up and spin down fermions. We select a scattering length $a=5.6{r_\mathrm{s}}$ and effective range ${r_\mathrm{e}}=0$ to ensure that the superconducting coherence length is less than the size of the simulation cell.

The accumulated condensate fraction is shown in Fig. \[bcscfplot\]. The condensate fraction at $q=0$ was 8 sample standard deviations above zero while those at every other $q$ point were within 2 sample standard deviations of zero. The reduction in energy of the interacting system compared to the non-interacting system meanwhile was 0.54 ${E_\mathrm{F}}$ which agrees with that obtained from analytic calculation [@2dscaverhaar84; @fermigasreview] and other numerical studies [@shi]. The results obtained for the spin-balanced case are therefore in line with theoretical expectations of BCS theory [@bcs] and we proceed with confidence in the veracity of the simulations.

We note for completeness that the condensate fraction was also gathered for pairs of the same spin-species to confirm the presence or absence of induced p-wave superfluidity [@fflorevision3]. The values of the intra-spin condensate fraction were more than 10 orders of magnitude smaller than those for the inter-spin condensate fraction and were indistinguishable from zero at all pair momenta for both the spin-balanced case presented above and the spin-imbalanced cases discussed below.

