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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. [ABSTRACT FROM AUTHOR]

Since the pioneering works of Hanbury-Brown and Twiss, intensity-intensity correlations have been widely used in astronomical systems, for example, to detect binary stars. They reveal statistics effects and two-particle interference, and offer a decoherence-free probe of the coherence properties of light sources. In the quantum Hall edge channels, the concept of quantum optics can be transposed to electrons, and an analogous two-particle interferometry can be developed, in order to characterize single-electron states. We review in this article the recent experimental and theoretical progress on this topic. [ABSTRACT FROM AUTHOR]

We have studied the static and dynamical properties of a graphene microwave nanotransistor to be used as sensitive fast charge detectors. The channel consists of exfoliated graphene on SiO2 with a 120 nm long, 900–1500 nm wide top-gate deposited on 5 nm AlOx dielectric. The scattering parameters were measured up to 60 GHz from which we deduce the gate capacitance, the drain conductance and the transconductance as a function of gate voltage. The broad measuring band allows us to measure the current gain and to map its full spectrum so as to extract reliable values of the transit frequency fT. From these measurements, we could estimate the carrier mobility, the doping of the access leads, the gate capacitance and the transconductance. The transconductance per unit width and bias voltage is larger than 1 mS µm−1 V−1 which compares with the performance of high electron mobility transistors. High-frequency characterization is achieved using microwave probe stations. Finally, using recent noise thermometry measurements, we estimate the charge resolution of graphene nanotransistors. [ABSTRACT FROM AUTHOR]

Carrier mobility in solids is generally limited by electron-impurity or electron-phonon scattering, depending on the most frequently occurring event. Three-body collisions between carriers and both phonons and impurities are rare; they are denoted supercollisions. Elusive in electronic transport they should emerge in relaxation processes as they allow for larger energy transfers. This is the case in undoped graphene, where the small Fermi surface drastically restricts the allowed phonon energy in ordinary collisions. Using electrical heating and sensitive noise thermometry we report on supercollision cooling in diffusive monolayer graphene. At low carrier density and high phonon temperature the Joule power P obeys a PTe3 law as a function of electronic temperature Te. It overrules the linear law expected for ordinary collisions which has recently been observed in resistivity measurements. The cubic law is characteristic of supercollisions and departs from the Te4 dependence recently reported for doped graphene below the Bloch-Grüneisen temperature. These supercollisions are important for applications of graphene in bolometry and photo-detection. [ABSTRACT FROM AUTHOR]

We review the first experiment on dynamic transport in a phase-coherent quantum conductor. In our discussion, we highlight the use of time-dependent transport as a means of gaining insight into charge relaxation on a mesoscopic scale. For this purpose, we studied the ac conductance of a model quantum conductor, i.e. the quantum RC circuit. Prior to our experimental work, Buttiker et al (1993 Phys. Lett. A 180 364-9) first worked on dynamic mesoscopic transport in the 1990s. They predicted that the mesoscopic RC circuit can be described by a quantum capacitance related to the density of states in the capacitor and a constant charge-relaxation resistance equal to half of the resistance quantum h/2e&#sup2;, when a single mode is transmitted between the capacitance and a reservoir. By applying a microwave excitation to a gate located on top of a coherent submicronic quantum dot that is coupled to a reservoir, we validate this theoretical prediction on the ac conductance of the quantum RC circuit. Our study demonstrates that the ac conductance is directly related to the dwell time of electrons in the capacitor. Thereby, we observed a counterintuitive behavior of a quantum origin: as the transmission of the single conducting mode decreases, the resistance of the quantum RC circuit remains constant while the capacitance oscillates. [ABSTRACT FROM AUTHOR]

We propose a quantum tomography protocol to measure single-electron coherence in quantum Hall edge channels, and therefore access for the first time the wavefunction of single-electron excitations propagating in ballistic quantum conductors. Its implementation would open the way to quantitative studies of single-electron decoherence and would provide a quantitative tool for analyzing single- to few-electron sources. We show how this protocol could be implemented using ultrahigh-sensitivity noise measurement schemes. [ABSTRACT FROM AUTHOR]

