Real-time decoherence of Landau and Levitov quasiparticles in quantum Hall edge channels

Electron wave and quantum optics in graphene

In the last decade, graphene has become an exciting platform for electron optical experiments, in some aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states,e.g., snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers.

Heat Pulses in Electron Quantum Optics

Electron quantum optics aims to realize ideas from the quantum theory of light with the role of photons being played by charge pulses in electronic conductors. Experimentally, the charge pulses are excited by time-dependent voltages; however, one could also generate heat pulses by heating and cooling an electrode. Here, we explore this intriguing idea by formulating a Floquet scattering theory of heat pulses in mesoscopic conductors. The adiabatic emission of heat pulses leads to a heat current that in linear response is given by the thermal conductance quantum. However, we also find a high-frequency component, which ensures that the fluctuation-dissipation theorem for heat currents, whose validity has been debated, is fulfilled. The heat pulses are uncharged, and we probe their electron-hole content by evaluating the partition noise in the outputs of a quantum point contact. We also employ a Hong-Ou-Mandel setup to examine if the pulses bunch or antibunch. Finally, to generate an electric current, we use a Mach-Zehnder interferometer that breaks the electron-hole symmetry and thereby enables a thermoelectric effect. Our Letter paves the way for systematic investigations of heat pulses in mesoscopic conductors, and it may stimulate future experiments.

Time-resolved Coulomb collision of single electrons

A series of recent experiments have shown that collision of ballistic electrons in semiconductors can be used to probe the indistinguishability of single-electron wavepackets. Perhaps surprisingly, their Coulomb interaction has not been seen due to screening. Here we show Coulomb-dominated collision of high-energy single electrons in counter-propagating ballistic edge states, probed by measuring partition statistics while adjusting the collision timing. Although some experimental data suggest antibunching behaviour, we show that this is not due to quantum statistics but to strong repulsive Coulomb interactions. This prevents the wavepacket overlap needed for fermionic exchange statistics but suggests new ways to utilize Coulomb interactions: microscopically isolated and time-resolved interactions between ballistic electrons can enable the use of the Coulomb interaction for high-speed sensing or gate operations on flying electron qubits.

Two-particle time-domain interferometry in the fractional quantum Hall effect regime

Quasi-particles are elementary excitations of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. Here, we consider anyons, the fractionally charged quasi-particles of the Fractional Quantum Hall Effect occurring in two-dimensional electronic conductors in high magnetic fields. They obey anyonic statistics, intermediate between fermionic and bosonic. Surprisingly, anyons show large quantum coherence when transmitted through the localized states of electronic Fabry-Pérot interferometers, but almost no quantum interference when transmitted via the propagating states of Mach-Zehnder interferometers. Here, using a novel interferometric approach, we demonstrate that anyons do keep quantum coherence while propagating. Performing two-particle time-domain interference measurements sensitive to the two-particle Hanbury Brown Twiss phase, we find 53 and 60% visibilities for anyons with charges e/5 and e/3. Our results give a positive message for the challenge of performing controlled quantum coherent braiding of anyons.

Multi-Particle Interference in an Electronic Mach-Zehnder Interferometer

The development of dynamic single-electron sources has made it possible to observe and manipulate the quantum properties of individual charge carriers in mesoscopic circuits. Here, we investigate multi-particle effects in an electronic Mach-Zehnder interferometer driven by a series of voltage pulses. To this end, we employ a Floquet scattering formalism to evaluate the interference current and the visibility in the outputs of the interferometer. An injected multi-particle state can be described by its first-order correlation function, which we decompose into a sum of elementary correlation functions that each represent a single particle. Each particle in the pulse contributes independently to the interference current, while the visibility (given by the maximal interference current) exhibits a Fraunhofer-like diffraction pattern caused by the multi-particle interference between different particles in the pulse. For a sequence of multi-particle pulses, the visibility resembles the diffraction pattern from a grid, with the role of the grid and the spacing between the slits being played by the pulses and the time delay between them. Our findings may be observed in future experiments by injecting multi-particle pulses into a Mach-Zehnder interferometer.

