  We study two-body correlations in a spin-balanced ultracold harmonically
trapped Fermi gas of $^6$Li atoms in the crossover from the
Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein-Condensate (BEC) regime.
For this, we precisely measure Tan's contact using a novel method based on
photoexcitation of atomic pairs, which was recently proposed by Wang et al.
[Phys. Rev. A 104 063309 (2021)]. We map out the contact in the entire phase
diagram of the BCS-BEC crossover for various temperatures and interaction
strengths, probing regions in phase-space that have not been investigated yet.
Our measurements reach an uncertainty of $\approx 2 \%$ and thus represent a
precise quantitative benchmark. We compare our data to theoretical predictions
and interpolations and localize the regions in phase space where the latter
give valid results. In regions where the contact is already well known we find
excellent agreement with our measurements. Thus, our results demonstrate that
photoinduced loss is a precise probe to measure quantum correlations in a
strongly interacting Fermi gas.
