  In a two-mode Bose-Josephson junction formed by a binary mixture of ultracold
atoms, macroscopic superpositions of phase states are produced during the time
evolution after a sudden quench to zero of the coupling amplitude. Using
quantum trajectories and an exact diagonalization of the master equation, we
study the effect of one-, two-, and three-body atom losses on the
superpositions by analyzing separately the amount of quantum correlations in
each subspace with fixed atom number. The quantum correlations useful for atom
interferometry are estimated using the quantum Fisher information. We identify
the choice of parameters leading to the largest Fisher information, thereby
showing that, for all kinds of loss processes, quantum correlations can be
partially protected from decoherence when the losses are strongly asymmetric in
the two modes.
