  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.

Quantum Gases;Statistical Mechanics