Decoherence and interactions in an electronic Mach-Zehnder interferometer

Abstract

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 ${\ell }_{\varphi }$ that varies with temperature $T$ as ${\ell }_{\varphi }\propto T^{-3}$ in the first case and as ${\ell }_{\varphi }\propto T^{-1}{\ln }^2(T)$ in the second case.

12 pages, 8 figure. Published version

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