We report on the realization of a high sensitivity RF noise measurement scheme to study small current fluctuations of mesoscopic systems at milli-Kelvin temperatures. The setup relies on the combination of an interferometric amplification scheme and a quarter-wave impedance transformer, allowing the measurement of noise power spectral densities with gigahertz bandwidth up to five orders of magnitude below the amplifier noise floor. We simultaneously measure the high frequency conductance of the sample by derivating a portion of the signal to a microwave homodyne detection. We describe the principle of the setup, as well as its implementation and calibration. Finally, we show that our setup allows to fully characterize a subnanosecond on-demand single electron source. More generally, its sensitivity and bandwidth make it suitable for applications manipulating single charges at GHz frequencies. [ABSTRACT FROM AUTHOR]

In the original discussion of the Kondo effect, the increase of the resistance in an alloy such as Cu0.998Fe0.002 at low temperature was explained by the antiferromagnetic coupling between a magnetic impurity and the spin of the host’s conduction electrons. This coupling has since emerged as a very generic property of localized electronic states coupled to a continuum. Recently, the possibility to design artificial magnetic impurities in nanoscale conductors has opened avenues to the study of this many-body phenomenon in a controlled way and, in particular, in out-of-equilibrium situations. So far though, measurements have focused on the average current. Current fluctuations (noise) on the other hand are a sensitive probe that contains detailed information about electronic transport. Here, we report on noise measurements in artificial Kondo impurities realized in carbon-nanotube devices. We find a striking enhancement of the current noise within the Kondo resonance, in contradiction with simple non-interacting theories. Our findings provide a sensitive test bench for one of the most important many-body theories of condensed matter in out-of-equilibrium situations and shed light on the noise properties of highly conductive molecular devices. [ABSTRACT FROM AUTHOR]

The high-frequency transconductance and current noise of top-gated single carbon nanotube transistors have been measured and used to investigate hot electron effects in one-dimensional transistors. Results are in good agreement with a theory of one-dimensional nanotransistor. In particular the prediction of a large transconductance correction to the Johnson–Nyquist thermal noise formula is confirmed experimentally. Experiment shows that nanotube transistors can be used as fast charge detectors for quantum coherent electronics with a resolution of [formula] in the 0.2–0.8 GHz band. [ABSTRACT FROM AUTHOR]

Coulomb interactions have a major role in one-dimensional electronic transport. They modify the nature of the elementary excitations from Landau quasiparticles in higher dimensions to collective excitations in one dimension. Here we report the direct observation of the collective neutral and charge modes of the two chiral co-propagating edge channels of opposite spins of the quantum Hall effect at filling factor 2. Generating a charge density wave at frequency f in the outer channel, we measure the current induced by inter-channel Coulomb interaction in the inner channel after a 3-?m propagation length. Varying the driving frequency from 0.7 to 11?GHz, we observe damped oscillations in the induced current that result from the phase shift between the fast charge and slow neutral eigenmodes. We measure the dispersion relation and dissipation of the neutral mode from which we deduce quantitative information on the interaction range and parameters. [ABSTRACT FROM AUTHOR]

Quantum Hall edge channels at integer filling factor provide a unique test bench to understand the decoherence and relaxation of single-electron excitations in a ballistic quantum conductor. In this Letter, we obtain a full visualization of the decoherence scenario of energy (Landau)- and time (Levitov)-resolved single-electron excitations at filling factor ν = 2. We show that the Landau excitation exhibits a fast relaxation followed by spin-charge separation whereas the Levitov excitation only experiences spin-charge separation. We finally suggest to use Hong-Ou-Mandel-type experiments to probe specific signatures of these different scenarios. [ABSTRACT FROM AUTHOR]

Recent electron quantum optics experiments performed with on-demand single electron sources call for a mixed time/frequency approach to electronic quantum coherence. Here, we present a Wigner function representation of first-order electronic coherence and show that it provides a natural visualization of the excitations emitted by recently demonstrated single electron sources. It also gives a unified perspective on single particle and two particle interferometry experiments. In particular, we introduce a nonclassicality criterion for single electron coherence and discuss it in the context of Mach-Zehnder interferometry. Finally, the electronic Hanbury Brown and Twiss and the Hong-Ou-Mandel experiments are interpreted in terms of overlap of Wigner function, thus connecting them to signal processing. [ABSTRACT FROM AUTHOR]

