  We explore the zero-temperature phase diagram of bosons interacting via
Feshbach resonant pairing interactions in one dimension. Using DMRG (Density
Matrix Renormalization Group) and field theory techniques we characterize the
phases and quantum phase transitions in this low-dimensional setting. We
provide a broad range of evidence in support of an Ising quantum phase
transition separating distinct paired superfluids, including results for the
energy gaps, correlation functions and entanglement entropy. In particular, we
show that the Ising correlation length, order parameter and critical properties
are directly accessible from a ratio of the atomic and molecular two-point
functions. We further demonstrate that both the zero-momentum occupation
numbers and the visibility are in accordance with the absence of a purely
atomic superfluid phase. We comment on the connection to recent studies of
boson pairing in a generalized classical XY model.
