  Low-density neutron matter has been studied extensively for many decades,
with a view to better understanding the properties of neutron-star crusts and
neutron-rich nuclei. Neutron matter is beyond experimental control, but in the
past decade it has become possible to create systems of fermionic ultracold
atomic gases in a regime close to low-density neutron matter. In both these
contexts pairing is significant, making simple perturbative approaches
impossible to apply and necessitating ab initio microscopic simulations. Atomic
experiments have also probed polarized matter. In this work, we study
population-imbalanced neutron matter (possibly relevant to magnetars and to
density functionals of nuclei) arriving at the lowest-energy configuration to
date. For small to intermediate relative fractions the system turns out to be
fully normal, while beyond a critical polarization we find phase coexistence
between a partially polarized normal neutron gas and a balanced superfluid gas.
As in cold atoms, a homogeneous polarized superfluid is close to stability but
not stable with respect to phase separation. We also study the dependence of
the critical polarization on the density.
