Polarons and dressed molecules near narrow Feshbach resonances

The properties of impurities immersed in a large Fermi sea are naturally described in terms of dressed quasiparticles: attractive and repulsive polarons, and dressed molecules. Motivated by recent experiments on narrow Feshbach resonances, we analyze here how the quasiparticle properties are affected by a non-zero resonance range. We find two interesting analytic results. For large range, the ground-state energy close to resonance is shown to become perturbative in the inverse range. In the limit of broad resonance instead, we provide a new Tan's relation linking the impurity ground-state energy E-down arrow to the number of atoms in its dressing cloud Delta N. As a corollary, at unitarity one finds Delta N = -E-down arrow/is an element of(F), with is an element of(F) the Fermi energy of the bath. Copyright (C) EPLA, 2012