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

Abstract

By using a well established 'ab initio' theoretical approach developed in the past to quantitatively study the superconductivity of condensed matter systems, based on the Kohn-Sham Density Functional theory, I study the superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional layers of fermionic dipolar molecules, where the pairing mechanism leading to superfluidity is provided by the inter-layer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one were the fermions in each layer are confined by a square optical lattice are studied at half filling conditions, and for different values of the strength of the confining optical potential. The T=0 results for the homogeneous system are found to be in excellent agreement with Diffusion Monte Carlo results. The superfluid transition temperature in the BCS region is found to increase, for a given inter-layer coupling, with the strength of the confining optical potential. A transition occurs at sufficiently small interlayer distances, where the fermions becomes localized within the optical lattice sites in a square geometry with an increased effective lattice constant, forming a system of localized composite bosons. This transition should be signalled by a sudden drop in the superfluid fraction of the system.

Superfluid and supersolid phases in optical lattices in two dimensions

“…Besides the experiments performed in cuprates, metals and He 4 , the study of the second order phase transitions referred above can also be addressed from the ultracold atomic physics area, either experimentally [6,7,8,9,10] or theoretically [11,12,13,14,15]. As its is well known those systems are excellent candidates to simulate the physics of superconductors because of the analogies existent among electrically charged materials having null resistance and the neutral ultracold gases having zero viscosity.…”

Supersolid phases of dipolar fermions in a two-dimensional-lattice bilayer array

“…However, at finite temperature, the distribution of the density profile remains homogeneous at the center of the trap, while the gap structure shows a decreasing ratio as temperature is increased until they vanishes at a temperature of k B T /t = 0.28. In previous studies [16,17] reported a BCS superfluid phase in the weakly interacting regime while occurring formation of dimers in the strong interaction regime, leading those dimers to a Bose superfluid. In the present work we focus on the BCS superfluid to DW-Supersolid phase transition.…”

“…There is however an alternative way of handling either the range and direction of interactions in ultracold neutral gases, which is by confining dipolar atoms or molecules in optical lattices. As it has been shown from the theoretical perspective, the combination of both, the long range anisotropic character of dipolar interactions and the controllable lattice structure where the atoms/molecules lie, make the many-body physics becomes very rich [11][12][13][14].In this work we consider a model proposed previously [15][16][17] to demonstrate that ordered density wave (DW), SS and SF phases can be accessed by changing the external fields that set the system. In Fig.…”

Density-wave instability and collective modes in a bilayer system of antiparallel dipoles

“…The ground state properties and instabilities of fermionic bilayers have been studied within the Hartree-Fock [32][33][34] as well as STLS methods [35]. The QMC simulations [36], as well as DFT calculations [37], have been employed to study the crossover from BEC to Bardeen-Cooper-Schrieffer state too. For bosonic bilayers, on the other hand, Hufnagl and Zillich [38] have used the hypernetted-chain (HNC) approximation to calculate the ground-state quantities of a bilayer system of tilted dipolar bosons.…”