Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement

Entangled many body systems have recently attracted significant attention in various contexts. Among them, spin squeezed atoms and ions have raised interest in the field of precision measurements, as they allow to overcome quantum noise of uncorrelated particles. Precise quantum state engineering is also required as a resource for quantum computation, and spin squeezing can be used to create multi-partite entangled states. Two-mode spin squeezed systems have been used for elementary quantum communication protocols. Until now spin squeezing has been always achieved via generation of entanglement between different atoms of the ensemble. In this Letter, we demonstrate for the first time ensemble spin squeezing generated by engineering the quantum state of each individual atom. More specifically, we entangle the nuclear and electronic spins of $10^{12}$ Cesium atoms at room temperature. We verify entanglement and ensemble spin squeezing by performing quantum tomography on the atomic state.