BCS-BEC crossover in bilayers of cold fermionic polar molecules

We examine collective modes, stability, and BCS pairing in a quasi-two-dimensional gas of dipolar fermions aligned by an external field. By using the (conserving) Hartree-Fock approximation, which treats direct and exchange interactions on an equal footing, we obtain the spectrum of single-particle excitations and long wavelength collective modes (zero sound) in the normal phase. It appears that exchange interactions result in strong damping of zero sound when the tilting angle between the dipoles and the normal to the plane of confinement is below some critical value. In particular, zero sound cannot propagate if the dipoles are perpendicular to the plane of confinement. At intermediate coupling we find unstable modes that can lead either to collapse of the system or the formation of a density wave. The BCS transition to a superfluid phase, on the other hand, occurs at arbitrarily weak strengths of the dipole-dipole interaction, provided the tilting angle exceeds a critical value. We determine the critical temperature of the transition taking into account many-body effects as well as virtual transitions to higher excited states in the confining potential, and discuss prospects of experimental observations.

Section: Discussionmentioning

confidence: 99%

Collective modes, stability, and superfluid transition of a quasi-two-dimensional dipolar Fermi gas

Sieberer

Baranov

2011

“…Various aspects have been discussed regarding this system in literature, in particular, the emergence and beyond mean-field description of the topological p x + ip y phase for microwave-dressed polar molecules [12,19], interlayer superfluids in bilayer and multilayer systems [13,15,20,33], and the emergence of density-wave phases for tilted dipoles [17,18,[21][22][23][24]. The case of superfluid pairing for tilted dipoles in the quasi-2D geometry beyond the simple BCS approach has been discussed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Fermi liquid of two-dimensional polar molecules

Shlyapnikov

2012

We study Fermi-liquid properties of a weakly interacting two-dimensional gas of single-component fermionic polar molecules with dipole moments d oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean-field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r 3 at large distances r, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter k F r * , where k F is the Fermi momentum and r * = md 2 /h 2 is the dipole-dipole length, with m being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in k F r * and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, as it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.

“…The resulting coupling is predicted to cause superfluid behavior at sufficiently low temperatures [17][18][19][20]. Moreover, a cross-over is expected by varying the inter-layer distance, as the system evolves from the weak-coupling BCS regime of largely overlapping Cooper pairs to the strong-coupling BEC regime of composite bosons [21,22].…”

Section: Introductionmentioning

confidence: 99%

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

Ancilotto

2016

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.