We consider fermionic polar molecules in a bilayer geometry where they are oriented perpendicularly to the layers, which permits both low inelastic losses and superfluid pairing. The dipole-dipole interaction between molecules of different layers leads to the emergence of interlayer superfluids. The superfluid regimes range from BCS-like fermionic superfluidity with a high Tc to Bose-Einstein (quasi-)condensation of interlayer dimers, thus exhibiting a peculiar BCS-BEC crossover. We show that one can cover the entire crossover regime under current experimental conditions. PACS numbers: 03.75.Ss, Ultracold gases of dipolar particles attract great interest because the dipole-dipole interaction drastically changes the nature of quantum degenerate regimes compared to ordinary short-range interacting gases [1,2]. This has been demonstrated in experiments with Bosecondensed chromium atoms which have a magnetic moment of 6µ B equivalent to an electric dipole moment of 0.05 D [3][4][5]. The recent experiments on creating polar molecules in the ground ro-vibrational state [6,7] and cooling them towards quantum degeneracy [6] have made a breakthrough in the field. For such molecules polarized by an electric field the dipole-dipole interaction is several orders of magnitude larger than for atomic magnetic dipoles. This opens fascinating prospects for the observation of new quantum phases [1,2,[8][9][10][11][12]. The main obstacle is the decay of the system due to ultracold chemical reactions, such as KRb+KRb⇒K 2 +Rb 2 found in JILA experiments [13]. These reactions are expected to be suppressed by the intermolecular repulsion in 2D geometries where the molecules are oriented perpendicularly to the plane of their translational motion [14].In this Letter we consider fermionic polar molecules in a bilayer geometry where the dipoles are oriented perpendicularly to the layers (Fig. 1), which leads to low inelastic losses and allows for the possibility of superfluid pairing. The interaction between dipoles of different layers may lead to the emergence of an interlayer superfluid, that is a superfluid 2D gas where Cooper pairs are formed by fermionic molecules of different layers. We show that the interlayer dipole-dipole interaction provides a higher superfluid transition temperature than that for 2D spin-1/2 fermions with attractive short-range interaction.Interestingly, an increase in the interlayer dipole-dipole coupling leads to a novel BCS-BEC crossover resembling that studied for atomic fermions near a Feshbach resonance [15,16]. The reason is that two dipoles belonging to different layers can always form a bound state [17]. As long as the binding energy ǫ b is much smaller than the Fermi energy E F , or equivalently the size of the interlayer two-body bound state greatly exceeds the intermolecular spacing in the {x, y} plane, the ground state of the system is the BCS-paired interlayer superfluid. Once a reduction of the interlayer spacing λ or an increase of the molecular dipole moment d by an electric field make ǫ b >> E...
Low-energy two-dimensional scattering is particularly sensitive to the existence and the properties of weakly bound states. We show that interaction potentials V (r) with vanishing zero-momentum Born approximation drrV (r) = 0 lead to an anomalously weak bound state which crucially modifies the two-dimensional scattering properties. This anomalous case is especially relevant in the context of polar molecules in bilayer arrangements.
We investigate the number fluctuations in small cells of quantum gases pointing out important deviations from the thermodynamic limit fixed by the isothermal compressibility. Both quantum and thermal fluctuations in weakly as well as highly compressible fluids are considered. For the two-dimensional (2D) superfluid Bose gas we find a significant quenching of fluctuations with respect to the thermodynamic limit, in agreement with recent experimental findings. An enhancement of the thermal fluctuations is instead predicted for the 2D dipolar superfluid Bose gas, which becomes dramatic when the size of the sample cell is of the order of the wavelength of the rotonic excitation induced by the interaction.Comment: 6 pages, 5 figure
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