Simplified approach to generate controlled-NOT gates with single trapped ions for arbitrary Lamb-Dicke parameters

TL;DR

This paper presents a simplified method to implement controlled-NOT gates with single trapped ions for any Lamb-Dicke parameter, using a single off-resonant laser pulse, improving flexibility and practicality over previous approaches.

Contribution

It introduces a novel approach that enables CNOT gate realization for arbitrary Lamb-Dicke parameters using only one off-resonant laser pulse, avoiding complex phase corrections.

Findings

Effective CNOT gates achieved for arbitrary Lamb-Dicke parameters.

Pulse durations can be accurately set within decoherence times.

Elimination of unwanted phase factors with a single off-resonant laser pulse.

Abstract

For certain {\it specific} (or {\it"magic"}) Lamb-Dicke (LD) parameters, Monroe {\it et al} showed [Phys. Rev. {\bf 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 {\it arbitrarily} selected LD parameters. Instead of the so-called "$\pi$-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.