Decoherence and interactions in an electronic Mach-Zehnder interferometer

We develop a theoretical description of a Mach-Zehnder interferometer built from integer quantum Hall edge states, with an emphasis on how electron-electron interactions produce decoherence. We calculate the visibility of interference fringes and noise power, as a function of bias voltage and of temperature. Interactions are treated exactly, by using bosonization and considering edge states that are only weakly coupled via tunneling at the interferometer beam-splitters. In this weak-tunneling limit, we show that the bias-dependence of Aharonov-Bohm oscillations in source-drain conductance and noise power provides a direct measure of the one-electron correlation function for an isolated quantum Hall edge state. We find the asymptotic form of this correlation function for systems with either short-range interactions or unscreened Coulomb interactions, extracting a dephasing length $\ell_{\phi}$ that varies with temperature $T$ as $\ell_{\phi} \propto T^{-3}$ in the first case and as $\ell_{\phi} \propto T^{-1} \ln^2(T)$ in the second case.