Separation of neutral and charge modes in one-dimensional chiral edge channels

Bocquillon, Erwann; Freulon, Vincent; Berroir, Jean-Marc; Degiovanni, Pascal; Plaçais, Bernard; Cavanna, A.; Jin, Yong; Fève, Gwendal

doi:10.1038/ncomms2788

Cited by 129 publications

(211 citation statements)

References 43 publications

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“…Previous experiments [14,23,24] use other types of electron-transport data to estimate the electron velocity. Furthermore, electronelectron interactions can cause the formation of multiple collective modes traveling at different velocities, leading to decoherence [14,17,25]. In order to perform the measurements of bare group velocity by time-resolved methods, we need a robust edge-state waveguide system where the interactions between the transmitted electrons and other electrons in the background can be suppressed.…”

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confidence: 99%

“…Such direct velocity measurements have been difficult with electron wave packets because gate pulses would also affect the background Fermi sea. Previous experiments [14,23,24] use other types of electron-transport data to estimate the electron velocity. Furthermore, electronelectron interactions can cause the formation of multiple collective modes traveling at different velocities, leading to decoherence [14,17,25].…”

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confidence: 99%

“…The demonstration of entanglement and multiparticle interference with such wave packets would set the stage for quantum-technology applications such as quantum information processing [1]. Various theoretical proposals [2][3][4][5][6][7] and experimental realizations [8][9][10][11][12][13][14][15][16][17] employ quantum Hall edge states [18] as electron waveguides. The group velocity and dispersion relation of edge states are important parameters for understanding and controlling electron wave packet propagation.…”

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Time-of-Flight Measurements of Single-Electron Wave Packets in Quantum Hall Edge States

et al. 2016

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We report time-of-flight measurements on electrons traveling in quantum Hall edge states. Hot-electron wave packets are emitted one per cycle into edge states formed along a depleted sample boundary. The electron arrival time is detected by driving a detector barrier with a square wave that acts as a shutter. By adding an extra path using a deflection barrier, we measure a delay in the arrival time, from which the edgestate velocity v is deduced. We find that v follows 1=B dependence, in good agreement with theẼ ×B drift. The edge potential is estimated from the energy dependence of v using a harmonic approximation. DOI: 10.1103/PhysRevLett.116.126803 Electronic analogues of photonic quantum-optics experiments, so-called "electron quantum optics," can be performed using the beams of single-electron wave packets. The demonstration of entanglement and multiparticle interference with such wave packets would set the stage for quantum-technology applications such as quantum information processing [1]. Various theoretical proposals [2][3][4][5][6][7] and experimental realizations [8][9][10][11][12][13][14][15][16][17] employ quantum Hall edge states [18] as electron waveguides. The group velocity and dispersion relation of edge states are important parameters for understanding and controlling electron wave packet propagation. For edge magnetoplasmons, the velocity can be deduced by time-of-flight measurements with gate pulses [19][20][21][22]. Such direct velocity measurements have been difficult with electron wave packets because gate pulses would also affect the background Fermi sea. Previous experiments [14,23,24] use other types of electron-transport data to estimate the electron velocity. Furthermore, electronelectron interactions can cause the formation of multiple collective modes traveling at different velocities, leading to decoherence [14,17,25]. In order to perform the measurements of bare group velocity by time-resolved methods, we need a robust edge-state waveguide system where the interactions between the transmitted electrons and other electrons in the background can be suppressed.In this Letter, we demonstrate an experimental method for probing the bare edge-state velocity of electrons traveling in a depleted edge of a two-dimensional system. Electrons are emitted from a tunable-barrier single-electron pump [26][27][28] approximately 100 meV above the Fermi energy [13,29]. These electrons are injected into an edge where the background two-dimensional electron gas (2DEG) is depleted to avoid the influence of electron-electron interactions. The arrival time of these wave packets is detected by an energyselective detector barrier with a picosecond resolution [13,16]. The travel length between the source and detector is switched by a deflection barrier. The time of flight of the extra path is measured as a delay in the arrival time at the detector [30]. The edge-state velocity is calculated from the length of the extra path and the time of flight. We find that the edge-state velocity is inversely propor...

