In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the BEC limit. In the low-density limit, we show how this dimer-fermion interaction gives the $s$ -wave scattering length ${a}_{\mathit{BF}}=1.18{a}_{F}$ ( ${a}_{F}$ is the $s$ -wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the BEC limit. In the low-density limit, we show how this dimer-fermion interaction gives the $s$-wave scattering length ${a}_{\mathit{BF}}=1.18{a}_{F}$ (${a}_{F}$ is the $s$-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.

arXiv:cond-mat/0703433Physical Review AAug 28, 200716 citations

Superfluidity in system with fermion condensate

VICTOR A. KHODEL, Vasily R. Shaginyan

JETPLMay 1, 199081 citations

A new perturbation theory for the superfluid Fermi gas in the molecular Bose-Einstein condensed state

Shina Tan

We demonstrate how solutions to quantum few-fermion scattering problems can be the point-of-departure of a new treatment of a generalized many-body wave function. Our focus is on a particular ansatz for the ground state wave function of a superfluid Fermi gas introduced earlier (cond-mat/0506293). Our method is perturbative in the sense that the probability amplitudes for few-fermion scattering processes are treated as small quantities; it is also NONPERTURBATIVE in the sense that whenever such scattering events occur, nonperturbative quantum few-fermion scattering physics dominates. This approach can be viewed as a new diagrammatic methodology, based on a wave function as distinct from a perturbation series in the interparticle interactions. Some generic properties of the wave function are studied, and its parameters in the Bose-Einstein condensed limit are computed beyond mean-field. These results enable us to predict many observable properties of this Fermi gas with well-controlled accuracy, such as the superfluid pairing function, the four-fermion and six-fermion correlation functions, the momentum distribution, and the two-body reduced density matrix, etc.We demonstrate how solutions to quantum few-fermion scattering problems can be the point-of-departure of a new treatment of a generalized many-body wave function. Our focus is on a particular ansatz for the ground state wave function of a superfluid Fermi gas introduced earlier (cond-mat/0506293). Our method is perturbative in the sense that the probability amplitudes for few-fermion scattering processes are treated as small quantities; it is also NONPERTURBATIVE in the sense that whenever such scattering events occur, nonperturbative quantum few-fermion scattering physics dominates. This approach can be viewed as a new diagrammatic methodology, based on a wave function as distinct from a perturbation series in the interparticle interactions. Some generic properties of the wave function are studied, and its parameters in the Bose-Einstein condensed limit are computed beyond mean-field. These results enable us to predict many observable properties of this Fermi gas with well-controlled accuracy, such as the superfluid pairing function, the four-fermion and six-fermion correlation functions, the momentum distribution, and the two-body reduced density matrix, etc.

arXiv:cond-mat/0510055Oct 3, 20050 citations

SUPERFLUIDITY IN BOSE AND FERMI LIQUIDS.

Ph. Nozières

Oct 31, 19671 citation

Bose spectrum of superfluid Fermi gas

Victor Nikolaevich Popov

Cambridge University Press eBooksJan 7, 19880 citations

s

-wave scattering length

{a}_{\mathit{BF}}=1.18{a}_{F}

(

{a}_{F}

is the

s

-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.