  We investigate the phase diagram of bosons interacting via Feshbach-resonant
pairing interactions in a one-dimensional lattice. Using large scale density
matrix renormalization group (DMRG) and field theory techniques we explore the
atomic and molecular correlations in this low-dimensional setting. We provide
compelling evidence for an Ising deconfinement transition occurring between
distinct superfluids and extract the Ising order parameter and correlation
length of this unusual superfluid transition. This is supported by results for
the entanglement entropy which reveal both the location of the transition and
critical Ising degrees of freedom on the phase boundary.
