Bell Correlations In A Split Two-Mode-Squeezed Bose-Einstein Condensate

Spin squeezed states are an example of a multi partite entangled state which constitute an essential resource for quantum technologies such as quantum computing,quantum communication,and quantum metrology.In this thesis,we study two spatially separated twomode-spin-squeezed Bose-Einstein condensates(BECs),We introduced method of preparing a desired state,to witness a Bell correlations,and propose several strategies for observing a violation of the Clauser-Horne-Shimony-Holt(CHSH)Bell inequality.Firstly,to prepare the Bell-correlated state,spin-changing collisions are used to first prepare a two-mode squeezed BEC.This is then split into two BECs by controlling the spatial wavefunction such as modifying the trapping potential.Finally,spin-changing collisions are also applied locally,to compensate local squeezing terms.Secondly,the correlators appearing in the inequality are evaluated using three different approaches.In the first approach,correlators are estimated using normalized expectation values of number operators,in a similar way to evaluating continuous-variable Bell inequalities.An improvement to this approach is developed using the sign-binning of total spin measurements,which allows for the construction of two-outcome measurements and violations of the CHSH inequality without auxiliary assumptions.We show a third approach where maximal violations of the CH inequality can be obtained by assigning zero values to local vacuum outcomes under a no-enhancement assumption.The effect of decoherence by loss and imperfect detection efficiency is investigated and the observed violations are found to be robust in the presence of noise.