Many-particle entanglement, Einstein-Podolsky-Rosen steering and Bell correlations in Bose-Einstein condensates

According to quantum mechanics, the results of measurements performed on different systems can show correlations that are stronger than what is classically possible. Three important types of nonclassical correlations that have been identified are entanglement (nonseparability), Einstein-Podolsky-Rosen correlations (steering) and Bell correlations (nonlocality). Apart from shedding light on the foundations of quantum theory and on how nature behaves, they represent different resources for applications that are inaccessible by classical means. While such correlations have been extensively investigated in systems composed of a few particles, their role in many-body systems is much less explored.
In this thesis I present both experimental and theoretical results on quantum correlations in many-body systems. Specifically, I report experiments where we prepare a Bose-Einstein condensate of approximately 600 Rubidium-87 atoms on an atom chip in a spin squeezed state, and analyze the correlations between the constituent atoms. First, I show state-of-the-art detection of entanglement, and of its depth, using collective measurements. For a state with a Wineland spin squeezing parameter of -6.8 dB we conclude an entanglement depth of approximately 56 particles. Then, I describe the first detection of Bell correlations in a many-body system. This result was enabled by deriving a witness for Bell correlations which involves only collective measurements on the atomic ensemble. Moreover, we present a sufficient criterion to close the statistics loop-hole, derive additional multi-partite inequalities and witnesses detecting Bell correlations in a larger class of states, and report ways to quantify their depth. Applying these to our experimental data, we conclude the presence of at least 6-partite Bell correlations. As a new tool, we provide a method to detect Bell correlations in experimental data by running a computer algorithm consisting in a hierarchy of semi-definite programs bounding the set of classical correlations.
Finally, I present the first observation of Einstein-Podolsky-Rosen steering between spatially separated regions in an ensemble of massive particles. This result was obtained by high resolution imaging of an expanded spin-squeezed Bose-Einstein condensate in order to measure spin correlations between spatially separated parts.
Our experimental and theoretical studies of quantum correlations in many-body systems are an important step towards exploring the predictions of quantum mechanics in macroscopic systems, and could enable a variety of quantum information tasks. Our experiments show that Bose-Einstein condensates on atom chips are an ideal platform for the implementation and investigation of such many-body quantum correlations.