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arXiv:1609.09138 · Physical Review Letters

Topological Superfluid in a Fermi-Bose Mixture with a High Critical Temperature

Zhigang Wu, Georg M. Bruun

Published Dec 9, 2016• 55 citations
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Abstract

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.

DOI
10.1103/physrevlett.117.245302

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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 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.
Cooper pairing caused by an induced interaction represents a paradigm in our description of fermionic superfluidity. Here, we present a strong coupling theory for the critical temperature of p-wave pairing between spin polarized fermions immersed in a Bose-Einstein condensate. The fermions interact via the exchange of phonons in the condensate, and our self-consistent theory takes into account the full frequency and momentum dependence of the resulting induced interaction. We demonstrate that both retardation and self-energy effects are important for obtaining a reliable value of the critical temperature. Focusing on experimentally relevant systems, we perform a systematic analysis varying the boson-boson and boson-fermion interaction strength as well as their masses, and identify the most suitable system for realizing a p-wave superfluid. Our results show that such a superfluid indeed is experimentally within reach using light bosons mixed with heavy fermions.
The recent experimental progress in realizing Bose-Fermi mixtures and dipolar quantum gases has created the exciting possibility of creating dipolar Bose-Fermi mixtures with intriguing and unique properties. In a dipolar condensate, the dipole-dipole interaction represents a control knob inaccessible to nondipolar Bosons. Thus, mixing dipolar bosons with fermions may open up new possibilities for creating superfluids with unconventional pairings. We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in a three-dimensional setting in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We develop a procedure which allows us to determine the parameters such as densities and scattering lengths that are required to achieve optimal critical temperature before the system starts to phase separate. We perform a systematic investigation, finding that a superfluid with a critical temperature, that is orders of magnitude higher than achievable in nondipolar mixtures, can be realized in dipolar mixtures at experimentally accessible densities and scattering lengths before the system phase separates.
A mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate is considered in which sss-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction long-range and anisotropic in nature and tunable by the dipolar interaction. It is shown that such an interaction can significantly increase the prospect of realizing a superfluid with a gap parameter characterized with a coherent superposition of all odd partial waves. In the spirit of the Hartree-Fock-Bogoliubov mean-field approach, a theory is formulated that allows the estimation of the critical temperature when the anisotropic Fock potential is taken into consideration and the determination of the system parameters that optimize the critical temperature at which such a superfluid emerges before the system begins to phase separate.
One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological p p ix y+ superfluid for identical fermions in two dimensions (2D).The expectations of reaching the critical temperature T c through p-wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes.Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background.Within the weak-coupling regime, we calculate the critical temperature T c for the fermionic pair formation using the Bethe-Salpeter formalism, and show that it is significantly boosted by higher-order diagrammatic terms, such as phonon dressing and vertex corrections.We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p-wave superfluid is at reach with state-of-the-art experiments.
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.