Spin-polarized Fermi superfluids as Bose-Fermi mixtures

Abstract

In the strong-coupling 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 superfluid phase at finite temperatures. In the low-density limit, we show how this dimer-fermion interaction gives the s-wave scattering length $a_{BF}=1.18a_F$ ($a_F$ is the s-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.

The expurgated version; accepted for publication in PRA

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Cited by in corpus (13)

• Theory of ultracold Fermi gases
• Imbalanced Feshbach-resonant Fermi gases
• Phase separation in a polarized Fermi gas at zero temperature
• Fermi-Fermi Mixtures in the Strong Attraction Limit
• Finite temperature effective field theory and two-band superfluidity in Fermi gases
• Low-density molecular gas of tightly-bound Rashba-Dresselhaus fermions
• Stable Sarma State in Two-band Fermi Systems
• Pair excitations and parameters of state of imbalanced Fermi gases at finite temperatures
• Density profiles of polarized Fermi gases confined in harmonic traps
• Dissipative Effects on the Superfluid to Insulator Transition in Mixed-dimensional Optical Lattices
• Equation of state of a polarized Fermi gas in the Bose-Einstein Condensate limit
• Correcting inconsistencies in the conventional superfluid path integral scheme
• Atom-dimer and dimer-dimer scatterings in a spin-orbit coupled Fermi gas