Quantum Entanglement and Geomtric Phases

With the reliance in the processing of quantum information on a maximally entangled pure state resource combined with the field interaction, we look, in this thesis, at various means of recovering the pure entangled states. Primarily, we investigate the quantum entropy and Pancharatnam phase in some optical systems. \par To be more precisely, the aim of this thesis is, on one side, to illustrate and analyze various puzzling phenomena that are due to the quantum entanglement and related to the atom-field interaction.On the other side, the aim of the thesis is to discuss some main basic concepts, methods and results of the already very rich body of knowledge obtained recently at the attempts to understand, qualitatively and quantatively, quantum phase (qp) as well as its properties, structures and potentials for applications. The Pancharatnam phase of a $\Lambda$-configuration three-level atom placed in a photonic band gap (PBG) material driven by a classical laser field and coupled to a continuum of vacuum modes of an electromagnetic field is disussed.