Entanglement of two distant Bose-Einstein condensates by detection of Bragg-scattered photons

We show that it is possible to generate entanglement between two distant Bose-Einstein condensates by detection of Hanbury Brown-Twiss type correlations in photons Bragg-scattered by the condensates. Upon coincident detection of two photons by two detectors, the projected joint state of two condensates is shown to be non-Gaussian. We verify the existence of entanglement by showing that the partially transposed state is negative. Further we use the inequality in terms of higher order moments to confirm entanglement. Our proposed scheme can be generalized for multiple condensates and also for spinor condensates with Bragg scattering of polarized light with the latter capable of producing hyper entanglement.