Bell correlations are a foundational demonstration of how quantum entanglement contradicts the classical notion of local realism. Rigorous validation of quantum nonlocality have only been achieved ...between solid-state electron spins, internal states of trapped atoms, and photon polarisations, all weakly coupling to gravity. Bell tests with freely propagating massive particles, which could provide insights into the link between gravity and quantum mechanics, have proven to be much more challenging to realise. Here we use a collision between two Bose-Einstein condensates to generate spin entangled pairs of ultracold helium atoms, and measure their spin correlations along uniformly rotated bases. We show that correlations in the pairs agree with the theoretical prediction of a Bell triplet state, and observe a quantum mechanical witness of Bell correlations with Formula: see text significance. Extensions to this scheme could find promising applications in quantum metrology, as well as for investigating the interplay between quantum mechanics and gravity.
We review the Bogoliubov theory in the context of recent experiments, where atoms are scattered from a Bose-Einstein condensate into two well-separated regions. We find the full dynamics of the ...pair-production process, calculate the first and second order correlation functions and show that the system is ideally number-squeezed. We calculate the Fisher information to show how the entanglement between atoms from the two regions changes in time. We also provide a simple expression for the lower bound of the useful entanglement in the system in terms of the average number of scattered atoms and the number of modes they occupy. We then apply our theory to a recent 'twin-beam' experiment (Bücker et al 2011 Nature Phys. 7 608). The only numerical step of our semi-analytical description can be easily solved and does not require implementation of any stochastic methods.
We derive the asymptotic maximum-likelihood phase estimation uncertainty for any interferometric protocol where the positions of the probe particles are measured to infer the phase, but where ...correlations between the particles are not accessible. First, we apply our formula to the estimation of the phase acquired in the Mach-Zehnder interferometer and recover the well-known momentum formula for the phase sensitivity. Then, we apply our results to interferometers with two spatially separated modes, which could be implemented with a Bose-Einstein condensate trapped in a double-well potential. We show that in a simple protocol which estimates the phase from an interference pattern, a sub-shot-noise phase uncertainty of up to Δθ∝N−2 3 can be achieved. One important property of this estimation protocol is that its sensitivity does not depend on the value of the phase θ, contrary to the sensitivity given by the momentum formula for the Mach-Zehnder transformation. Finally, we study the experimental implementation of the above protocol in detail, by numerically simulating the full statistics as well as by considering the main sources of detection noise, and argue that the shot-noise limit could be surpassed with current technology.
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