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

Abstract

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 one recovers that of a single layer of composite bosons with twice the particle mass and the dipole moment. The superfluid gap varies from the exponentially small BCS result to half of the large two-body binding energy in the Bose-Einstein condensate (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.

Kohn-Sham approach to Fermi gas superfluidity: The bilayer of fermionic polar molecules

“…(3) in Ref. 24). These corrections (once the energy of a singlelayer dipolar Fermi liquid , E/N = 0.6931 ǫ F [38], has been subtracted from the DMC results) can be written in the form:Ẽ…”

“…Corrections to the mean-field approximation for the inter-layer interaction energy are incorporated in the correlation energy functionalẼ C . Informations about this term come from the results of DMC calculations for the homogeneous bilayer system [24], where the corrections to mean-field results have been computed as a function of k F λ (see Fig. (3) in Ref.…”

“…Additional interest in bilayers of fermions is due to the strong analogies with the physics of electron-hole bilayers in semiconductor heterostructures [23]. The BCS-BEC crossover in a (homogeneous) bilayer of fermionic dipoles has been recently studied at zero-temperature by means of Diffusion Monte Carlo (DMC) simulations [24].…”

“…[37] to study the superfluid behavior of a homogeneous bilayer of (polarized) dipolar fermionic molecules, for which accurate T=0 results exist to compare with, obtained by using QMC simulations [24]. To underline the capabilities of the method to treat in particular inhomogeneous systems (which are often difficult to study using QMC methods), I will also calculate the finite-temperature superfluid properties of this system in the presence of an additional external potential which simulates an optical 2D square lattice acting on the dipoles in each layer.…”

“…I will compute, throughout the BCS-BEC crossover, the normal-state density, the superconducting gap, the condensate fraction and the superfluid transition temperature, and their changes as a function of the interlayer distances and the depth of the confining optical potential wells. The exchangecorrelation energy of the homogeneous system, which is an essential ingredient of the KS-DFT method, will be provided by virtually exact Diffusion Monte Carlo calculations [24,38].…”