Quantized AC-Stark shifts and their use for multiparticle entanglement and quantum gates

A single Ca-40(+)-ion is trapped and laser-cooled to its motional ground state. Laser radiation which couples off-resonantly to a motional sideband of the ion's S-1/2 to D-3/2 transition causes a phase shift proportional to the ions motional quantum state \n>. As the phase shift is conditional upon the ion's motion; we are able to demonstrate a universal 2-qubit quantum gate operation where the electronic target. state {S, D} is flipped depending on the motional qubit state \n) = {\0>, \1>}. Finally; we discus scaling properties of this universal quantum gate for linear ion crystals and present, numerical Simulations for the generation of a maximally entangled state of five ions.