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Fixed-node diffusion Monte Carlo study of the BCS-BEC crossover in a bilayer system of fermionic dipoles

We investigate the BCS-BEC crossover in a bilayer system of fermionic dipoles at zero temperature using the fixed-node diffusion Monte Carlo technique. The dipoles are confined on two parallel planes separated by a distance $λ$ and are aligned perpendicular to the planes by an external field. The interlayer pairing, which is responsible for the superfluid behavior of the system, crosses from a weak to a strong-coupling regime by reducing the separation distance $λ$. For a fixed in-plane density, equal in the two layers, we calculate the ground-state energy, the chemical potential, the pairing gap and the quasiparticle dispersion as a function of the interlayer separation. At large $λ$ one recovers the ground-state energy of a single layer of fermions and at small $λ$ the one of a single layer of composite bosons with twice the particle mass and the dipole moment. The superfluid gap varies instead from the exponentially small BCS result to half of the large two-body binding energy in the BEC regime of strong interlayer pairing. Results are compared with the predictions of the simplest mean-field theory valid in the low-density limit and deviations are observed both in the BCS regime, where in-plane repulsions are important, and in the BEC regime where the mean-field approach fails to describe the physics of composite dipolar bosons.