  Impurities in a Fermi sea, or Fermi polarons, experience a Casimir
interaction induced by quantum fluctuations of the medium. When there is
short-range attraction between impurities and fermions, also the induced
interaction between two impurities is strongly attractive at short distance and
oscillates in space for larger distances. We theoretically investigate the
scattering properties and compute the scattering phase shifts and scattering
lengths between two heavy impurities in an ideal Fermi gas at zero temperature.
While the induced interaction between impurities is weakly attractive for weak
impurity-medium interactions, we find that impurities strongly and attractively
interacting with the medium exhibit resonances in the induced scattering with a
sign change of the induced scattering length and even strong repulsion. These
resonances occur whenever a three-body Efimov bound state appears at the
continuum threshold. At energies above the continuum threshold, we find that
the Efimov state in medium can turn into a quasibound state with a finite decay
width.
