Electron interference and entanglement in coupled 1D systems with noise

Buscemi, Fabrizio; Bordone, Paolo; Bertoni, Alberto

doi:10.1140/epjd/e2012-30469-5

Cited by 9 publications

(12 citation statements)

References 42 publications

(96 reference statements)

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“…Experimentally, we measure the correlation between the current fluctuations in Drains D2 (System) and D4 (Detector) 22,28 , proportional to the reduced joint-probability for simultaneously detecting electrons at the two drains (see supplemental material and Ref. 18), (8) ( )…”

Section: Joint Detectionmentioning

confidence: 99%

An electronic quantum eraser

Weisz

Choi

Sivan

et al. 2014

Science

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2 IntroductionComplementarity, the incomplete nature of a quantum measurement -a core concept in quantum mechanics -stems from the choice of the measurement apparatus 1 . The notion of complementarity is closely related to Heisenberg's uncertainty principle, but the exact relation between the two remains a source of debate [2][3][4][5][6][7][8] . For example, knowledge of a particle's position in a double slit interference experiment will quench its wave-like nature and, vice versa, observing the wave property via interference implies lack of knowledge of the particle's path. A canonical system for exploring complementarity is the quantum eraser (QE), predominantly studied thus far in photonic systems [9][10][11][12][13][14] . A QE is an interference experiment consisting of two stages. First, one of the interfering paths is coupled to a 'which path' (WP) detectordemonstrating loss of interference due to acquisition of WP information. Second, the WP information is being 'erased' by projecting the detector's wavefunction on a particular basis; this renders the WP information inaccessible, thus allowing reconstruction of the interference pattern.In this work, we present a first implementation of a QE in an electronic system. Our system consists of two identical electronic Mach-Zehnder interferometers (MZIs) 15 entangled via Coulomb interactions. Such novel setup has already attracted a considerable theoretical attention [16][17][18] . With one MZI serving as a path detector and the other as the system interferometer, the visibility of the Aharonov-Bohm oscillation in the System can be controlled by the Detector. We demonstrate how a continuous change of the measurement basis, followed by post selection (via cross correlation of current fluctuations), allows a smooth transition between keeping and erasing the WP information. Theory Mach-Zehnder interferometerAn electronic MZI is formed by manipulating quasi one dimensional, chiral edge channels, which are formed in the integer quantum Hall effect regime 15 . Such a realization allows directing the path of electrons at will -leading to high visibility interference pattern. Potential barriers, formed by quantum point contacts (QPCs), take the role of optical beam splitters, transmitting and reflecting impinging electrons with amplitudes i t and i r , respectively, with 1 2 2Two such coupled MZIs are shown in Fig. 1, where the coupling is mediated by the lower path of the System and the upper path of the Detector, referred to as interacting paths (shaded area in Fig. 1a). Starting with the System, an electron injected from Source S1 arrives at SQPC1 and is put into a superposition of being reflected into the interacting path and transmitted into the noninteracting path, namely: Here, e h = Φ 0 is the magnetic flux quantum, A the area enclosed by the two paths, and B the magnetic field. The visibility of the interfering pattern at D2 is defined asThroughout our experiments, all the QPCs were tuned to have equal transmission and reflection amplitudes, Entangling tw...

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Section: Joint Detectionmentioning

confidence: 99%

An electronic quantum eraser

Weisz

Choi

Sivan

et al. 2014

Science

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“…On the other hand, experimental realizations of electronic interferometry based on edge-channel transport seem more mature, to the point of demonstrating not only single-electron 10,11 but also two-electron interference 12 . Also, "whichpath" detectors or quantum erasers [13][14][15][16][17] have been implemented and the formation of quantum entanglement between indistinguishable particles has been demonstrated 12,[18][19][20][21] . While specific features of electronic Mach-Zehnder Interferometers (MZIs) 22 are still under investigation and involve possibly many-particle effects 21,23,24 , their basic functioning can be explained in terms of stationary electron waves interference, like their more common optical counterpart.…”

Section: Introductionmentioning

confidence: 99%

“…However, leviton-based MZI has not been realized experimentally so far. The majority of the literature on electron MZIs in ESs deals with electronic currents 10,12,13,17,22 , and the prevalent theoretical models for the transport are based upon delocalized scattering states [14][15][16]18,30,31 , with few notable exceptions 32,33 . In this work we address, both from numerical and analytical points of view, the interference properties of a Mach-Zehnder device based on ES channels tuned to filling factor ν=1 and quantum point contacts used as splitting elements, when the electron travelling inside it is strongly localized.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent simulation and analytical modelling of electronic Mach–Zehnder interferometry with edge-states wave packets

Beggi¹,

Bordone²,

Buscemi³

et al. 2015

J. Phys.: Condens. Matter

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We compute the exact single-particle time-resolved dynamics of electronic Mach-Zehnder interferometers based on Landau edge-states transport, and assess the effect of the spatial localization of carriers on the interference pattern. The exact carrier dynamics is obtained by solving numerically the time-dependent Schrödinger equation with a suitable 2D potential profile reproducing the interferometer design. An external magnetic field, driving the system to the quantum Hall regime with filling factor one, is included. The injected carriers are represented by a superposition of edge states and their interference pattern reproduces the results of [Y. Ji et al., Nature 422, 415 (2003)]. By tuning the system towards different regimes, we find two additional features in the transmission spectra, both related to carrier localization, namely a damping of the Aharonov-Bohm oscillations with increasing difference in the arms length, and an increased mean transmission that we trace to the energy-dependent transmittance of quantum point contacts. Finally, we present an analytical model, also accounting for the finite spatial dispersion of the carriers, able to reproduce the above effects.

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“…However, such analytical 1D model requires a number of approximations on the energy dependence of the transmission coefficient and does not include the exact Coulomb repulsion for interacting particles. Additionally, electron-electron interactions in a 2D scenario generally differ from the 1D case [89], as proved by the computation of bunching probability of two strongly-interacting particles, later described in Sec. 6.1.…”

Section: )mentioning

confidence: 97%

Quantum computing with quantum-Hall edge state interferometry

Bordone

Bellentani

Bertoni

2019

Semicond. Sci. Technol.

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Electron interferometers based on Hall edge states proved to be robust demonstrators of the coherent quantum dynamics of carriers. Several proposals to expose their capability to build and control quantum entanglement and to exploit them as building block for quantum computing devices has been presented. Here, we review the time-dependent numerical modeling of Hall interferometers operating at the single-carrier level at integer filling factor (FF). By defining the qubit state either as the spatial localization (at FF 1) or the Landau index (at FF 2) of a single carrier propagating in the edge state, we show how a generic one-qubit rotation can be realized. By a proper design of the 2DEG potential landscape, an entangling two-qubit gate can be implemented by exploiting Coulomb interaction, thus realizing a universal set of quantum gates. We also assess how the shape of the edge confining potential affects the visibility of the quantum transformations.

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Electron interference and entanglement in coupled 1D systems with noise

Cited by 9 publications

References 42 publications

An electronic quantum eraser

An electronic quantum eraser

Time-dependent simulation and analytical modelling of electronic Mach–Zehnder interferometry with edge-states wave packets

Quantum computing with quantum-Hall edge state interferometry

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