Dressed-molecules in resonantly-interacting ultracold atomic Fermi gases

TL;DR

This paper provides a comprehensive theoretical analysis of dressed molecules in ultracold Fermi gases near Feshbach resonances, deriving exact many-body properties and exploring the BEC-BCS crossover.

Contribution

It introduces an exact many-body T-matrix derivation for the two-channel model, connecting it to single-channel results and analyzing narrow resonance effects.

Findings

Exact many-body T-matrix derived for the two-channel theory

Analytical formulas incorporate two-body physics without fitting parameters

Relation established between single-channel and two-channel dressed molecules

Abstract

We present a detailed analysis of the two-channel atom-molecule effective Hamiltonian for an ultracold two-component homogeneous Fermi gas interacting near a Feshbach resonance. We particularly focus on the two-body and many-body properties of the dressed molecules in such a gas. An exact result for the many-body T-matrix of the two-channel theory is derived by both considering coupled vertex equations and the functional integral methods. The field theory incorporates exactly the two-body physics of the Feshbach scattering by means of simple analytical formulas without any fitting parameters. New interesting many-body effects are discussed in the case of narrow resonances. We give also a description of the BEC-BCS crossover above and below T_C. The effects of different approximations for the selfenergy of the dressed molecules are discussed. The single-channel results are derived as a special limit for broad resonances. Moreover, through an analytic analysis of the BEC limit, the relation between the composite boson of the single-channel model and the dressed-molecule of the two-channel model is established.