Mach-Zehnder interference of fractionalized electron-spin excitations

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.