Motional Quantum-State Engineering and Implementation of aQuantum Phase-Gate for Multiple TrappedIons

Abstract

We propose a scheme to generate a superposition of motionalcoherent states with arbitrary coefficients on a line in phasespace and implement a quantum controlled phase-gate for multipletrapped ions with a single standing-wave laser pulse whose carrierfrequency is tuned to the ions transition. In the scheme each iondoes not need to be exactly positioned at the node of the standingwave, which is very important from viewpoint of experiment.Furthermore, our scheme may allow the generation of asuperposition of coherent states with large mean phonon number fora large number of trapped ions in a fast way by choosing suitablelaser intensity. We show that it can also be used to generatemaximally entangled states of multiple trapped ions.