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

Abstract

A single ⁴⁰Ca⁺-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_5/2 transition causes a phase shift proportional to the ion's 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 discuss 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.