Simplified approach to generate controlled-NOT gates with single trapped ions for arbitrary Lamb-Dicke parameters
Abstract
For certain specific (or "magic") Lamb-Dicke (LD) parameters, Monroe et al showed [Phys. Rev. A 55, R2489 (1997)] that a two-qubit quantum operation, between the external and internal degrees of freedom of a single trapped ion, could be implemented by applying a single carrier laser pulse. Here, we further show that, such a two-qubit operation (which is equivalent to the standard CNOT gate, only apart from certain phase factors) could also be significantly-well realized for arbitrarily selected LD parameters. Instead of the so-called "π-pulses" used in the previous demonstrations, the durations of the pulses applied in the present proposal are required to be accurately set within the decoherence times of the ion. % We also propose a simple approach by using only one off-resonant (e.g., blue-sideband) laser pulse to eliminate the unwanted phase factors existed in the above two-qubit operations for generating the standard CNOT gates.