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A light impurity in a Fermi sea undergoes a transition from a polaron to amolecule for increasing interaction. We develop a new method to compute thespectral functions of the polaron and molecule in a unified framework based onthe functional renormalization group with full self-energy feedback. We discussthe energy spectra and decay widths of the attractive and repulsive polaronbranches as well as the molecular bound state and confirm the scaling of theexcited state decay rate near the transition. The quasi-particle weight of thepolaron shifts from the attractive to the repulsive branch across thetransition, while the molecular bound state has a very small residuecharacteristic for a composite particle. We propose an experimental procedureto measure the repulsive branch in a Li6 Fermi gas using rf-spectroscopy andcalculate the corresponding spectra.

Excitation spectra and rf-response near the polaron-to-molecule transition from the functional renormalization group