Polaron residue and spatial structure in a Fermi gas

We consider a mobile impurity of mass M interacting via a s-wave broad or narrow Feshbach resonance with a Fermi sea of particles of mass m. Truncating the Hilbert space to at most one pair of particle-hole excitations of the Fermi sea, we study ground-state properties of the polaronic branch other than energy, namely the quasiparticle residue Z, and the impurity-to-fermion pair correlation function G(x). We show that G(x) − 1 vanishes at large distances as −(A4 + B4 cos 2kFx)/(kFx)4, with kF the Fermi wave vector; since A4 > 0 and B4 > 0, the polaron has a diverging rms radius and shows Friedel-like oscillations. For weak attractions, we obtain analytical results. They detect the failure of Hilbert space truncation for diverging M/m, as expected from the Anderson orthogonality catastrophe; at distances from ∼1/kF to the asymptotic distance where the 1/x4 law applies, they reveal an intriguing multiscale structure of G(x)