  Ultracold Fermi gases with tuneable interactions represent a unique test bed
to explore the many-body physics of strongly interacting quantum systems. In
the past decade, experiments have investigated a wealth of intriguing
phenomena, and precise measurements of ground-state properties have provided
exquisite benchmarks for the development of elaborate theoretical descriptions.
Metastable states in Fermi gases with strong repulsive interactions represent
an exciting new frontier in the field. The realization of such systems
constitutes a major challenge since a strong repulsive interaction in an atomic
quantum gas implies the existence of a weakly bound molecular state, which
makes the system intrinsically unstable against decay. Here, we exploit
radio-frequency spectroscopy to measure the complete excitation spectrum of
fermionic 40K impurities resonantly interacting with a Fermi sea of 6Li atoms.
In particular, we show that a well-defined quasiparticle exists for strongly
repulsive interactions. For this "repulsive polaron" we measure its energy and
its lifetime against decay. We also probe its coherence properties by measuring
the quasiparticle residue. The results are well described by a theoretical
approach that takes into account the finite effective range of the interaction
in our system. We find that a non-zero range of the order of the interparticle
spacing results in a substantial lifetime increase. This major benefit for the
stability of the repulsive branch opens up new perspectives for investigating
novel phenomena in metastable, repulsively interacting fermion systems.
