Local And Nonlocal Entanglement For Quasiparticle Pairs Induced By Andreev Reflection

Quantum computation and quantum information have been attracting great attention in recent years. Production and detection of entangled particles are of importance and necessity for the quantum computation and quantum information procedure. In this paper, we studied the entangled quasi-particles created by local and nonlocal Andreev reflection in a structure of normal metal-superconductor-normal metal (NSN). Using the method of scattering matrix, we find that several types of entanglement are generated and the direction of entanglement can be modulated according to our requirement for this model.The thesis consists of three chapters. In chapter one, we introduce and describe briefly the importance of entanglement in solid state, the physical nature and the mathematical form of the entanglement state, the origin and the purpose of Bell Inequality, the scattering matrix method and the cooper pairs in a superconductor as well as how an electron will be reflected by a superconductor.Chapter two is the core part of the thesis, in which my own work is concretely explained. In a 2-dimensional NSN structure, a bias V make the chemical potential of one of the normal conductors eV(eV < Δ) higher than the superconductor Fermi level. The separation between the two normal conductors should be comparable to the superconducting length. This makes sure that nonlocal Andreev reflection may take place with the generation of local one. Due to the nonlocal Andreev reflection, more than one type of entanglement are produced and one of them is completely not our expectation. As a result, we can modulate the direction of the entanglement through the adjustment of the tunneling barriers between the superconductor and the normal metals. We have found, after some calculation, that the concurrence and the Bell-CHSH parameter have simple dependence on the eigenvalues of the normal and Andreev reflection matrices, and possess a one-to-one correspondence in the tunneling limit(T << 1). Possible experimental realization is also discussed.In chapter three a summary of the work and an outlook of this aspect is given.