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Time-of-Flight Measurements of Single-Electron Wave Packets in Quantum Hall Edge States

et al. 2016

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“…The TL eigenmodes have been identified by measuring interference of density waves 9 , shot noise generation [10][11][12] , and charge-density correlation between two paths in a Hong-Ou-Mandel experiment 13 . Dynamics of the charge-and spin-density excitations, that is, their excitation, propagation, and attenuation, are elementary processes of nonequilibrium phenomena in the 1D system.…”

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Waveform measurement of charge- and spin-density wavepackets in a chiral Tomonaga–Luttinger liquid

et al. 2017

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In contrast to a free-electron system, a Tomonaga-Luttinger (TL) liquid in a one-dimensional (1D) electron system hosts charge and spin excitations as independent entities 1-4 . When an electron is injected into a TL liquid, it transforms into chargeand spin-density wavepackets that propagate at di erent group velocities and move away from each other. This process, known as spin-charge separation, is the hallmark of TL physics. While spin-charge separation has been probed in momentumor frequency-domain measurements in various 1D systems 5-9 , waveforms of separated excitations, which are a direct manifestation of the TL behaviour, have been long awaited to be measured. Here, we present a waveform measurement for the pseudospin-charge separation process in a chiral TL liquid comprising quantum Hall edge channels 9-13 . The chargeand pseudospin-density waveforms are captured by utilizing a spin-resolved sampling scope that records the spin-up or -down component of the excitations. This experimental technique provides full information for time evolution of the 1D electron system, including not only propagation of TL eigenmodes but also their decay in a practical device 14 .Co-propagating spin-up and -down edge channels of the quantum Hall (QH) state at filling factor ν = 2 form a prototypical system for the study of TL physics. The TL eigenmodes have been identified by measuring interference of density waves 9 , shot noise generation [10][11][12] , and charge-density correlation between two paths in a Hong-Ou-Mandel experiment 13 . Dynamics of the charge-and spin-density excitations, that is, their excitation, propagation, and attenuation, are elementary processes of nonequilibrium phenomena in the 1D system. For investigating these processes, a waveform measurement for each density excitation is highly desirable. In this study, we developed a spin-resolved sampling scope comprising a spin filter and a time-resolved charge detector 15,16 , which enables one to perform the waveform measurement. We actually observe charge-and pseudospin-density excitations separated over a distance exceeding 200 µm. The TL parameters (group velocities of charge-(v C ) and pseudospin-density (v S ≤ v C ) waves and mixing angle θ, which is introduced later) are directly read out from the waveforms; this is the first experiment in which all the TL parameters are estimated from a single measurement. Moreover, attenuation of TL wavepackets is evaluated from distortion of the waveforms. These results give quantitative information on various non-equilibrium phenomena in QH edge channels-for example, heat transport 17-20 and decoherence in interferometers 21,22 .The 1D electron dynamics in the co-propagating channels are formulated by the wave equation for the spin-up and -down charge densities ρ ↑,↓ (x, t) 23-25where U X is the inter-channel interaction and v ↑ (v ↓ ) is the group velocity renormalized by the intra-channel interaction in the spin-up (down) channel. While conventional TL theory assumes v ↑ = v ↓ , we consider a more general ...

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“…Upon diagonalization, the fully interacting problem can be recast into a much simpler form using a rotation of angle θ defined as tan(2θ) = 2u/(v 1 − v 2 ). In what follows, we focus on the so-called strong coupling regime, corresponding to θ = π/4 (and thus to v 1 = v 2 = v), as it seems to be the most relevant case from the experimental standpoint [36]. The rotated fields are then given by ϕ ±,r = (ϕ 2,r ± ϕ 1,r )/ √ 2 and the eigenvelocities reduce to v ± = v ± u so that the full Hamiltonian reads…”

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confidence: 99%

Electron interferometry in integer quantum Hall edge channels

Rech¹,

Wahl²,

Jonckheere³

et al. 2016

J. Stat. Mech.

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Abstract.We consider the electronic analog of the Hong-Ou-Mandel interferometer from quantum optics. In this realistic condensed matter device, single electrons are injected and travel along opposite chiral edge states of the integer quantum Hall effect, colliding at a quantum point contact (QPC). We monitor the fate of the colliding excitations by calculating zero-frequency current correlations at the output of the QPC. In the simpler case of filling factor ν = 1, we recover the standard result of a dip in the current noise as a function of the time delay between electron injections. For simultaneous injection, the current correlations exactly vanish, as dictated by the Pauli principle. This picture is however dramatically modified when interactions are present, as we show in the case of a filling factor ν = 2. There, each edge state is made out of two co-propagating channels, leading to charge fractionalization, and ultimately to decoherence. The latter phenomenon reduces the degree of indistinguishability between the two electron wavepackets, yielding a reduced contrast in the HOM signal. This naturally brings about the question of stronger interaction, offering a natural extension of the present work to the case of fractional quantum Hall effect where many open and fascinating questions remain.

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Separation of neutral and charge modes in one-dimensional chiral edge channels

Cited by 129 publications

References 43 publications

Time-of-Flight Measurements of Single-Electron Wave Packets in Quantum Hall Edge States

Time-of-Flight Measurements of Single-Electron Wave Packets in Quantum Hall Edge States

Waveform measurement of charge- and spin-density wavepackets in a chiral Tomonaga–Luttinger liquid

Electron interferometry in integer quantum Hall edge channels

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