Geometric Phase for Two-Mode Entangled Coherent States

In this paper, the geometric phase (GP) of a superposition state of two bipartite pure states is formulated. Specially, we have focused on the GP of superposition states with two-bipartite pure coherent states. We have investigated under which conditions the superposition term in the dynamical phase expression can be removed. We have calculated the cyclic GP of two-mode balanced and unbalanced entangled coherent states (ECSs), undergoing a unitary evolution and the results are discussed. Similar to the concurrence measure which can be used to determine the degree of entanglement of quantum states, it is demonstrated that the dynamical phase of the introduced states can also be a witness to the quantum entanglement. It is found out that the responses of dynamical phase and concurrence to the evolution of a model parameter are opposite to each other, i.e. an increase in one of them is accompanied by a decrease in the other. In addition, it is shown that these two states are local unitary equivalent. Finally, we suggest an experimental interferometry setup to produce the evolved ECS for the balanced states.