Preparation of Entangled States and Quantum Teleportation with Atomic Qubits

Quantum information processing has been the subject of intense study for the past ten years. Entanglement is an essential ingredient in order to achieve the exponential speed-up promised by certain quantum algorithms. One system proposed for the implementation of quantum information processing is a string of ions in a linear Paul trap. In this thesis the ability to deterministically prepare and manipulate entangled states of two and three ions with such an experimental setup is investigated. The essential tools for an ion trap quantum computer, in particular a two ion controlledNOT gate, were demonstrated. The entangled states could be controlled with such precision that it was possible to realize a deterministic quantum state teleportation between ions. The experiments described were carried out with 40Ca+ ions stored in a linear Paul trap. The physical representation of the qubits was with the S1/2 ground state and the metastable D5/2 state of the Ca+ ions. The operations necessary for entangling the ionic qubits were implemented with a series of laser pulses at 729 nm, addressing the quadrupole transition between the S1/2 and D5/2 states. With this experimental setup two ionic qubits were prepared in all four Bell states and three ionic qubits were prepared in both possible classes of tripartite entangled states, namely GHZand W-states. The entangled states were investigated using quantum state tomography, which provided complete information about the quantum system in the form of its density matrix. The lifetime of these entangled states were studied. As predicted by theory, some particular types of entangled state were found to be particulary stable against the predominant source of noise in our experiment, namely correlated phase noise due to laser frequency fluctuations. A technique to measure the state of one ionic qubit without affecting the other qubits in the ion string was implemented. The effect of such a measurement on GHZand W-states was studied. Furthermore the experimental setup was improved, such that single-qubit operations could be applied depending on the outcome of a previous measurement of one or more qubits. This technique was used to transform a GHZ-state into a pure bipartite entangled state using only local operations. Finally, the advanced techniques developed to manipulate the entanglement of the ionic qubits were combined to allow the implementation of a quantum teleportation protocol. This was the first demonstration of a completely deterministic teleportation protocol with massive particles. In particular, it was possible to use the outcome of a complete Bell-measurement to reconstruct the input state, a step which was omitted in all previous experimental realizations of teleportation.