Ground-state thermodynamic quantities of homogeneous spin-$1/2$ fermions from the BCS region to the unitarity limit

TL;DR

This study precisely measures thermodynamic properties of interacting spin-1/2 fermions from the BCS to unitarity limit at zero temperature, validating strong-coupling theories and linking superfluid parameters with spectroscopic and quantum Monte Carlo results.

Contribution

It provides highly accurate experimental data across the BCS-BEC crossover, enabling comparison with many-body theories and advancing understanding of strong-coupling superfluid fermions.

Findings

Extended T-matrix approximation reproduces experimental data well

Superfluid gap parameter aligns with spectroscopic and Monte Carlo results

Thermodynamic quantities are accurate within 4% near unitarity

Abstract

We experimentally determined various thermodynamic quantities of interacting two-component fermions at the zero-temperature limit from the Bardeen-Cooper-Schrieffer (BCS) region to the unitarity limit. The obtained results are very accurate in the sense that the systematic error is within 4% around the unitarity limit. Using this advantage, we can compare our data with various many-body theories. We found that an extended ${\it T}$-matrix approximation, which is a strong-coupling theory involving fluctuations in the Cooper channel, well reproduces our experimental results. We also found that the superfluid order parameter ${\it \Delta}$ calculated by solving the ordinary BCS gap equation with the chemical potential of interacting fermions is close to the binding energy of the paired fermions directly observed in a spectroscopic experiment and that obtained using a quantum Monte Carlo method. Since understanding the strong-coupling properties of a superfluid Fermi gas in the BCS-BEC (Bose-Einstein condensation) crossover region is a crucial issue in condensed matter physics and nuclear physics, the results of the present study are expected to be useful in the further development of these fields.