Transition Slow-Down by Rydberg Interaction of Neutral Atoms and a Fast Controlled-NOT Quantum Gate

Exploring controllable interactions lies at the heart of quantum science. Neutral Rydberg atoms provide a versatile route toward flexible interactions between single quanta. Previous efforts mainly focused on the excitation annihilation~(EA) effect of the Rydberg blockade due to its robustness against interaction fluctuation. We study another effect of the Rydberg blockade, namely, the transition slow-down~(TSD). In TSD, a ground-Rydberg cycling in one atom slows down a Rydberg-involved state transition of a nearby atom, which is in contrast to EA that annihilates a presumed state transition. TSD can lead to an accurate controlled-{\footnotesize NOT}~({\footnotesize CNOT}) gate with a sub-$\mu$s duration about $2\pi/\Omega+\epsilon$ by two pulses, where $\epsilon$ is a negligible transient time to implement a phase change in the pulse and $\Omega$ is the Rydberg Rabi frequency. The speedy and accurate TSD-based {\footnotesize CNOT} makes neutral atoms comparable~(superior) to superconducting~(ion-trap) systems.