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We propose and analyse a pumped Bose-Hubbard dimer as a source ofcontinuous-variable Einstein-Podolsky-Rosen (EPR) steering with non-Gaussianstatistics. We use the truncated Wigner representation to calculate third andfourth order cumulants, finding clear signals of non-Gaussianity. We alsocalculate the products of inferred quadrature variances which indicate thatstates demonstrating the EPR paradox are present. Our proposed experimentalconfiguration is extrapolated from current experimental techniques and addsanother possibility to the current toolbox of quantum atom optics.

Pseudo steady-state non-Gaussian EPR-steering of massive particles in pumped and damped Bose-Hubbard dimers