Precision Measurement and Compensation of Optical Stark Shifts for an Ion-Trap Quantum Processor

Using optical Ramsey interferometry, we precisely measure the laser-induced ac-Stark shift on the $S_{1/2}–D_{5/2}$ “quantum bit” transition near 729 nm in a single trapped ${}^{40}\mathrm{C}\mathrm{a}^{+}$ ion. We cancel this shift using an additional laser field. This technique is of particular importance for the implementation of quantum information processing with cold trapped ions. As a simple application we measure the atomic phase evolution during a $n\times 2\pi$ rotation of the quantum bit.