Multiparticle interference in electronic Mach-Zehnder interferometers

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.

20 pages, 15 figures, final version as published

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• Relaxation in driven integer quantum Hall edge states
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• Parity detection and entanglement with a Mach-Zehnder interferometer
• Measuring Which-Path Information with Coupled Electronic Mach-Zehnder Interferometers
• Edge Probes of Topological Order
• Theory of fractional quantum Hall interferometers
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• Spectral distribution and wavefunction of electrons emitted from a single particle source in the quantum Hall regime
• Counting Statistics and Dephasing Transition in an Electronic Mach-Zehnder Interferometer
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• Nonequilibrium functional bosonization of quantum wire networks
• Two-particle entanglement in capacitively coupled Mach-Zehnder interferometers
• Interactions in Electronic Mach-Zehnder Interferometers with Copropagating Edge Channels
• Many-particle correlations in non-equilibrium Luttinger liquid
• Edge channel mixing induced by potential steps in an integer quantum Hall system
• Solution of a model for the two-channel electronic Mach-Zehnder interferometer
• Correlations in non-equilibrium Luttinger liquid and singular Fredholm determinants
• Dynamical resurrection of the visibility in a Mach-Zehnder interferometer
• Three Mach Zehnder Interferometers Setup for Production and Observation of GHZ-entanglement of Electrons
• Visibility recovery by strong interaction in an electronic Mach-Zehnder interferometer
• Measuring the Luttinger liquid parameter with shot noise
• Mach-Zehnder interference of fractionalized electron-spin excitations
• FQHE interferometers in strong tunneling regime. The role of compactness of edge fields