Clock shift and contact of a unitary Fermi gas inferred by dimer association

Interaction shifts of spectroscopic lines are a nuisance for atomic clocks, but also a signature of two-body correlations. We prepare a unitary Fermi gas of potassium-40, where atom-atom correlations manifest in the radiofrequency (rf) transfer spectra between internal states. In certain cases, the complete spectrum has a negative total clock shift, in seeming disagreement with the well studied positive high-frequency tail governed by the contact parameter. We report that the “missing link” is a relatively deeply bound ac dimer. With a highly concentrated spectral weight, rf pulses on microsecond timescales can produce significant dimer-association rates, while Fourier broadening does not convolve the bare atomic resonance. We calibrate a Fourier-width-dominated dimer lineshape and observe that the integrated spectral weight and clock shift are directly proportional to correlations in the initial state extracted from the usual high-frequency tail. The results are compared both to an analytic model with finite effective range and to a coupled-channels calculation. Our measurements inform the complete rf spectra of a unitary Fermi gas and provide a new tool for rapid observation of pair correlation dynamics.