  Many complex electronic systems exhibit so-called pseudogaps, which are
poorly-understood suppression of low-energy spectral intensity in the absence
of an obvious gap-inducing symmetry. Here we investigate the superconductor
$Ba_{1-x}K_{x}BiO_{3}$ near optimal doping, where unconventional transport
behavior and evidence of pseudogap(s) have been observed above the
superconducting transition temperature $T_{c}$, and near an insulating phase
with long-range lattice distortions. Angle-resolved photoemission spectroscopy
(ARPES) reveals a dispersive band with vanishing quasiparticle weight and
"tails" of deep-energy intensity that strongly decay approaching the Fermi
level. Upon cooling below a transition temperature $T_{p} > T_{c}$, which
correlates with a change in the slope of the resistivity vs. temperature, a
partial transfer of spectral weight near $E_{F}$ into the deep-binding energy
tails is found to result from metal-insulator phase separation. Combined with
simulations and Raman scattering, our results signal that insulating islands of
ordered bipolarons precipitate out of a disordered polaronic liquid and provide
evidence that this process is regulated by a crossover in the electronic mean
free path.
