employed two forms of simulation cell; a rhomboidal and square box, giving triangular and square tilings respectively in momentum space. Both geometries gave quantitatively similar results. A triangular lattice has the densest possible tiling of momentum points in 2D, giving the closest to circular Fermi surfaces and thereby minimizing finite size effects [@finitesizeeffect; @simdark]. This was confirmed by varying the number of particles simulated in our DMC studies varied from 26 to 164, which compares favourably with DMC studies conducted on other systems [@dmcN1; @dmcN2]. Finally, in the non-interacting and balanced system limits the results obtained compared favourably to known analytical results in the thermodynamic limit. Therefore, in these paradigmatic systems our simulations were free of finite size effects.

Results {#sec:results}
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Spin-balanced BCS state {#subsec:bcscf}
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![Plot of the condensate fraction in pair-momentum space for the spin-balanced case with 37 fermions of each species. The wavevectors are scaled in units of the reciprocal lattice vector $G$ and black lines denote the $q$-space grid.[]{data-label="bcscfplot"}](1_1){width="0.9\linewidth"}

We start from the well-established spin-balanced BCS system to confirm the accuracy of our simulations, and later explore imbalance. To build our investigation from a solid platform, we first study a spin-balanced system with 37 spin 