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arXiv:1505.03811 · Annalen der Physik

Superfluidity of a dipolar Fermi gas in 2D optical lattices bilayer

Arturo Camacho-Guardian, R. Paredes

Published Jul 26, 2016• 7 citations
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Abstract

Ultracold Fermi molecules lying in 2D square optical lattices bilayers with its dipole moment perpendicularly aligned to the layers, having interlayer finite range s‐wave interactions, are shown to form superfluid phases, both, in the Bardeen, Cooper and Schrieffer (BCS) regime of Cooper pairs, and in the condensate regime of bound dimeric molecules. We demonstrate this result using a functional integral scheme within the Ginzburg‐Landau theory. For the deep Berezinskii‐Kosterlitz‐Thouless (BKT) phase transition, we predict critical temperatures around 5nK and 20nK for 23Na40K and OH molecules, which are within reach of current experiments [J. W. Park, S. Will and M. Zwierlein, Phys. Rev. Lett. 114, 205302 (2015)]. image

DOI
10.1002/andp.201600101

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•Jan 1, 2006•0 citations
Ultracold Fermi molecules lying in 2D square optical lattices bilayers with its dipole moment perpendicularly aligned to the layers, having interlayer finite range s‐wave interactions, are shown to form superfluid phases, both, in the Bardeen, Cooper and Schrieffer (BCS) regime of Cooper pairs, and in the condensate regime of bound dimeric molecules. We demonstrate this result using a functional integral scheme within the Ginzburg‐Landau theory. For the deep Berezinskii‐Kosterlitz‐Thouless (BKT) phase transition, we predict critical temperatures around 5nK and 20nK for 23Na40K and OH molecules, which are within reach of current experiments [J. W. Park, S. Will and M. Zwierlein, Phys. Rev. Lett. 114, 205302 (2015)]. image
Abstract The superfluid phases in an ultracold gas of dipolar Fermi molecules lying in two parallel square lattices in 2D are investigated. As shown by a two‐body study, dipole moments oriented in opposite directions in each layer are the key ingredients in our mean‐field analysis from which unconventional superfluidity is predicted. The phase diagram summarizes our findings: stable and metastable superfluid phases appear as a function of both, the dipole–dipole interaction coupling parameter and filling factor. A first‐order phase transition, and thus a mixture of superfluid phases at different densities, is revealed from the coexistence curves in the metastable region. The model predicts that these superfluid phases can be observed experimentally at 10 nK in molecules of NaK confined in optical lattices of size nm. Other routes to reach higher temperatures require the use of subwavelength confinement technique.
We investigate the formation of Cooper pairs, bound dimers and the dimer‐dimer elastic scattering of ultracold dipolar Fermi molecules confined in a 2D optical lattice bilayer configuration. While the energy and their associated bound states are determined in a variational way, the correlated two‐molecule pair is addressed as in the original Cooper formulation. We demonstrate that the 2D lattice confinement favors the formation of zero center mass momentum bound states. Regarding the Cooper pairs binding energy, this depends on the molecule populations in each layer. Maximum binding energies occur for non‐zero (zero) pair momentum when the Fermi system is polarized (unpolarized). We find an analytic expression for the dimer‐dimer effective interaction in the deep BEC regime. The present analysis represents a route for addressing the BCS‐BEC crossover in dipolar Fermi gases confined in 2D optical lattices within the current experimental panorama.
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.
This work addresses the study of superfluid and supersolid phases of dipolar Fermi molecules lying in a two dimensional space. The prediction of these phases, performed within a mean field analysis, results from proposing a model in which interacting Fermi molecules are confined in a bilayer array of parallel lattices with square symmetry. As a result of the repulsive intralayer and attractive interlayer interactions between dipolar molecules, a checkerboard pattern and a paired superfluid regimes can emerge. The supersolid phase is identified as the spatial coexistence of density ordered and superfluid phases. The model here proposed can be implemented within the current experimental capabilities as a function of the interlayer separation and the application of an external electric field varying the dipolar interaction between molecules.
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.
This thesis concerns ultracold two-dimensional atomic gases and the associated novel superfluid phases in an optical lattice subjected to staggered rotations. In the first part, we study the Berezinskii-Kosterlitz-Thouless (BKT) transition in a two-dimensional Bose gas. Motivated by recent experiments on the cold gas in the BKT regime, we employ a modified Popov theory and a renormalization group theory to describe the system. The two-dimensional renormalization group flow equations display unique features, which we interpret as precursors of the BKT physics. We further calculate higher correlation functions close to the BKT transition, which can serve as observables for detecting effects beyond mean-field. Finally, we obtain the density profile under the conditions of the experiment performed in the group of Dalibard in Paris, France. In the second part of the thesis, we study a recent experimental proposal of a time-dependent optical lattice with staggered rotations. We show that in the tight-binding regime, the system can be effectively described by a (Bose-)Hubbard model subjected to an artificial staggered magnetic field. The staggered magnetic field (flux) in the lattice leads to conical points in the band structure which possesses distinct minima for different strength, and can give rise to Dirac-like dispersions. For bosons, we show that besides the homogenous superfluid phase, a staggered-vortex superfluid phase is stabilized for large flux values. We show that the staggered flux renormalizes the phase boundary and find a multi-critical point separating the two superfluid phases and the Mott insulating phase. Finally, the full phase diagram of the generalized Bose-Hubbard model at zero temperature is determined. We then generalize the model for a mixture of ultracold bosons and spin-1/2 fermions. By using the Bogoliubov theory for the bosonic sector, we show that the bosonic superfluid mediates attractive interactions between fermions up to the nearest-neighbor site. The resulting model is an extended Hubbard model in the presence of a staggered magnetic field, where the on-site and the nearest-neighbor attractive interactions can be tuned independently. We then employ the Bardeen-Cooper-Schrieffer theory for superconductivity, by considering an on-site pairing order parameter competing with a nearest-neighbor resonating-valence-bond order parameter. Due to conical points in the energy band, the system possesses quantum critical property and the resulting phase diagram displays features which are strikingly similar to that of high-critical-temperature superconductors or heavy-fermion superconductors.