Ultracold atoms as quantum simulators for neutron matter

Progress in atomic physics has enabled the experimental realization
of the "Unitary Fermi Gas". This is a system of non-relativistic spin 1/2
fermions interacting via a potential tuned to zero range but infinite
scattering length. The emergent quantum many body system is a scale
invariant, strongly correlated quantum fluid. It is linked, by universality,
to other systems in nature, in particular dilute neutron matter. Static
properties of the unitary gas are accessible by imaginary time quantum
Monte Carlo calculations on classical computers, but the real time response
is not. I review some old result on the equation of state and transport
properties of the unitary gas, discuss more recent work on linear response,
and present some goals for the future.