In a two-mode Bose-Josephson junction formed by a binary mixture of ultracoldatoms, macroscopic superpositions of phase states are produced during the timeevolution after a sudden quench to zero of the coupling amplitude. Usingquantum trajectories and an exact diagonalization of the master equation, westudy the effect of one-, two-, and three-body atom losses on thesuperpositions by analyzing separately the amount of quantum correlations ineach subspace with fixed atom number. The quantum correlations useful for atominterferometry are estimated using the quantum Fisher information. We identifythe choice of parameters leading to the largest Fisher information, therebyshowing that, for all kinds of loss processes, quantum correlations can bepartially protected from decoherence when the losses are strongly asymmetric inthe two modes.
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