We show how NOON states may be generated in ion traps. We use the individual interactions of light with each of the two vibrational modes of the ion to entangle them. This allows us to generate NOON states with N =8.
In the first part of this thesis, by using the two-photon Jaynes - Cummings Model (JCM),\nwe show how NOON states may be generated entangling two cavities, by passing atoms\nthrough them. The atoms interact with each cavity via two-photon resonant transitions.\nWe take advantage of the fact that depending on the state the atom enters (excited or\nground), it leaves or takes two photons per interaction and leaves the cavities in a pure\nstate.\nIn the second part of this thesis, we consider the Hamiltonian of a single ion vibrating in\ntwo dimensions interacting with a laser, we show how NOON states may be generated in\nion traps. We use the individual interaction of light with each of two vibrational modes of\nthe ion to entangle them. This allows us to generate NOON states with N = 8.