  Inter-channel Coulomb interaction mixes charge excitations in copropagating
quantum Hall edge channels, generating coupled excitation eigenmodes
propagating at different speeds. This mode transformation causes an electron
state to split into fragments, corresponding to the Tomonaga-Luttinger liquid
model of a chiral one-dimensional electronic system. This paper reports the
coherent evolution of an electron state under the fractionalization process in
a Mach-Zehnder interferometer employing copropagating spin-up and spin-down
channels as the interference paths. We observe the interference visibility
oscillations as a function of the voltage bias applied between the interference
paths, which are attributed to the second-order interference between the
fractionalized spin excitations with different phase evolutions. This
observation contrasts with the single-particle picture that predicts only the
first-order interference, reflecting the phase evolution of a spin-up and
spin-down superposition state during the one-way transport. The second-order
interference manifests the coherent splitting of the superposition state to the
mutually independent fast and slow excitations. Our observation offers the
fractionalization process as a novel way to encode an electron spin state to
spatially separated fragments.
