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arXiv:1405.7588 · Physical Review A

Fixed-node diffusion Monte Carlo study of the BCS-BEC crossover in a bilayer system of fermionic dipoles

N. Matveeva, S. Giorgini

Published Nov 17, 2014• 19 citations
arXivHTMLPDF

Abstract

We investigate the BCS-BEC crossover in a bilayer system of fermionic dipoles at zero temperature using the fixed-node diffusion Monte Carlo technique. The dipoles are confined on two parallel planes separated by a distance $\ensuremath{\lambda}$ and are aligned perpendicular to the planes by an external field. The interlayer pairing, which is responsible for the superfluid behavior of the system, crosses from a weak- to a strong-coupling regime by reducing the separation distance $\ensuremath{\lambda}$. For a fixed in-plane density equal in the two layers, we calculate the ground-state energy, the chemical potential, the pairing gap, and the quasiparticle dispersion as a function of the interlayer separation. At large $\ensuremath{\lambda}$ one recovers the ground-state energy of a single layer of fermions, and at small $\ensuremath{\lambda}$ one recovers that of a single layer of composite bosons with twice the particle mass and the dipole moment. The superfluid gap varies from the exponentially small BCS result to half of the large two-body binding energy in the Bose-Einstein condensate (BEC) regime of strong interlayer pairing. Results are compared with the predictions of the simplest mean-field theory valid in the low-density limit, and deviations are observed both in the BCS regime, where in-plane repulsions are important, and in the BEC regime, where the mean-field approach fails to describe the physics of composite dipolar bosons.

DOI
10.1103/physreva.90.053620

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We investigate the BCS-BEC crossover in a bilayer system of fermionic dipoles at zero temperature using the fixed-node diffusion Monte Carlo technique. The dipoles are confined on two parallel planes separated by a distance \ensuremathλ\ensuremath{\lambda}\ensuremathλ and are aligned perpendicular to the planes by an external field. The interlayer pairing, which is responsible for the superfluid behavior of the system, crosses from a weak- to a strong-coupling regime by reducing the separation distance \ensuremathλ\ensuremath{\lambda}\ensuremathλ. For a fixed in-plane density equal in the two layers, we calculate the ground-state energy, the chemical potential, the pairing gap, and the quasiparticle dispersion as a function of the interlayer separation. At large \ensuremathλ\ensuremath{\lambda}\ensuremathλ one recovers the ground-state energy of a single layer of fermions, and at small \ensuremathλ\ensuremath{\lambda}\ensuremathλ one recovers that of a single layer of composite bosons with twice the particle mass and the dipole moment. The superfluid gap varies from the exponentially small BCS result to half of the large two-body binding energy in the Bose-Einstein condensate (BEC) regime of strong interlayer pairing. Results are compared with the predictions of the simplest mean-field theory valid in the low-density limit, and deviations are observed both in the BCS regime, where in-plane repulsions are important, and in the BEC regime, where the mean-field approach fails to describe the physics of composite dipolar bosons.
In a bilayer system of fermionic dipoles, full control over the strength of the attractive interactions between two layers leads to the BCS-BEC crossover. Here, using the BCS mean-field theory, we study such a crossover in symmetric bilayers of ultracold dipolar fermions with their dipole moments perpendicular to layers. In particular, we investigate how the pairing between two layers and the many-body screening of interlayer interaction affect each other. We compare results for pairings obtained with three different approximations for the interlayer interactions, namely, bare dipole-dipole interaction, the random-phase approximation for screening obtained in the normal phase, and the self-consistent superfluid phase screening within the random-phase approximation. We find that at weak couplings the screening further suppresses the pairing, while at strong couplings, the screening is suppressed due to the pairing gap in the quasiparticle spectrum. Therefore a self-consistent treatment of both screening and pairing on equal footings is necessary for obtaining the correct picture of the phase diagram and order parameter at both small and large layer spacings and densities. We also notice that the signals of highly speculated density-wave instability in dipolar bilayers only appear in the normal phase screened interlayer interaction.
We consider the ground state of a bilayer system of dipolar bosons, where dipoles are oriented by an external field in the direction perpendicular to the parallel planes. Quantum Monte Carlo methods are used to calculate the ground-state energy, the one-body and two-body density matrix, and the superfluid response as a function of the separation between layers. We find that by decreasing the interlayer distance for fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from a single-particle to a pair superfluid. The single-particle superfluid is characterized by a finite value of both the atomic condensate and the super-counterfluid density. The pair superfluid phase is found to be stable against formation of many-body cluster states and features a gap in the spectrum of elementary excitations.
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 investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T = 0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. We also consider the highly polarized gas and the competition between a polaronic and a molecular picture.
We study the ground state of a bilayer system of dipolar bosons with dipoles oriented by an external field perpendicularly to the two parallel planes. By decreasing the interlayer distance, for a fixed value of the strength of the dipolar interaction, the system undergoes a quantum phase transition from an atomic to a pair superfluid. We investigate the excitation spectrum on both sides of this transition by using two microscopic approaches. Quantum Monte Carlo methods are employed to obtain the static structure factors and intermediate scattering functions in imaginary time. The dynamic response is calculated using both the correlated basis functions (CBF) method and the approximate inversion of the Laplace transform of the quantum Monte Carlo imaginary time data. In the atomic phase, both the density and spin excitations are gapless. However, in the pair-superfluid phase a gap opens in the excitation energy of the spin mode. For small separation between layers, the minimal spin excitation energy equals the binding energy of a dimer and is twice the gap value.