We have investigated the energy loss of hot electrons in metallic graphene by means of GHz noise thermometry at liquid helium temperature. We observe the electronic temperature T α V at low bias in agreement with the heat diffusion to the leads described by the Wiedemann-Franz law. We report on T ∞ V behavior at high bias, which corresponds to a T4 dependence of the cooling power. This is the signature of a 2D acoustic phonon cooling mechanism. From a heat equation analysis of the two regimes we extract accurate values of the electron-acoustic phonon coupling constant Σ in monolayer graphene. Our measurements point to an important effect of lattice disorder in the reduction of Σ, not yet considered by theory. Moreover, our study provides a strong and firm support to the rising field of graphene bolometric detectors. [ABSTRACT FROM AUTHOR]

We have realized a quantum optics like Hanbury Brown-Twiss (HBT) experiment by partitioning, on an electronic beam splitter, single elementary electronic excitations produced one by one by an on-demand emitter. We show that the measurement of the output currents correlations in the HBT geometry provides a direct counting, at the single charge level, of the elementary excitations (electron-hole pairs) generated by the emitter at each cycle. We observe the antibunching of low energy excitations emitted by the source with thermal excitations of the Fermi sea already present in the input leads of the splitter, which suppresses their contribution to the partition noise. This effect is used to probe the energy distribution of the emitted wave packets. [ABSTRACT FROM AUTHOR]

The controlled and accurate emission of coherent electronic wave packets is of prime importance for future applications of nanoscale electronics. Here, we present a theoretical and experimental analysis of the finite-frequency noise spectrum of a periodically driven single-electron emitter. The electron source consists of a mesoscopic capacitor that emits single electrons and holes into a chiral edge state of a quantum Hall sample. We compare experimental results with two complementary theoretical descriptions: on the one hand, the Floquet scattering theory that leads to accurate numerical results for the noise spectrum under all relevant operating conditions, and on the other hand, a semiclassical model that enables us to develop an analytic description of the main sources of noise when the emitter is operated under optimal conditions. We find excellent agreement between experiment and theory. Importantly, the noise spectrum provides us with an accurate description and characterization of the mesoscopic capacitor when operated as a periodic single-electron emitter. [ABSTRACT FROM AUTHOR]

We demonstrate a hybrid architecture consisting of a quantum dot circuit coupled to a single mode of the electromagnetic field. We use single wall carbon nanotube based circuits inserted in superconducting microwave cavities. By probing the nanotube dot using a dispersive readout in the Coulomb blockade and the Kondo regime, we determine an electron-photon coupling strength which should enable circuit QED experiments with more complex quantum dot circuits. [ABSTRACT FROM AUTHOR]

We have investigated electron dynamics in top gated graphene by measuring the gate admittance of a diffusive graphene capacitor in a broad frequency range as a function of carrier density. The density of states, conductivity, and diffusion constant are deduced from the low-frequency gate capacitance, its charging time, and their ratio. The admittance evolves from an rc-like to a skin-effect response at GHz frequency with a crossover given by the Thouless energy. The scattering time is found to be independent of energy in the 0- to 200-meV investigated range at room temperature. This is consistent with a random mass model for Dirac fermions. [ABSTRACT FROM AUTHOR]

Breakdown of the quantum Hall effect (QHE) is commonly associated with an electric field approaching the inter-Landau-level (LL) Zener field, the ratio of the Landau gap and the cyclotron radius. Eluded in semiconducting heterostructures, in spite of extensive investigation, the intrinsic Zener limit is reported here using high-mobility bilayer graphene and high-frequency current noise. We show that collective excitations arising from electron-electron interactions are essential. Beyond a noiseless ballistic QHE regime a large super-Poissonian shot noise signals the breakdown via inter-LL scattering. The breakdown is ultimately limited by collective excitations in a regime where phonon and impurity scattering are quenched. The breakdown mechanism can be described by a Landau critical velocity as it bears strong similarities with the roton mechanism of superfluids. In addition, we show that breakdown is a precursor of an electric-field induced QHE-metal transition. [ABSTRACT FROM AUTHOR]

