the great advantage of being suitable for large quantum systems of various kinds of nonlinearities.

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