Optimal control of entanglement in atom pairs with dipole-dipole interaction by quantum phase space formalism

We investigate the entanglement in a two -particle system with continuous degree of freedom constituted by trapped neutral atoms interacting via tunable dipole -dipole interaction. We describe the system in the quantum Wigner phase space representation. The atom entanglement is measured in terms of violation of the non separability condition or of some Bell inequalities. By an optimal control procedure, we design the control parameters that steer the system toward a maximally entangled state. We estimate the robustness of the control by considering the presence of an external source of noise weakly interacting with the atoms.