Dephasing in Mach-Zehnder interferometer by an Ohmic contact

We study dephasing in an electronic Mach-Zehnder (MZ) interferometer based on quantum Hall (QH) edge states by a micromiter-sized Ohmic contact embedded in one of its arms. We find that at the filling factor $\nu=1$, as well as in the case where an Ohmic contact is connected to an MZ interfeoremter by a quantum point contact (QPC) that transmits only one electron channel, the phase coherence may not be fully suppressed. Namely, if the voltage bias $\Delta \mu$ and the temperature $T$ are small compared to the charging energy of the Ohmic contact $E_C$, the free fermion picture is manifested, and the visibility saturates at its maximum value. At large biases, $\Delta \mu \gg E_C$, the visibility decays in a power-law manner.