  We study two-component atomic gas mixtures in one dimension involving both
bosons and fermions. When the inter-species interaction is attractive, we
report a rich variety of coherent ground-state phases that vary with the
intrinsic and relative strength of the interactions. We avoid any artifacts of
lattice discretization by developing a novel implementation of a continuous
matrix product state ansatz for mixtures and priorly demonstrate the validity
of our approach on the integrable point that exists for mixtures with equal
masses and interactions (Lai-Yang model) where we find that the ansatz
correctly and systematically converges towards the exact results.
