Carlos A. González-Gutiérrez

We derive an analytical approximate solution of the time-dependent state vector in terms of material Bell states and coherent states of the field for a generalized two-atom Tavis-Cummings model with nonlinear intensity dependent matter-field interaction. Using this solution, we obtain simple expressions for the atomic concurrence and purity in order to study the entanglement in the system at specific interaction times. We show how to implement entangling atomic operations through measurement of the field. We illustrate how these operations can lead to a complete Bell measurement. Furthermore, when considering two orthogonal states of the field as levels of a third qubit, it is possible to implement a unitary three-qubit gate capable of generating authentic tripartite entangled states such as the Greenberger-Horne-Zeilinger (GHZ) state and the W-state. As an example of the generic model, we present an ion-trap setting employing the quantized mode of the center of mass motion instead of the photonic field, showing that the implementation of realistic entangling operations from intrinsic nonlinear matter-field interactions is indeed possible.

We introduce a complete Bell measurement on atomic qubits based on two photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single-mode of the radiation field, which is known to effectively generate a non-linear two-photon interaction between the field and two states of each atom. For initial coherent states with large mean photon number, the field state is well represented by two coherent states at half revival time. For certain product states of the atoms, we prove the coherent generation of GHZ states with two atomic qubits and two orthogonal Schrödinger cat states as a third qubit. For arbitrary atomic states, we show that discriminating the two states of the field corresponds to different operations in the Bell basis of the atoms. By repeating this process with a second cavity with a dephased coherent state, we demonstrate the implementation of a complete Bell measurement. Experimental feasibility of our protocols is discussed for cavity-QED, circuit-QED and trapped ions setups.