  Electrons in two dimensions and strong magnetic fields effectively lose their
kinetic energy and display exotic behavior dominated by Coulomb forces. When
the ratio of electrons to magnetic flux quanta in the system is near 5/2, the
unique correlated phase that emerges is predicted to be gapped with
fractionally charged quasiparticles and a ground state degeneracy that grows
exponentially as these quasiparticles are introduced. Interestingly, the only
way to transform between the many ground states would be to braid the
fractional excitations around each other, a property with applications in
quantum information processing. Here we present the first observation of
localized quasiparticles at nu=5/2, confined to puddles by disorder. Using a
local electrometer to compare how quasiparticles at nu=5/2 and nu=7/3 charge
these puddles, we are able to extract the ratio of local charges for these
states. Averaged over several disorder configurations and samples, we find the
ratio to be 4/3, suggesting that the local charges are e/3 at seven thirds and
e/4 at five halves, in agreement with theoretical predictions. This
confirmation of localized e/4 quasiparticles is necessary for proposed
interferometry experiments to test statistics and computational ability of the
state at nu=5/2.
