Theoretical studies of atom-atom, atom-photon and photon-photon entanglement

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. Entanglement is now believed to be an essential resource for realizing some non-classical tasks, such as teleportation.; We first study a model system in the cavity QED setup. Cavity QED has proved to be excellent in the coherent manipulation of atoms and cavity photons. By using a four-level atom and two resonant cavity modes, we can generate atom-photon entanglement almost deterministically. The generated photon can be distributed which is ideal for quantum communication.; 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. The overall process can be divided into two steps. In each step, a cavity photon will be generated and leak out of the cavity. The final state of the atom becomes disentangled with both photons. Thus, the whole process generates an almost maximally entangled photon pair with very high probability.; We then investigate the atom-atom entanglement in a 1D harmonic trap. At low temperature, the atom-atom interaction is dominated by the s-wave/p-wave scattering, further simplified as a contact interaction. We 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 1D systems, we briefly discuss the "Fermi-Bose duality" in this simple 1D system.; While the entanglement properties of a single-channel model has recently been obtained for 1D and 3D systems, we study the entanglement of a multi-channel process in a cylindrical harmonic trap. We adopt a model system consisting of two fermionic atoms with opposite spins. The open-channel atomic pair can be converted to a closed-channel bosonic molecule, or vice versa, leading to orbital deformation and entanglement. We carry out calculations in the so-called "broad resonance" regime and discuss the dependence of entanglement on the trap geometry.; Finally we present detailed studies of the spin mixing between two 87Rb atoms in a single lattice site. Staring from the spin-1 manifold, we discuss various motional state approximations which turn out to cause observable errors. Then, we include the dipolar interaction for a complete study. We find that while the dipolar effect can be negligible in a spherical harmonic trap, the dipolar interaction can lead to an experimentally observable frequency shift in a cylindrical harmonic trap with very large aspect ratio. We also consider the spin-2 manifold and discuss the corresponding spin mixing.