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 iota(phi) that varies with temperature T as iota(phi)proportional to T(-3) in the first case and as iota(phi)proportional to T(-1)ln(2)(T) in the second case.