Generation of long-range entanglement in a macroscopic spin singlet

We report the generation of long-range entanglement in a macroscopic spin singlet (MSS) [1,2] via collective quantum non-demolition (QND) measurement [3] a global entanglement method predicted [4] to produce entan- glement at all length scales. In a cold $^{87}$Rb spin ensemble of up to $2\times10^6$ atoms, we generate a MSS, entangling at least half of the atoms. Using a gradient field to convert singlets to triplets, we detect the decay of entanglement in the MSS via spin noise spectroscopy [4] consistent with a mean entanglement length comparable to the size of the atom cloud ($\sim4$mm), three orders of magnitude larger than previously detected in atomic spin systems [5]. [1] N. Behbood {\it et al.}, Phys. Rev. Lett. {\bf 113}, 093601 (2014). [2] G. T\'{o}th and M.W. Mitchell, New J. Phys. {\bf 12}, 053007 (2010). [3] R. J. Sewell {\it et al.}, Nat. Photon. {\bf 7}, 517 (2013). [4] I. Urizar-Lanz {\it et al.}, Phys. Rev. A {\bf 88}, 013626 (2013). [5] D. Greif {\it et al.}, Science {\bf 340}, 1307 (2013).