Towards quantitative precision in ultracold atoms with functional renormalisation

TL;DR

This paper uses an improved functional renormalisation group method to accurately compute the equation of state, gap, and density fluctuations of a superfluid Fermi gas across the BEC-BCS crossover, aligning well with experimental data.

Contribution

It introduces a refined FRG approach that leverages higher order density fluctuations, enabling precise calculations without fine-tuning of microscopic parameters.

Findings

Good quantitative agreement with experimental data in unitarity and BEC regimes

Circumvents fine-tuning issues of density parameters

Establishes a foundation for more precise future calculations

Abstract

We compute the equation of state, the gap as well as the density fluctuations of a two-component superfluid Fermi gas over the whole range of BEC-BCS crossover at vanishing temperature within the functional renormalisation group approach. With an improved understanding of the relation between density and chemical potential, already a rather simple truncation yields a very good quantitative agreement with experimental data and theoretical results, in particular in the unitarity limit and on the BEC side. The current approach utilises higher order density fluctuations as a fundamental building block for the computation of the density as a function of the chemical potential. This circumvents the fine-tuning problem of the density-related fundamental parameters on the microscopic level that has been observed in previous approaches. The quantitative reliability of the functional renormalisation group approach already within simple approximations opens the path towards precision results in more elaborate truncations.