Edge-magnetoplasmon resonators have been proposed as a powerful tool to detect anyons by introducing a quantum point contact into an isolated quantum Hall system probed via radiofrequency radiation. In this paper, we study the effect of a quantum point contact embedded within an edge-magnetoplasmon resonator and how its polarization influences the propagating magnetoplasmonic mode. Combining dc and rf measurements, we unambiguously evidence the signature of both integer (ν= 1 and 2) and fractional quantum Hall states (ν= 4/3 and 2/3) within the radiofrequency transmission signal. Using electrostatic gating, we determine the physical parameters characterizing the electrostatic edge of an AlGaAs/GaAs based two-dimensional electron gas. We extract the dependence of the cavity perimeter with the gate voltage of the quantum point contact and fully characterize the path followed by edge magnetoplasmons in this system. Finally, we provide a geometric model in good agreement with experimental results.

Characterizing quantum states of the electromagnetic field at microwave frequencies requires fast and sensitive detectors that can simultaneously probe the field time-dependent amplitude and its quantum fluctuations. In this work, we demonstrate a quantum sensor that exploits the phase of a single electron wavefunction, measured in an electronic Fabry-Perot interferometer, to detect a classical time-dependent electric field. The time resolution, limited by the temporal width of the electronic wavepacket, is a few tens of picoseconds. The interferometry technique provides a voltage resolution of a few tens of microvolts, corresponding to a few microwave photons. Importantly, our detector simultaneously probes the amplitude of the field from the phase of the measured interference pattern and its fluctuations from the interference contrast. This capability paves the way for on-chip detection of quantum radiation, such as squeezed or Fock states.

In this study, we investigate the potential of electronic interferometers for probing the quantum state of electromagnetic radiation on a chip at sub-nanosecond time scales. We propose to use single electron excitations propagating within an electronic Mach-Zehnder interferometer in the Aharonov-Bohm dominated regime. We discuss how information about the quantum state of the electromagnetic radiation is encoded into the interference contribution to the average outgoing electrical current. By investigating squeezed radiation and single edge magnetoplasmons probed by Leviton pulses in a realistic setup, we show that single electron interferometers have the potential to probe quantum radiation in the time domain with sub-nanosecond to pico-second time resolution. Our research could have significant implications for probing the fundamental properties of light in the microwave to tera-Hertz domains at extremely short time scales.

Quantum Hall systems are platforms of choice to study topological properties of condensed matter systems and anyonic exchange statistics. In this work we have developed a tunable radiofrequency edge magnetoplasmonic resonator controlled by both the magnetic field and a set of electrostatic gates, meant to serve as a versatile platform for future interferometric devices designed to evidence non-abelian anyons. In our device, gates allow us to change both the size of the resonant cavity and the electronic density of the two-dimensional electron gas. We show that we can continuously control the frequency response of our resonator, making it possible to develop an edge magnetoplasmon interferometer. As we reach smaller sizes of our resonator, finite size effects caused by the measurement probes manifest. In the future, such device will be a valuable tool to investigate the properties of non-abelian anyons in the fractional quantum Hall regime. Edge-magnetoplasmon interferometers have been proposed as a tool to investigate anyonic properties of quasiparticles in the regime of the Fractional Quantum Hall effect. In this work, the authors demonstrate the possibility to control electrostatically the resonance frequency of EMP resonators of micrometric size and explain the role of gates, paving the way toward the realization of anyonic interferometers.

Squeezing of the quadratures of the electromagnetic field has been extensively studied in optics and microwaves. However, previous works focused on the generation of squeezed states in a low impedance (Z_{0}≈50  Ω) environment. We report here on the demonstration of the squeezing of bosonic edge magnetoplasmon modes in a quantum Hall conductor whose characteristic impedance is set by the quantum of resistance (R_{K}≈25  kΩ), offering the possibility of an enhanced coupling to low-dimensional quantum conductors. By applying a combination of dc and ac drives to a quantum point contact, we demonstrate squeezing and observe a noise reduction 18% below the vacuum fluctuations. This level of squeezing can be improved by using more complex conductors, such as ac driven quantum dots or mesoscopic capacitors.

The emergence of an objective classical picture is the core question of quantum Darwinism. How does this reconstructed classical picture depends on the resources available to observers? In this Letter, we develop an experimentally relevant model of a qubit coupled dispersively to a transmission line and use time-frequency signal processing techniques to understand if and how the emergent classical picture is changed when we have the freedom to choose the fragment decomposition and the type of radiation sent to probe the system. We show the crucial role of correlations in the reconstruction procedure and point to the importance of studying the type of measurements that must be done to access an objective classical data.

