Polaron residue and spatial structure in a Fermi gas

Laboratoire Kastler Brossel, École Normale Supérieure and CNRS, UPMC 24 rue Lhomond, 75231 Paris, France, EU

Received: 30 October 2012
Accepted: 23 January 2013

Abstract

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 2k_Fx)/(k_Fx)⁴, with k_F 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/k_F to the asymptotic distance where the 1/x⁴ law applies, they reveal an intriguing multiscale structure of G(x).