Narrow Results

The problem of a two-level atom interacting with single mode cavity field is considered, however, the optical cavity is filled with new structure of a generalized nonlinear Stark shift via Ξ configuration. One starts with a three-level trapped atom interacting with the quantized field of center of mass motion thus a Hamiltonian for one-phonon process with nonlinearities is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, we generate a new structure of effective Hamiltonian for a two-level atom with a nonlinear Stark shift. The temporal evolution of the atomic inversion is studied, we introduce that in the presence of the Stark shift parameter the atom leaves in a maximal entangled sate. We use the von Neuman entropy to measure the degree of entanglement between the atom and the field. After adding the nonlinear Stark shift the system never reaches the pure state. Also we study the Q-function for obtaining more information in phase space for this system. These aspects are sensitive to changes in the Stark shift parameter. The results shows that the effect of the nonlinearity in the Stark shift changes the quasiperiod of the field entropy and hence the entanglement between the particle and the field.

Entangled Markov chains (EMC) were so baptized on the basis of the conjecture that they provide examples of states, on infinite tensor products of matrix algebras, which are in some sense "entangled".² In this paper we introduce the notion of multiple (or "many-body") entanglement and extend the two-body criterion of entanglement obtained in Ref. 17 to this case. We then apply this extension to EMC and prove that "generically" they satisfy the entanglement conditions.

A measure to quantify the degree of entanglement for two qubits (2×2) in a pure state is presented in Phys. Rev.A65, 044303 (2002). We generalize their results to 2×n quantum systems. An analytical expression of the entanglement of formation for quantum mixed states of 2×n quantum systems is obtained. Moreover for multipartite quantum systems a generalized "measure" is presented to judge if a pure state is separable or maximally entangled.