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arXiv:0903.3349 · Physical Review Letters

Noise-Induced Phase Transition in the Electronic Mach-Zehnder Interferometer

Ivan P. Levkivskyi, Eugene V. Sukhorukov

Published Jul 13, 2009• 70 citations
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Abstract

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.

DOI
10.1103/physrevlett.103.036801

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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.
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.
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.
We study fermions in a Mach-Zehnder interferometer, subject to a quantum-mechanical environment leading to inelastic scattering, decoherence, renormalization effects, and time-dependent conductance fluctuations. We present a method to derive both the loss of interference contrast as well as the shot noise, using equations of motion and leading-order perturbation theory. The dependence of the shot noise on the Aharonov-Bohm phase acquires an unexpected average phase shift, due to correlations between the fluctuating renormalized phase shift and the output current. We discuss the limiting behaviours at low and high voltages, compare with simpler models of dephasing, and present implications for experiments.
We analyze shot noise under the influence of dephasing in an electronic Mach-Zehnder interferometer, of the type that was realized recently [Nature (London) 422, 415 (2003)]]. Using a model of dephasing by a fluctuating classical field, we show how the usual partition noise expression T(1-T) is modified. We study the dependence on the power spectrum of the field, which is impossible in simpler approaches such as the dephasing terminal, against which we compare. We remark on shot noise as a tool to distinguish thermal smearing from genuine dephasing.
In controlled dephasing a controlled environment causes dephasing of transport through a mesoscopic system. As a result of their interaction the states of the two subsystems are entangled. In this paper we discuss how their entanglement influences dephasing using as an example the ``which path detector,'' where the dephasing of transport through a quantum dot (QD) due to the interaction with a quantum point contact (QPC) is detected by means of an Aharonov-Bohm (AB) interferometer. In particular, we calculate the suppression $\ensuremath{\nu}$ of AB oscillations as a function of the bias eV\mathrm{eV}eV applied to the QPC and the coupling $\ensuremath{\Gamma}$ of the QD to the leads. At low temperatures the entanglement produces a smooth crossover from $\ensuremath{\nu}\ensuremath{\propto}(eV/\ensuremath{\Gamma}{)}^{2},$ when $\mathrm{eV}\ensuremath{\ll}\ensuremath{\Gamma}$ to $\ensuremath{\nu}\ensuremath{\propto}eV/\ensuremath{\Gamma},$ for $\mathrm{eV}\ensuremath{\gg}\ensuremath{\Gamma}.$