Dephasing of mesoscopic interferences from electron fractionalization

We investigate the dephasing of mesoscopic interferences by electron-electron interactions in a strictly one-dimensional geometry composed of two weakly coupled (clean and very long) Luttinger liquids. We demonstrate that interactions can produce a visible attenuation of Aharonov-Bohm oscillations. Through a Nyquist-noise-type description of the interactions and a direct (exact) calculation based on the Luttinger theory, we firmly stress that the dephasing time results from the electron fractionalization time.