Demonstration of a Mesoscopic Quantum Gate*

Rydberg atoms are an exciting platform for large scale quantum computing with demonstrations of high fidelity entanglement and coherent control. The strong, long-range dipole-dipole interaction between Rydberg atoms creates a ‘dipole blockade’ which prevents the excitation of more than one atom within a radius $R<10~\mu$m to the Rydberg state. Using this effect we have previously demonstrated ground-state entanglement between a pair of atoms with a fidelity of 81\%. However, scaling from single atoms to atomic ensembles for optical interfacing introduces challenges due to the collective $\sqrt{N}$-enhancement from blockade giving number sensitivity to the excitation pulses. \\ We present recent results demonstrating an alternative mesoscopic gate scheme based on electromagnetically induced transparency (EIT), originally proposed by M\"{u}ller \emph{et al.}. This protocol provides a scalable approach to performing entanglement of large ensembles using a single control atom whilst circumventing challenges of the collective Rabi frequency. The resulting CNOT$^N$ gate protocol is therefore robust against number fluctuations and provides a route to creating useful entangled states for high-precision measurements beyond the standard quantum limit.