Multiparticle interference in electronic Mach-Zehnder interferometers

TL;DR

This paper provides a theoretical analysis of multiparticle interference effects in electronic Mach-Zehnder interferometers built from quantum Hall edge states, explaining experimental observations of AB oscillation visibility patterns under bias.

Contribution

It offers an exact bosonization solution for electron interactions within the interferometer, accurately modeling the observed lobe pattern in visibility and phase behavior at zero temperature.

Findings

Visibility exhibits a lobe pattern with decreasing amplitude as voltage increases.

AB phase remains constant within lobes but jumps by π at minima.

Model matches experimental data when contact transparency is near 50%.

Abstract

We study theoretically electronic Mach-Zehnder interferometers built from integer quantum Hall edge states, showing that the results of recent experiments can be understood in terms of multiparticle interference effects. These experiments probe the visibility of Aharonov-Bohm (AB) oscillations in differential conductance as an interferometer is driven out of equilibrium by an applied bias, finding a lobe pattern in visibility as a function of voltage. We calculate the dependence on voltage of the visibility and the phase of AB oscillations at zero temperature, taking into account long range interactions between electrons in the same edge for interferometers operating at a filling fraction $\nu=1$. We obtain an exact solution via bosonization for models in which electrons interact only when they are inside the interferometer. This solution is non-perturbative in the tunneling probabilities at quantum point contacts. The results match observations in considerable detail provided the transparency of the incoming contact is close to one-half: the variation in visibility with bias voltage consists of a series of lobes of decreasing amplitude, and the phase of the AB-fringes is practically constant inside the lobes but jumps by $\pi$ at the minima of the visibility. We discuss in addition the consequences of approximations made in other recent treatments of this problem. We also formulate perturbation theory in the interaction strength and use this to study the importance of interactions that are not internal to the interferometer.