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arXiv:cond-mat/0602201 · Physical Review Letters

Strong-Coupling Theory for the Superfluidity of Bose-Fermi Mixtures

Daw-Wei Wang

Published Apr 13, 2006• 29 citations
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Abstract

We develop a strong-coupling theory for the superfluidity of fermion pairing phase in a Bose-Fermi mixture. Dynamical screening, self-energy renormalization, and a pairing gap function are included self-consistently within the adiabatic limit (i.e., the phonon velocity is much smaller than the Fermi velocity). An analytical solution for the transition temperature (T(c)) is derived within reasonable approximations. Using typical parameters of a 40K-87Rb mixture, we find that the calculated T(c) is several times larger than that obtained in the weak coupling theory, and can be up to several percent of the Fermi temperature.

DOI
10.1103/physrevlett.96.140404

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Cambridge University Press eBooks•Apr 6, 1995•1 citation
We develop a strong-coupling theory for the superfluidity of fermion pairing phase in a Bose-Fermi mixture. Dynamical screening, self-energy renormalization, and a pairing gap function are included self-consistently within the adiabatic limit (i.e., the phonon velocity is much smaller than the Fermi velocity). An analytical solution for the transition temperature (T(c)) is derived within reasonable approximations. Using typical parameters of a 40K-87Rb mixture, we find that the calculated T(c) is several times larger than that obtained in the weak coupling theory, and can be up to several percent of the Fermi temperature.
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.
We examine a two-dimensional mixture of single-component fermions and dipolar bosons. We calculate the self-enregies of the fermions in the normal state and the Cooper-pair channel by including first-order vertex correction to derive a modified Eliashberg equation. We predict the appearance of superfluids with various nonstandard pairing symmetries at experimentally feasible transition temperatures within the strong-coupling limit of the Eliashberg equation. Excitations in these superfluids are anyonic and follow non-Abelian statistics.
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 investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
The zero-temperature pairing gap is a fundamental property of interacting Fermions, providing a crucial test of many-body theories in strong coupling. We analyze recent cold-atom experiments on imbalanced Fermi systems using Quantum Monte Carlo results for the superfluid and normal phases. Through this analysis we extract, for the first time, the experimental zero-temperature pairing gap in the fully paired superfluid state at unitarity where the two-body scattering length is infinite. We find that the zero-temperature pairing gap is greater than 0.4 times the Fermi energy E(F), with a preferred value of (0.45+/-0.05) E(F). The ratio of the pairing gap to the Fermi Energy is larger here than in any other Fermi system measured to date.
The two-particle spectrum in a dense Fermion system is treated using a thermodynamic Green function approach. A self-consistent description of possible bound states and a superfluid condensate in a correlated medium is given. A detailed understanding of superfluidity and superconductivity in correlated Fermion systems, especially the transition from the Cooper-paired state (weak-coupling limit) to the Bose condensed state of tightly bound pairs of Fermions (strong coupling limit) [1], is of great interest for very different physical systems. The problem of a unified treatment of Bose–Einstein condensation (BEC) and the Bardeen–Cooper–Schrieffer (BCS) phase arises not only in describing the electron structure of strongly correlated electron superfluids such as superconductors [2], the electronhole system in semiconductors [3], spin-polarized hydrogen and liquid He [4], but also in the theory of nuclear matter [5] and quark–gluon systems [6]. Recently, there have been several new approaches to this stimulating problem. A Monte-Carlo simulation of a finite He system at zero temperature has been performed in Ref. [7]. The microscopic theory of strongly coupled quantum fluids has been treated within the Jastrow approximation (cf. Ref. [8]) to obtain the ground state and low-lying excited states of strongly correlated boson quantum fluids. The crossover from weak to strong coupling superconductivity has been considered using a functional integral representation [2] (see also Ref. [7]).