  The Jaynes-Cummings model (JCM) describes the interaction of a two-level atom
with a single quantised field mode in an optical cavity. In this BSc project we
derive the basic Rabi model Hamiltonian and show how it leads to the JCM
Hamiltonian. The results are then used to analyse the general time evolution of
a bipartite atom-field system and its properties, such as entanglement. We
extend a scheme developed by Browne and Plenio [D. Browne and M. B. Plenio,
Physical Review A, vol. 67, no. 1, Jan. 2003.] to entangle two cavities that
interact with an atom. Our scheme allows to produce states that are arbitrarily
close to a Bell state with a success probability greater than 0.75, whereas the
success rate of the original method tends to 0 for perfect fidelity. Further,
we extend both schemes by allowing the atom or the cavity to be in a thermal
state and find that the fidelity of the produced states is reduced with
increasing temperature. Finally, we apply our scheme to quantum teleportation,
where we find that the fidelity of the teleported state compared to the
original state also decreases as the temperature is increased.
