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arXiv:1211.5951 · Physical Review B

Counting statistics and dephasing transition in an electronic Mach-Zehnder interferometer

A. Helzel, Leonid V. Litvin, Ivan P. Levkivskyi, Eugene V. Sukhorukov, W. Wegscheider, Christoph Strunk

Published Jun 16, 2015• 21 citations
arXivHTMLPDF

Abstract

In this paper the authors study the dependence of the visibility of the Aharonov-Bohm oscillations of an electronic Mach-Zehnder interferometer upon the transmission properties of an additional quantum point contact placed in front of the interferometer's input. According to a theory by I. P. Levkivskyi and E. V. Sukhorukov ( Phys. Rev. Lett. 103, 036801 (2009)), a non-equilibrium noise-induced phase transition is meant to occur when the transmission of the point contact equals 1/2. The authors present experimental evidence for the existence of this critical point.

DOI
10.1103/physrevb.91.245419

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In this paper the authors study the dependence of the visibility of the Aharonov-Bohm oscillations of an electronic Mach-Zehnder interferometer upon the transmission properties of an additional quantum point contact placed in front of the interferometer's input. According to a theory by I. P. Levkivskyi and E. V. Sukhorukov ( Phys. Rev. Lett. 103, 036801 (2009)), a non-equilibrium noise-induced phase transition is meant to occur when the transmission of the point contact equals 1/2. The authors present experimental evidence for the existence of this critical point.
We consider dephasing in the electronic Mach-Zehnder interferometer strongly coupled to current noise created by a voltage biased quantum point contact (QPC). We find the visibility of Aharonov-Bohm oscillations as a function of voltage bias and express it via the cumulant generating function of noise. In the large-bias regime, high-order cumulants of current add up to cancel the dilution effect of a QPC. This leads to an abrupt change in the dependence of the visibility on voltage bias which occurs at the QPC's transparency T=1/2. Quantum fluctuations in the vicinity of this point smear out the sharp transition.
We generalize the Levitov-Lesovik formula for the probability distribution function of the electron charge transferred through a phase coherent conductor, to include projective measurements that monitor the chiral propagation in quantum Hall edge modes. When applied to an electronic Mach-Zehnder interferometer, the monitoring reduces the visibility of the Aharonov-Bohm conductance oscillations while preserving the binomial form of the counting statistics, thereby removing a fundamental shortcoming of the dephasing-probe model of decoherence.
A non-perturbative treatment is developed for the dephasing produced by the shot noise of a one-dimensional electron channel. It is applied to two systems: a charge qubit and the electronic Mach-Zehnder interferometer (MZI), both of them interacting with an adjacent partitioned electronic channel acting as a detector. We find that the visibility (interference contrast) can display oscillations as a function of detector voltage and interaction time. This is a unique consequence of the non-Gaussian properties of the shot noise, and only occurs in the strong coupling regime, when the phase contributed by a single electron exceeds p. The resulting formula reproduces the recent surprising experimental observations reported in (I Neder et al 2006 Preprint cond-mat/0610634), and indicates a general explanation for similar visibility oscillations observed earlier in the MZI at large bias voltage. We explore in detail the full pattern of oscillations as a function of coupling strength, voltage and time, which might be observable in future experiments.
A non-perturbative treatment is developed for the dephasing produced by the shot noise of a one-dimensional electron channel. It is applied to two systems: a charge qubit and the electronic Mach–Zehnder interferometer (MZI), both of them interacting with an adjacent partitioned electronic channel acting as a detector. We find that the visibility (interference contrast) can display oscillations as a function of detector voltage and interaction time. This is a unique consequence of the non-Gaussian properties of the shot noise, and only occurs in the strong coupling regime, when the phase contributed by a single electron exceeds π. The resulting formula reproduces the recent surprising experimental observations reported in (I Neder et al 2006 Preprint cond-mat/0610634), and indicates a general explanation for similar visibility oscillations observed earlier in the MZI at large bias voltage. We explore in detail the full pattern of oscillations as a function of coupling strength, voltage and time, which might be observable in future experiments.