  A binary mixture of interacting Bose-Einstein condensates (BEC) in the
presence of fragmentation-driving external lattice potentials forms two
interdependent mean-field lattices made of each component. These effective
mean-field lattices, like ordinary optical lattices, can induce additional
fragmentation and phase coherence loss of BECs between lattice sites. In this
study, we consider the nonequilibrium dynamics of two hyperfine states of
one-dimensional Bose-Einstein condensates, subjected to state-dependent optical
lattices. Our numerical calculations using the truncated Wigner approximation
(TWA) show that phase coherence in a mixture of two-component BECs can be lost
not just by optical lattices, but by mean-field lattices gradually formed by
other components, and we reveal that such an effect of internal mean-field
lattices, however, is limited, contrary to external optical lattices, in regard
to phase decoherence.
