Functional Integral for Ultracold Fermionic Atoms

TL;DR

This paper introduces a functional integral approach to describe ultracold fermionic gases, capturing the BEC-BCS crossover, including fluctuations and different resonance regimes, with results aligning with quantum Monte Carlo simulations.

Contribution

It develops a comprehensive formalism for ultracold fermionic gases that incorporates fluctuations and distinguishes between narrow and broad Feshbach resonances.

Findings

Low temperature behavior matches Bogoliubov theory for bosons.

Results agree with quantum Monte Carlo simulations.

Formalism applicable to inhomogeneous trap situations.

Abstract

We develop a functional integral formalism for ultracold gases of fermionic atoms. It describes the BEC - BCS crossover and involves both atom and molecule fields. Beyond mean field theory we include the fluctuations of the molecule field by the solution of gap equations. In the BEC limit, we find that the low temperature behavior is described by a Bogoliubov theory for bosons. For a narrow Feshbach resonance these bosons can be associated with microscopic molecules. In contrast, for a broad resonance the interaction between the atoms is approximately pointlike and microscopic molecules are irrelevant. The bosons represent now correlated atom pairs or composite ``dressed molecules''. The low temperature results agree with quantum Monte Carlo simulations. Our formalism can treat with general inhomogeneous situations in a trap. For not too strong inhomogeneities the detailed properties of the trap are not needed for the computation of the fluctuation effects - they enter only in the solutions of the field equations.