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arXiv:1805.11302 · Physical Review A

Stabilizing Fulde-Ferrell-Larkin-Ovchinnikov superfluidity with long-range interactions in a mixed-dimensional Bose-Fermi system

Jonatan Melkær Midtgaard, Georg M. Bruun

Published Jul 24, 2018• 4 citations
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Abstract

We analyze the stability of inhomogeneous superfluid phases in a system consisting of identical fermions confined in two layers that are immersed in a Bose-Einstein condensate (BEC). The fermions in the two layers interact via an induced interaction mediated by the BEC, which gives rise to pairing. We present zero-temperature phase diagrams varying the chemical potential difference between the two layers and the range of the induced interaction, and show that there is a large region where an inhomogeneous superfluid phase is the ground state. This region grows with increasing range of the induced interaction and it can be much larger than for a corresponding system with a short-range interaction. The range of the interaction is controlled by the healing length of the BEC, which makes the present system a powerful tunable platform to stabilize inhomogeneous superfluid phases. We furthermore analyze the melting of the superfluid phases in the layers via phase fluctuations as described by the Berezinskii-Kosterlitz-Thouless mechanism and show that the normal, homogeneous, and inhomogeneous superfluid phases meet in a tricritical point. The superfluid density of the inhomogeneous superfluid phase is reduced by inherent gapless excitations, and we demonstrate that this leads to a significant suppression of the critical temperature as compared to the homogeneous superfluid phase.

DOI
10.1103/physreva.98.013624

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We analyze the stability of inhomogeneous superfluid phases in a system consisting of identical fermions confined in two layers that are immersed in a Bose-Einstein condensate (BEC). The fermions in the two layers interact via an induced interaction mediated by the BEC, which gives rise to pairing. We present zero-temperature phase diagrams varying the chemical potential difference between the two layers and the range of the induced interaction, and show that there is a large region where an inhomogeneous superfluid phase is the ground state. This region grows with increasing range of the induced interaction and it can be much larger than for a corresponding system with a short-range interaction. The range of the interaction is controlled by the healing length of the BEC, which makes the present system a powerful tunable platform to stabilize inhomogeneous superfluid phases. We furthermore analyze the melting of the superfluid phases in the layers via phase fluctuations as described by the Berezinskii-Kosterlitz-Thouless mechanism and show that the normal, homogeneous, and inhomogeneous superfluid phases meet in a tricritical point. The superfluid density of the inhomogeneous superfluid phase is reduced by inherent gapless excitations, and we demonstrate that this leads to a significant suppression of the critical temperature as compared to the homogeneous superfluid phase.
We calculate the phase diagram of identical fermions in a two-dimensional lattice immersed in a three-dimensional Bose-Einstein condensate (BEC). The fermions exchange density fluctuations in the BEC, which gives rise to an attractive induced interaction. The resulting zero-temperature phase diagram exhibits topological px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid phases as well as a phase separation region. We show how to use the flexibility of the Bose-Fermi mixture to tune the induced interaction, so that it maximizes the pairing between nearest-neighbor sites, whereas phase separation originating from long-range interactions is suppressed. Finally, we calculate the Berezinskii-Kosterlitz-Thouless critical temperature of the topological superfluid in the lattice and discuss experimental realizations.
We study s-wave pairing of population imbalanced Fermi atoms in quasi two dimensions using a mean field theory. At zero temperature, we map out the phase diagram in the entire Bardeen, Cooper and Schrieffer-Bose Einstein condensation (BCS-BEC) crossover region by investigating the effect of weak atom tunneling between layers. We find that the superfluid phase stabilizes as one decreases the atom tunneling between layers. This allows one to control the superfluid-normal first order phase transition by tuning a single experimental parameter. Further, we find that a tunneling induced polarized superfluid phase appears in a narrow parameter region in the BEC regime. At Finite temperatures, we use a Landau-Ginzberg functional approach to investigate the possibility of spatially inhomogeneous Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in the weakly interacting BCS limit near the tricritical point of spatially homogenous superfluid, FFLO, and normal phases. We find that the normal-FFLO phase transition is first order transition as opposed to the continues transition predicted in zero temperature theories.
We investigate the homogeneous superfluid mixtures of a Bardeen-Cooper-Schrieffer (BCS) superfluid originating from pairing two-species fermionic atoms and superfluidity stemming from condensation of bosonic atoms. By integrating out the freedoms associated with the BCS superfluid, we derive the fermion-mediated interactions between bosons, which is attractive and can be tuned from long range in the BCS region to short range in the region of Bose-Einstein condensation of molecular dimers. By analyzing the Bogoliubov spectrum and the damping rate of bosonic superfluid, we map out the phase diagram spanned by the boson-fermion mass ratio and the boson-fermion coupling strength, which consists of a phase separation region and two phase-mixing regions with and without Landau damping. The three different phases can coexist at a tricritical point, which moves toward a low boson-fermion mass ratio and a high boson-fermion scattering length as the fermion-fermion interaction strength is tuned up on the BCS side.
We show that a 2D spin-polarized Fermi gas immersed in a 3D Bose-Einstein condensate constitutes a very promising system for realizing a p_{x}+ip_{y} superfluid. The fermions attract each other via an induced interaction mediated by the bosons, and the resulting pairing is analyzed with retardation effects fully taken into account. This is further combined with Berezinskii-Kosterlitz-Thouless (BKT) theory to obtain reliable results for the superfluid critical temperature. We show that both the strength and the range of the induced interaction can be tuned experimentally, which can be used to make the critical temperature approach the maximum value allowed by general BKT theory. Moreover, this is achieved while keeping the Fermi-Bose interaction weak so that three-body losses are small. Our results show that realizing a topological superfluid with atomic Fermi-Bose mixtures is within experimental reach.
We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.
Current experiments on atomic gases in highly anisotropic traps present the opportunity to study in detail the low temperature phases of two-dimensional inhomogeneous systems. Although, in an ideal gas, the trapping potential favors Bose-Einstein condensation at finite temperature, interactions tend to destabilize the condensate, leading to a superfluid Kosterlitz-Thouless-Berezinskii phase with a finite superfluid mass density but no long-range order, as in homogeneous fluids. The transition in homogeneous systems is conveniently described in terms of dissociation of topological defects (vortex-antivortex pairs). However, trapped two-dimensional gases are more directly approached by generalizing the microscopic theory of the homogeneous gas. In this paper, we first derive, via a diagrammatic expansion, the scaling structure near the phase transition in a homogeneous system, and then study the effects of a trapping potential in the local density approximation. We find that a weakly interacting trapped gas undergoes a Kosterlitz-Thouless-Berezinskii transition from the normal state at a temperature slightly below the Bose-Einstein transition temperature of the ideal gas. The characteristic finite superfluid mass density of a homogeneous system just below the transition becomes strongly suppressed in a trapped gas.