  In unconventional superconductors, it is generally believed that
understanding the physical properties of the normal state is a pre-requisite
for understanding the superconductivity mechanism. In conventional
superconductors like niobium or lead, the normal state is a Fermi liquid with a
well-defined Fermi surface and well-defined quasipartcles along the Fermi
surface. Superconductivity is realized in this case by the Fermi surface
instability in the superconducting state and the formation and condensation of
the electron pairs (Cooper pairing). The high temperature cuprate
superconductors, on the other hand, represent another extreme case that
superconductivity can be realized in the underdoped region where there is
neither well-defined Fermi surface due to the pseudogap formation nor
quasiparticles near the antinodal regions in the normal state. Here we report a
novel scenario that superconductivity is realized in a system with well-defined
Fermi surface but without quasiparticles along the Fermi surface in the normal
state. High resolution laser-based angle-resolved photoemission measurements
have been performed on an optimally-doped iron-based superconductor
(Ba$_{0.6}$K$_{0.4}$)Fe$_2$As$_2$. We find that, while sharp superconducting
coherence peaks emerge in the superconducting state on the hole-like Fermi
surface sheets, no quasiparticle peak is present in the normal state. Its
electronic behaviours deviate strongly from a Fermi liquid system. The
superconducting gap of such a system exhibits an unusual temperature dependence
that it is nearly a constant in the superconducting state and abruptly closes
at T$_c$. These observations have provided a new platform to study
unconventional superconductivity in a non-Fermi liquid system.
