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arXiv:1008.3264 · Physical Review Letters

Interlayer Superfluidity in Bilayer Systems of Fermionic Polar Molecules

Alexander Pikovski, Michael Klawunn, Gora V. Shlyapnikov, Luis Santos

Published Nov 17, 2010• 111 citations
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Abstract

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-Bose-Einstein condensation crossover. We show that one can cover the entire crossover regime under current experimental conditions.

DOI
10.1103/physrevlett.105.215302

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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-Bose-Einstein condensation crossover. We show that one can cover the entire crossover regime under current experimental conditions.
We investigate the quantum and thermal phase diagram of fermionic polar molecules loaded in a bilayer trapping potential with perpendicular dipole moment. We use both a BCS-theory approach that is most reliable at weak coupling and a strong-coupling approach that considers the two-body bound dimer states with one molecule in each layer as the relevant degree of freedom. The system ground state is a Bose-Einstein condensate (BEC) of dimer bound states in the low-density limit and a paired superfluid (BCS) state in the high-density limit. At zero temperature, the intralayer repulsion is found to broaden the regime of BCS-BEC crossover and can potentially induce system collapse through the softening of roton excitations. The BCS theory and the strongly coupled dimer picture yield similar predictions for the parameters of the crossover regime. The Berezinskii-Kosterlitz-Thouless transition temperature of the dimer superfluid is also calculated. The crossover can be driven by many-body effects and is strongly affected by the intralayer interaction which was ignored in previous studies.
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 interlayer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one where 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 interlayer 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 signaled by a sudden drop in the superfluid fraction of the system.
We study the BCS superfluid transition in a single-component fermionic gas of dipolar particles loaded in a tight bilayer trap, with the electric dipole moments polarized perpendicular to the layers. Based on the detailed analysis of the interlayer scattering, we calculate the critical temperature of the interlayer superfluid pairing transition when the layer separation is both smaller (dilute regime) and on the order or larger (dense regime) than the mean interparticle separation in each layer. Our calculations go beyond the standard BCS approach and include the many-body contributions resulting in the mass renormalization, as well as additional contributions to the pairing interaction. We find that the many-body effects have a pronounced effect on the critical temperature and can either decrease (in the very dilute limit) or increase (in the dense and moderately dilute limits) the transition temperature as compared to the BCS approach.
Recent experimental progress in producing ultracold polar molecules with a net electric dipole moment opens up possibilities for realizing quantum phases governed by the long-range and anisotropic dipole-dipole interactions. In this work we predict the existence of experimentally observable broken-symmetry states with spontaneous interlayer coherence in cold polar molecule bilayers. These exotic states, which are manifestations of collective bilayer quantum entanglement, appear due to strong repulsive interlayer interactions and exhibit properties of superfluids, ferromagnets, and excitonic condensates.
We study the zero temperature phase diagram of an imbalanced bilayer of dipolar fermions. We consider perpendicularly aligned identical dipoles in two layers and investigate the effect of population imbalance on the ground state phase at different layer spacings and average densities. The attractive part of the interlayer interaction could lead to the BEC-BCS crossover and the Fermi surface mismatch between two layers results in interesting uniform and nonuniform superfluid phases, which we have investigated here using the BCS mean-field theory together with the superfluid-mass density criterion. The density imbalance reduces the pairing gap. At low densities, where the system is on the BEC side of the crossover, this reduction is quite smooth while a dense system rapidly becomes normal at intermediate density polarizations. Stable homogeneous superfluidity is predicted to appear on the phase diagram when the dipolar length exceeds both the layer spacing and the average intralayer distance between dipoles, a regime which should be readily accessible experimentally. This homogeneous superfluid phase becomes unstable at intermediate densities and layer spacings. We have also examined that these uniform and inhomogeneous superfluid phases survive when the effects of intralayer screenings are also incorporated in the formalism.
We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. Because of the competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high-temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light-scattering experiments to detect dimerization.