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, [Phys. Rev. A 55 (1997) R2489] showed 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.