  Quantum Monte Carlo methods have proven to be valuable in the study of
strongly correlated quantum systems, particularly nuclear physics and cold
atomic gases. Historically, such ab initio simulations have been used to study
properties of light nuclei, including spectra and form factors, low-energy
scattering, and high-momentum properties including inclusive scattering and
one- and two-body momentum distributions. More recently they have been used to
study the properties of homogeneous and inhomogeneous neutron matter and cold
atomic gases. There are close analogies between these seemingly diverse
systems, including the equation of state, superfluid pairing, and linear
response to external probes. In this paper, we compare and contrast results
found in nuclear and cold atom physics. We show updated lattice results for the
energy of the homogeneous unitary Fermi gas and comparisons with neutron
matter, as well as for the dependence of the cold atom energy on the mass ratio
between paired particles, which yields insights on the structure of the ground
state. We also provide new lattice and continuum results for the harmonically
trapped unitary gas, again comparing neutron matter and cold atoms.
