Detecting fractions of electrons in the high-$T_c$ cuprates

We propose several tests of the idea that the electron is fractionalized in the underdoped and undoped cuprates. These include the ac Josephson effect, and tunneling into small superconducting grains in the Coulomb blockade regime. In both cases, we argue that the results are qualitatively modified from the conventional ones if the insulating tunnel barrier is fractionalized. These experiments directly detect the possible existence of the chargon - a charge $e$ spinless boson - in the insulator. The effects described in this paper provide a means to probing whether the undoped cuprate (despite it's magnetism) is fractionalized. Thus, the experiments discussed here are complementary to the flux-trapping experiment we proposed in our earlier work(cond-mat/0006481).