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

Abstract

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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