Strongly paired fermions: Cold atoms and neutron matter

Experiments with cold Fermi atoms can be tuned to probe strongly-interacting fluids that are very similar to the low-density neutron matter found in the crusts of neutron stars. In contrast to traditional superfluids and superconductors, matter in this regime is very strongly paired, with gaps of the order of the Fermi energy. We compute the $T=0$ equation of state and pairing gap for cold atoms and low-density neutron matter as a function of the Fermi momentum times the scattering length. Results of quantum Monte Carlo calculations show that the equations of state are very similar. The neutron matter pairing gap at low densities is found to be very large but, except at the smallest densities, significantly suppressed relative to cold atoms because of the finite effective range in the neutron-neutron interaction.

Figure 1

Zero-temperature equation of state for cold atoms and neutron matter. Near zero density we show the analytical expansion of the ground-state energy of a normal fluid, and at high density we show the cold atom result at unitarity ($k_{F}a=\infty$, arrow). QMC calculations are shown as circles and squares for neutron matter and cold atoms, respectively.

Figure 2

Neutron matter pairing gap at $k_{F}a=-10$ versus particle number in periodic boundary conditions, BCS and QMC calculations.

Figure 3

Superfluid pairing gap versus $k_{F}a$ for cold atoms ($r_e\approx 0$) and neutron matter ($|r_e/a|\approx 0.15$). BCS (solid lines) and QMC results (points) are shown.

Figure 4

Superfluid pairing gap versus $k_{F}a$ for neutron matter compared to previous results.