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arXiv:1809.04812 · Physical Review Letters

Induced p -Wave Pairing in Bose-Fermi Mixtures

J. J. Kinnunen, Zhigang Wu, Georg M. Bruun

Published Dec 19, 2018• 63 citations
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Abstract

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.

DOI
10.1103/physrevlett.121.253402

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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.
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 consider a system of repulsively interacting Bose-Fermi mixtures of spin-polarized uniform atomic gases at zero temperature. We examine possible realization of ppp-wave superfluidity of fermions due to an effective attractive interaction via density fluctuations of Bose-Einstein condensate within mean-field approximation. We find the ground state of the system by direct energy comparison of the ppp-wave superfluid state in a single uniform mixed phase and normal Fermi gas state in a phase-separated phase, and suggest an occurrence of the ppp-wave superfluidity for a strong boson-fermion interaction regime. We study some signatures of the ppp-wave superfluid, such as anisotropic energy gap and quasiparticle energy in the axial state, that have not been observed in spin-unpolarized superfluid of atomic fermions. We also show that a Cooper pair is a tightly bound state, such as a diatomic molecule in the strong boson-fermion coupling regime, and suggest an observable indication of the ppp-wave superfluid in the real experiment.
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.
We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always attractive if the boson-boson on-site interaction is repulsive, and predict the existence of an enhanced BEC-BCS crossover as the strength of the lattice potential is varied. We show that for direct on-site fermion-fermion repulsion, the induced attraction can give rise to superfluidity via s-wave pairing at striking variance with the case of pure systems of fermionic atoms with direct repulsive interactions.
An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. This assumption is more appropriate for the actual experimental situations than the usual approximation of neglecting retardation effects. The effective interaction turns out to be attractive and, as a consequence, can give rise to a superconducting phase in the Fermi component of the mixture. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-lll channels. It has been found that the onset of the superconducting phase can occur at temperatures (>100nK)(>100\mathrm{nK})(>100nK) of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.