Some fifty years ago, in her seminal PhD thesis, Odile Macchi introduced permanental and determinantal point processes. Her initial motivation was to provide models for the set of detection times in fundamental bosonic or fermionic optical experiments, respectively. After two rather quiet decades, these point processes have quickly become standard examples of point processes with nontrivial, yet tractable, correlation structures. In particular, determinantal point processes have been since the 1990s a technical workhorse in random matrix theory and combinatorics, and a standard model for repulsive point patterns in machine learning and spatial statistics since the 2010s. Meanwhile, our ability to experimentally probe the correlations between detection events in bosonic and fermionic optics has progressed tremendously. In Part I of this survey, we provide a modern introduction to the concepts in Macchi's thesis and their physical motivation, under the combined eye of mathematicians, physicists, and signal processers. Our objective is to provide a shared basis of knowledge for later cross-disciplinary work on point processes in quantum optics, and reconnect with the physical roots of permanental and determinantal point processes.

We study the low frequency admittance of a quantum Hall bar of size much larger than the electronic coherence length. We find that this macroscopic conductor behaves as an ideal quantum conductor with vanishing longitudinal resistance and purely inductive behavior up to f<1MHz. Using several measurement configurations, we study the dependence of this inductance on the length of the edge channel and on the integer quantum Hall filling fraction. The experimental data are well described by a scattering model for edge magnetoplasmons taking into account effective long range Coulomb interactions within the sample. This demonstrates that the inductance's dependence on the filling fraction arises from the effective quantum inertia of charge carriers induced by Coulomb interactions within an ungated macroscopic quantum Hall bar.

Recent developments in the coherent manipulation of electrons in ballistic conductors include the generation of time-periodic electrical currents involving one to few electronic excitations per period. However, using individual electrons as carriers of quantum information for flying qubit computation or quantum metrology applications calls for a general method to unravel the single-particle excitations embedded in a quantum electrical current and how quantum information is encoded within it. Here, we propose a general signal-processing algorithm to extract the elementary single-particle states, called electronic atoms of signal, present in any periodic quantum electrical current. These excitations and their mutual quantum coherence describe the excess single-electron coherence in the same way musical notes and score describe a sound signal emitted by a music instrument. This method, which is the first step towards the development of signal processing of quantum electrical currents is illustrated by assessing the quality of experimentally relevant single electron sources. The example of randomized quantum electrical currents obtained by regularly clocked but randomly injected unit-charge Lorentzian voltage pulses enables us to discuss how interplay of the coherence of the applied voltage and the Pauli principle alter the quantum coherence between the emitted single-particle excitations.

We study the low frequency admittance of a quantum Hall bar of size much larger than the electronic coherence length. We find that this macroscopic conductor behaves as an ideal quantum conductor with vanishing longitudinal resistance and purely inductive behavior up to f 1 MHz. Using several measurement configurations, we study the dependence of this inductance on the length of the edge channel and on the integer quantum Hall filling fraction. The experimental data are well described by a scattering model for edge magnetoplasmons taking into account effective long range Coulomb interactions within the sample. This demonstrates that the inductance's dependence on the filling fraction arises from the effective quantum inertia of charge carriers induced by Coulomb interactions within an ungated macroscopic quantum Hall bar.

In quantum nanoelectronics, time-dependent electrical currents are built from few elementary excitations emitted with well-defined wavefunctions. However, despite the realization of sources generating quantized numbers of excitations, and despite the development of the theoretical framework of time-dependent quantum electronics, extracting electron and hole wavefunctions from electrical currents has so far remained out of reach, both at the theoretical and experimental levels. In this work, we demonstrate a quantum tomography protocol which extracts the generated electron and hole wavefunctions and their emission probabilities from any electrical current. It combines two-particle interferometry with signal processing. Using our technique, we extract the wavefunctions generated by trains of Lorentzian pulses carrying one or two electrons. By demonstrating the synthesis and complete characterization of electronic wavefunctions in conductors, this work offers perspectives for quantum information processing with electrical currents and for investigating basic quantum physics in many-body systems.

