High fidelity quantum gates for ion qubits in optical transitions

One of the most important challenges in ion trap quantum computing is the implementation of a high fidelity two--qubit quantum gate. For hyperfine qubits state dependend AC--Stark shifts were used to demonstrate a two qubit gate with a fidelity of 0.97 [1]. Here, we show that similar forces can also be employed for qubits based on optical transitions as for instance the $S_{1/2} \rightarrow D_{5/2}$ transition in Calcium. In contrast to previous work, our proposal can be applied to magnetic--field insensitive transitions. It also allows for negligible spontaneous emission rates and can be implemented with a pair of co--propagating beams. According to simulations with current experimental imperfections, the proposed gate will allow for fidelities exceeding 0.99. \newline \newline [1] D. Leibfried, {\it et al.}, Nature {\bf 422}, 412 (2003).