Dimer-projection contact and the clock shift of a unitary Fermi gas
Understanding the dynamics of short-range correlations is a central challenge in strongly interacting Fermi gases. In ultracold gases, these correlations are quantified by the contact parameter, yet measurements to date have been limited to equilibrium systems or relatively slow, global dynamics. Here, we introduce a rapid spectroscopic technique based on projection of the interacting state onto an alternate scattering channel with a low-lying dimer state. We demonstrate contact measurements on the microsecond timescale -- faster than the inverse Fermi energy. Using $^{40}$K near a broad $s$-wave Feshbach resonance, we show that the strength of the dimer-projection feature scales proportionally with the contact parameter extracted from the high-frequency tail of radio-frequency spectroscopy, in agreement with coupled-channels calculations. Analysis of the spectra further reveals that the dimer feature provides the dominant contribution to the clock shift of the unitary Fermi gas, allowing the first experimental bound on this quantity. The observed deviations from universal predictions highlight the importance of multichannel effects. Our results open new avenues for studying contact correlators, hydrodynamic attractors, and quantum critical behavior.