Quantum nanoelectronics has entered an era where quantum electrical currents are built from single to few on-demand elementary excitations. To date however, very limited tools have been implemented to characterize them. In this work, we present a quantum current analyzer able to extract single particle excitations present within a periodic quantum electrical current without any a priori hypothesis. Our analyzer combines two-particle interferometry and signal processing to extract the relevant electron and hole wavefunctions localized around each emission period and their quantum coherence from one emission period to the other. This quantum current analyzer opens new possibilities for the characterization and control of quantum electrical currents in nanoscale conductors and for investigations of entanglement in quantum electronics down to the single electron level.

Although interesting per se, decoherence and relaxation of single-electron excitations induced by strong effective screened Coulomb interactions in Quantum Hall edge channels are an important challenge for the applications of electron quantum optics in quantum information and quantum sensing. In this paper, we study intrinsic single-electron decoherence within an ideal single-electron channel with long-range effective Coulomb interactions to determine the influence of the material and sample properties. We find that weak-coupling materials characterized by a high velocity of hot-electron excitations may offer interesting perspectives for limiting intrinsic decoherence due to electron/electron interactions. We discuss quantitively how extrinsic decoherence due to the coupling with the channel's electromagnetic environment can be efficiently inhibited in specially designed samples at ν=2 with one closed edge channel and we propose a realistic geometry for testing decoherence control in an Hong Ou Mandel experiment.

The synchronized collision of two elementary electronic excitations in an electronic conductor constitutes the electronic analogue of the Hong–Ou–Mandel effect known from optics. Such an experiment can reveal the electrons' quantum nature by the measurement of the fluctuations of particle number at the outputs of an electron collider. Electrons in the same quantum state always exit in two different outputs as opposed to classical particles, which would be randomly partitioned towards any output. Experimental implementations of this two-particle interferometry and their theoretical analysis are reviewed by Marguerite et al. (article no. 1600618, see Back Cover) and by Glattli and Roulleau (1600650) in this special issue. In the image on the back cover, single electrons (blue) and holes (red) are emitted from two small quantum dots (bottom left and top right of the picture). Single particle wavepackets propagate along the edges of the two-dimensional conductor and can be guided towards a tuneable electron partitioner (center of picture) – the “collider”. The quantitative analysis of this twoparticle interference effect proves to be a very rich and sensitive probe of electronic quantum states dynamically generated in a nanoscale conductor as for example reported by Moskalets and Haack (1600616) and by Roussel et al. (1600621). More specifically, it can be used to address single electron decoherence, electron fractionalization, and full quantum state tomography. In this special issue the electronic Hong–Ou–Mandel effect is also studied in the context of entanglement generation (Hofer et al., 1600582) and in more exotic systems such as topological insulator setups (Ferraro et al., 1600531).

Quantum nanoelectronics has entered an era where quantum electrical currents built from single to few elementary excitations generated on demand. However, very limited tools have been implemented so far to characterize the emitted states. In this work, we present a two stage quantum analyzer able to extract single electron and hole excitations as well as their quantum coherences from a quantum electrical current. The first on-chip and quantum stage reconstructs, from two electron interferences, the Wigner distribution of an unknown electronic state without a priori knowledge. Using simple a.c. drives for demonstration, we reconstruct their Wigner distributions and can distinguish between quasi-classical and quantum drives. In the latter case, a second stage extracts through a signal procedure the relevant single electron and hole excitations localized within each emission period from the reconstructed Wigner distribution. This analysis is instrumental for characterizing and controlling single to few quantum excitations of the electronic fluid and for investigating electron/hole entanglement.

The recent developments of electron quantum optics in quantum Hall edge channels have given us new ways to probe the behavior of electrons in quantum conductors. It has brought new quantities called electronic coherences under the spotlight. In this paper, we explore the relations between electron quantum optics and signal processing through a global review of the various methods for accessing single- and two-electron coherences in electron quantum optics. We interpret electron quantum optics interference experiments as analog signal processing, converting quantum signals into experimentally observable quantities such as current averages and correlations. This point of view also gives us a procedure to obtain quantum information quantities from electron quantum optics coherences. We illustrate these ideas by discussing two-mode entanglement in electron quantum optics. We also sketch how signal processing ideas may open new perspectives for representing electronic coherences in quantum conductors and understand the properties of the underlying many-body electronic state.

Electron quantum optics is an emerging field aiming at understanding quantum transport using ideas from quantum optics. We propose a procedure to find the simplest representation of the single electron coherence emitted by a time-periodic electronic source in terms of electronic wavefunctions.