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

A light impurity in a Fermi sea undergoes a transition from a polaron to a molecule for increasing interaction. We develop a method to compute the spectral functions of the polaron and molecule in a unified framework based on the functional renormalization group with full self-energy feedback. We discuss the energy spectra and decay widths of the attractive and repulsive polaron branches as well as the molecular bound state, and confirm the scaling of the excited-state decay rate near the transition. The quasiparticle weight of the polaron shifts from the attractive to the repulsive branch across the transition, while the molecular bound state has a very small residue characteristic for a composite particle. We propose an experimental procedure to measure the repulsive branch in a Li-6 Fermi gas using rf spectroscopy and calculate the corresponding spectra.