  Ultracold atomic gases and low-density neutron matter are unique in that they
exhibit pairing gaps comparable to the Fermi energy which in this sense are the
largest in the laboratory and in nature, respectively. This strong pairing
regime, or the crossover between BCS and BEC regimes, requires non-perturbative
treatments. We describe Quantum Monte Carlo results useful to understand the
properties of these systems, including infinite homogeneous matter and trapped
inhomogeneous gases.