Electronic Wave-Packets in Integer Quantum Hall Edge Channels: Relaxation and Dissipative Effects

We theoretically investigate the evolution of the peak height of energy-resolved electronic wave-packets ballistically propagating along integer quantum Hall edge channels at filling factor equal to two. This is ultimately related to the elastic scattering amplitude for the fermionic excitations evaluated at different injection energies. We investigate this quantity assuming a short-range capacitive coupling between the edges. Moreover, we also phenomenologically take into account the possibility of energy dissipation towards additional degrees of freedom—both linear and quadratic—in the injection energy. Through a comparison with recent experimental data, we rule out the non-dissipative case as well as a quadratic dependence of the dissipation, indicating a linear energy loss rate as the best candidate for describing the behavior of the quasi-particle peak at short enough propagation lengths.

Relaxation and revival of quasiparticles injected in an interacting quantum Hall liquid

The one-dimensional, chiral edge channels of the quantum Hall effect are a promising platform in which to implement electron quantum optics experiments; however, Coulomb interactions between edge channels are a major source of decoherence and energy relaxation. It is therefore of large interest to understand the range and limitations of the simple quantum electron optics picture. Here we confirm experimentally for the first time the predicted relaxation and revival of electrons injected at finite energy into an edge channel. The observed decay of the injected electrons is reproduced theoretically within a Tomonaga-Luttinger liquid framework, including an important dissipation towards external degrees of freedom. This gives us a quantitative empirical understanding of the strength of the interaction and the dissipation.

Spectral features of voltage pulses in interacting helical channels

We investigate the interplay of voltage-driven excitations and electron-electron interactions in a pair of counterpropagating helical channels capacitively coupled to a time-dependent gate. By focusing on the non-equilibrium spectral properties of the system, we show how the spectral function is modified by external drives with different time profile in presence of Coulomb interactions. In particular, we focus on a Lorentzian drive and a square single pulse. In presence of strong enough electron-electron interactions, we find that both drives can result in minimal excitations, i.e. characterized by an excess spectral function with a definite sign. This is in contrast with what happens in the non-interacting case, where only properly quantized Lorentzian pulses are able to produce minimal excitations.

Electronic energy spectroscopy of monochromatic edge magnetoplasmons in the quantum Hall regime

We investigate electronic excitation in a quantum Hall edge channel when a monochromatic plasmon wave is excited by applying a radio-frequency voltage to a long surface gate on an AlGaAs/GaAs heterostructure. A quantum-dot energy spectrometer is employed to evaluate the amplitude of the potential wave and possible electronic heating. The potential wave is analyzed with a capacitance model. Non-monotonic frequency dependence observed under specific conditions can be explained by destructive plasmon interference in the gated region. The observed small heating effect suggests that the single plasmon mode is dominantly excited with this scheme.

Minimal Excitations in the Fractional Quantum Hall Regime

We study the minimal excitations of fractional quantum Hall edges, extending the notion of levitons to interacting systems. Using both perturbative and exact calculations, we show that they arise in response to a Lorentzian potential with quantized flux. They carry an integer charge, thus involving several Laughlin quasiparticles, and leave a Poissonian signature in a Hanbury Brown-Twiss partition noise measurement at low transparency. This makes them readily accessible experimentally, ultimately offering the opportunity to study real-time transport of Abelian and non-Abelian excitations.

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

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 edge-state velocity v is deduced. We find that v follows 1/B dependence, in good agreement with the E[over →]×B[over →] drift. The edge potential is estimated from the energy dependence of v using a harmonic approximation.

Hong-Ou-Mandel experiment for temporal investigation of single-electron fractionalization

Coulomb interaction has a striking effect on electronic propagation in one-dimensional conductors. The interaction of an elementary excitation with neighbouring conductors favours the emergence of collective modes, which eventually leads to the destruction of the Landau quasiparticle. In this process, an injected electron tends to fractionalize into separated pulses carrying a fraction of the electron charge. Here we use two-particle interferences in the electronic analogue of the Hong-Ou-Mandel experiment in a quantum Hall conductor at filling factor 2 to probe the fate of a single electron emitted in the outer edge channel and interacting with the inner one. By studying both channels, we analyse the propagation of the single electron and the generation of interaction-induced collective excitations in the inner channel. These complementary pieces of information reveal the fractionalization process in the time domain and establish its relevance for the destruction of the quasiparticle, which degrades into the collective modes.

A charge injected into the edge of a correlated one-dimensional system can split into separate charge packages. Freulon et al. now study this electron fractionalization on the picosecond timescale using Hong-Ou-Mandel interferometry.

Confinement effects of levitons in a graphene cosmology laboratory

Full confinement of the leviton/anti-leviton can occur inside a potential. Bifurcations in the wavefunction show the onset of internal vortex structures. Transmission and reflection occurs as a function of a leviton energy/potential barrier ratio.