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

Levkivskyi, Ivan P.; Sukhorukov, Eugene V.

doi:10.1103/physrevlett.103.036801

Cited by 65 publications

(104 citation statements)

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“…Interactions mix excitations in different channels, and in the minimal model eigenmodes are charactised using two velocities. Our approach combines refermionisation [20,21] with non-equilibrium bosonization methods [22][23][24][25][26]: by first bosonizing, then recombining bosons to form a new set of fermions, we transform the Hamiltonian for the interacting system into one for free particles. Under this transformation, the measured distribution (or more accurately, the spectral function probed by the tunnelling conductance) is expressed as a free-fermion determinant.…”

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confidence: 99%

Relaxation in Driven Integer Quantum Hall Edge States

Kovrizhin

Chalker

2012

Phys. Rev. Lett.

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A highly non-thermal electron distribution is generated when quantum Hall edge states originating from sources at different potentials meet at a quantum point contact. The relaxation of this distribution to a stationary form as a function of distance downstream from the contact has been observed in recent experiments [C. Altimiras et al. Phys. Rev. Lett. 105, 056803 (2010)]. Here we present an exact treatment of a minimal model for the system at filling factor ν=2, with results that account well for the observations. PACS numbers: 71.10. Pm, 42.25.Hz Introduction. The importance of understanding nonequilibrium dynamics and relaxation in many-body quantum systems has been recognised since the early years of quantum mechanics [1, 2]. Settings in which such problems are of high current interest include, among others, cold atomic gases [2] and nanoscale electronic devices. [3-14] As a particular example, recent experiments [3] on quantum Hall (QH) edge states driven out of equilibrium at a quantum point contact (QPC) provide very detailed information on the approach to a steady state in an electron system that appears to be wellisolated from other degrees of freedom. In this paper we describe the exact solution of a simple model for these experiments and compare our results with the measurements.In outline, the experiments we are concerned with [3] involve two sets of integer QH edge states, which meet at a QPC. When a bias voltage is applied to the QPC, tunneling between the edge states generates a non-equilibrium electron distribution. The form of this distribution in energy and its evolution as a function of distance downstream from the QPC are probed by monitoring the tunneling current from a point on the edge, through a quantum dot that has an isolated level of controllable energy. Close to the QPC, the measured distribution has two steps, reflecting the different energies of Fermi steps in each of the incident edges. With increasing distance from the QPC, the distribution relaxes to a single, broad step. The theoretical challenge presented by these observations is to understand and model this relaxation process.The relationship between these edge state experiments and other recent work on many-body quantum dynamics far from equilibrium has several aspects worth emphasising. First, in the context of QH edge states, these are the most recent of a series of striking observations of non-equilibrium effects in interferometers [6] and in thermal transport [7]. They are also the equivalent for a ballistic system of earlier studies [8] of local distributions in diffusive wires. Second, the measurements stand apart from earlier theory [13] and experiment [14] on non-equilibrium transport between fractional QH edge states, because they probe local distribution functions, rather than the global non-linear current-voltage characteristic. Third, and more broadly, the system studied is different in important ways from quantum impurity problems [9][10][11][12], as there is no impurity degree of freedom and interactions ...

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confidence: 99%

Relaxation in Driven Integer Quantum Hall Edge States

Kovrizhin

Chalker

2012

Phys. Rev. Lett.

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“…[4,38,71] and showed surprising behavior. This has been addressed in several theoretical works [48,49,53,54,55,100]. The main result of this chapter, Eqs.…”

Section: Spectroscopy Of Quantum Hall Edge States At Complex Filling mentioning

confidence: 91%

Mesoscopic Quantum Hall Effect

Levkivskyi

2012

Springer Theses

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“…The visibility will thus be suppressed by the charge fluctuations induced by partitioning of electrons at QPC-0. Most interestingly, the lobe pattern was predicted to undergo a sudden change at T 0 = 1 2 under such conditions [18]. This noise-induced transition provides a unique experimental signature of the non-Gaussian character of the noise in the MZI visibility.…”

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“…Here, we present experimental evidence for a noise-induced nonequilibrium phase transition that was predicted to occur at T 0 = 1 2 [18]. This peculiar type of nonequilibrium phase transition is caused by a singularity in the FCS generator h(λ) of the QPC occurring at λ = π , which leads to a singular dephasing rate of the interferometer under nonequilibrium QPC-1 and -2 are set to half transmission and QPC-0 is set to transmit the outer edge with probability T 0 .…”

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

et al. 2015

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It was recently suggested that a novel type of phase transition may occur in the visibility of electronic Mach-Zehnder interferometers. Here, we present experimental evidence for the existence of this transition. The transition is induced by strongly non-Gaussian noise that originates from the strong coupling of a quantum point contact to the interferometer. We provide a transparent physical picture of the effect by exploiting a close analogy to the neutrino oscillations of particle physics. In addition, our experiment constitutes a probe of the singularity of the elusive full counting statistics of a quantum point contact. The recent discovery of a lobe-type behavior in the visibility of Aharonov-Bohm oscillations in electronic Mach-Zehnder interferometers (MZI) has triggered extensive theoretical studies in this field. These interferometers were implemented in the edge channels in the integer quantum Hall effect (QHE), mostly for filling factor ff = 2 [see Figs. 1(a) and 1(b)] [1-3]. Many sophisticated theories have been proposed to explain the lobes in the differential visibility of Aharonov-Bohm oscillations as a function of the voltage bias [4][5][6][7][8][9][10][11]. While the central lobe and next side lobe are easy to explain, observation of additional side lobes in a number of experiments is considered to be a puzzling phenomenon. Here, we show that this effect can be explained in a rather simple way, if two interacting edge channels are present. The underlying phenomenon turns out to be very similar to that of neutrino oscillations in high-energy physics: neutrinos oscillate between different flavor states because they are created in a flavor eigenstate, which is not an eigenstate of the Hamiltonian. Similarly, when an electron wave packet is partitioned by a beam splitter, it excites a collective charge mode, which is not an eigenstate of our model Hamiltonian [6]. At the second beam splitter of the interferometer, this leads to a secondary interference between the collective modes as a function of the applied voltage bias. This model can explain many of the experimental observations [12][13][14][15][16], most importantly the visibility lobes [17] and the phase rigidity of the visibility [1,2].Dephasing of the Aharanov-Bohm interference results from random fluctuations of the phase that are averaged out by the detector. In our devices, fluctuations are generated by an additional quantum point contact (QPC-0) in front of the interferometer input, which can be controlled by its transmission probability T 0 . The noisy input current leads to charge fluctuations in the interferometer. The accumulated charge shifts the edge, which leads to the Aharonov-Bohm phase shift. Hence, the strong Coulomb interaction between the edge channels guarantees a strong coupling of the electrons in the interferometer to the noise. The visibility will thus be suppressed by the charge fluctuations induced by partitioning of electrons at QPC-0. Most interestingly, the lobe pattern was predicted to undergo a sudden change at T ...

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

Cited by 65 publications

References 23 publications

Relaxation in Driven Integer Quantum Hall Edge States

Relaxation in Driven Integer Quantum Hall Edge States

Mesoscopic Quantum Hall Effect

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

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