Coupled oscillator model of a trapped Fermi gas at the BEC-BCS crossover

We address theoretically the puzzling discontinuity of the radial quadrupole mode frequency observed in a trapped Fermi gas across the BEC-BCS crossover. We apply the scaling transformation to a two-channel model of a resonant Fermi superfluid and argue that the frequency downshift in the crossover region is due to Feshbach coupling of the molecular Bose-Einstein condensate (BEC) to the surrounding Fermi sea. The Bose and Fermi components of the gas act as coupled macroscopic oscillators. The frequency jump corresponds to the point where the closed-channel molecules are entirely converted into the Fermi sea. This implies linear scaling of the "critical" detuning between the scattering channels with the Fermi energy, which can be readily verified in an experiment.