  We numerically investigate mixtures of two interacting bosonic species with
unequal parameters in one-dimensional optical lattices. In large parameter
regions full phase segregation is seen to minimize the energy of the system,
but the true ground state is masked by an exponentially large number of
metastable states characterized by microscopic phase separation. The ensemble
of these quantum emulsion states, reminiscent of emulsions of immiscible
fluids, has macroscopic properties analogous to those of a Bose glass, namely a
finite compressibility in absence of superfluidity. Their metastability is
probed by extensive quantum Monte Carlo simulations generating a rich
correlated stochastic dynamics. The tuning of the repulsion of one of the two
species via a Feshbach resonance drives the system through a quantum phase
transition to the superfluid state.
