  The nature of the normal state of an ultracold Fermi gas in the BCS-BEC
crossover regime is an intriguing and controversial topic. While the many-body
ground state remains a condensate of paired fermions, the normal state must
evolve from a Fermi liquid to a Bose gas of molecules as a function of the
interaction strength. How this occurs is still largely unknown. We explore this
question with measurements of the distribution of single-particle energies and
momenta in a nearly homogeneous gas above $T_c$. The data fit well to a
function that includes a narrow, positively dispersing peak that corresponds to
quasiparticles and an "incoherent background" that can accommodate broad,
asymmetric line shapes. We find that the quasiparticle's spectral weight
vanishes abruptly as the strength of interactions is modified, which signals
the breakdown of a Fermi liquid description. Such a sharp feature is surprising
in a crossover.
