Theoretical studies of atom-atom, atom-photon and photon-photon entanglement
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In this thesis the entanglement properties of atom-atom, atom-photon, and photon-photon are investigated. The recent developments of quantum computation as well as quantum information and communication have attracted much interest in the generation of these entanglements in the laboratory. To generate atom-photon entanglement, I discuss a model system in the cavity QED setup. By using a four-level atom and two resonant cavity modes, we can generate atom-photon entanglement almost deterministically. An extension of the above model to a six-level atom and again two resonant cavity modes can generate entangled photon pairs by appropriately adjusting system parameters. I then investigate the atom-atom entanglement in a 1D harmonic trap. I show the dependence of the pair entanglement on the scattering length and temperature, as well as the particle symmetry requirement (bosons or fermions). Among many peculiar properties in a 1D system, we briefly discuss the Fermi-Bose duality". While the entanglement properties of a single-channel model have recently been obtained for 1D and 3D systems, I thus study the entanglement of a multi-channel process in a cylindrical harmonic trap. I discuss the dependence of entanglement on the trap geometry. Finally I present detailed studies of the spin mixing between two Rb87 atoms in a single lattice site. The topic is emphasized on various motional state approximations and dipolar effect. Various motional state approximations can cause up to 20% error to experimental data. I also find that the dipolar interaction can lead to an experimentally observable frequency shift in a cylindrical harmonic trap with very large aspect ratio. The spin mixing of spin-2 manifold has also been discussed.