We sudy the creation of nonlocal states with ultracold atoms trapped in an optical lattice. We show that these states violate Bell inequality by measuring one- and two-body correlations. Our scheme only requires beam splitting operations and global p
hase shifts, and can be realized within the current technology, employing single-site addressing. This proposal paves the way to study multipartite nonlocality and entanglement in ultracold atomic systems.
Differential interferometry (DI) with two coupled sensors is a most powerful approach for precision measurements in presence of strong phase noise. However DI has been studied and implemented only with classical resources. Here we generalize the theo
ry of differential interferometry to the case of entangled probe states. We demonstrate that, for perfectly correlated interferometers and in the presence of arbitrary large phase noise, sub-shot noise sensitivities -- up to the Heisenberg limit -- are still possible with a special class of entangled states in the ideal lossless scenario. These states belong to a decoherence free subspace where entanglement is passively protected. Our work pave the way to the full exploitation of entanglement in precision measurements in presence of strong phase noise.