It is well established that topological insulators sustain Dirac fermion surface states as a consequence of band inversion in the bulk. These states have a helical spin polarization and a linear dispersion with large Fermi velocity. We report on a set of experimental observations supporting the existence of additional massive surface states. These states are also confined by the band inversion at a topological-trivial semiconductor heterojunction. While first introduced by Volkov and Pankratov (VP) before the understanding of the topological nature of such a junction, they were not experimentally identified. Here we identify their signatures on transport properties at high electric field. By monitoring the ac admittance of HgTe topological-insulator field-effect capacitors, we access the compressibility and conductivity of surface states in a broad range of energies and electric fields. The Dirac states are characterized by a compressibility minimum, a linear energy dependence, and a high mobility persisting up to energies much larger than the transport band gap of the bulk. At higher energies, we observe multiple anomalous behaviors in conductance, charge metastability, and Hall resistance that point towards the contribution of massive surface states in transport scattering and charge transfer to the bulk. The spectrum of these anomalies agrees with predictions of a phenomenological model of VP states in a smooth topological heterojunction. The model accounts for the finite interface depth, the effect of electric fields including Dirac screening, and predicts the energy of the first VP state. The massive surface states are a hallmark of topological heterojunctions, whose understanding is crucial for transport studies and applications. [ABSTRACT FROM AUTHOR]

We study the decoherence and relaxation of a single elementary electronic excitation propagating in a one-dimensional chiral conductor. Using two-particle interferences in the electronic analog of the Hong-Ou-Mandel experiment, we analyze quantitatively the decoherence scenario of a single electron propagating along a quantum Hall edge channel at filling factor 2. The decoherence results from the emergence of collective neutral excitations induced by Coulomb interaction and leading, in one dimension, to the destruction of the elementary quasiparticle. This study establishes the relevance of electron quantum optics setups to provide stringent tests of strong interaction effects in one-dimensional conductors described by the Luttinger liquids paradigm. [ABSTRACT FROM AUTHOR]

Engineering and studying few-electron states in ballistic conductors is a key step towards understanding entanglement in quantum electronic systems. In this Rapid Communication, we introduce the intrinsic two-electron coherence of an electronic source in quantum Hall edge channels and relate it to two-electron wave functions and to current noise in a Hanbury Brown-Twiss interferometer. Inspired by the analogy with photon quantum optics, we propose to measure the intrinsic two-electron coherence of a source using low-frequency current correlation measurements at the output of a Franson interferometer. To illustrate this protocol, we discuss how it can distinguish between a time-bin-entangled pure state and a statistical mixture of time-shifted electron pairs. [ABSTRACT FROM AUTHOR]

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.

This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving a Coulomb-induced quantum state transfer. Extending to out-of-equilibrium regimes, aimed at triggered single electron emission, we illustrate how inelastic effects become crucial, requiring approaches beyond LFLs, shedding new light on past experimental data by showing clear interaction effects in the dynamics of mesoscopic capacitors.

Topological effects in edge states are clearly visible on short lengths only, thus largely impeding their studies. On larger distances, one may be able to dynamically enhance topological signatures by exploiting the high mobility of edge states with respect to bulk carriers. Our work on microwave spectroscopy highlights the response of the edges which host very mobile carriers, while bulk carriers are drastically slowed down in the gap. Though the edges are denser than expected, we establish that charge relaxation occurs on short timescales and suggest that edge states can be addressed selectively on timescales over which bulk carriers are frozen.

The engineering of cooling mechanisms is a bottleneck in nanoelectronics. Thermal exchanges in diffusive graphene are mostly driven by defect-assisted acoustic phonon scattering, but the case of high-mobility graphene on hexagonal boron nitride (hBN) is radically different, with a prominent contribution of remote phonons from the substrate. Bilayer graphene on a hBN transistor with a local gate is driven in a regime where almost perfect current saturation is achieved by compensation of the decrease in the carrier density and Zener-Klein tunnelling (ZKT) at high bias. Using noise thermometry, we show that the ZKT triggers a new cooling pathway due to the emission of hyperbolic phonon polaritons in hBN by out-of-equilibrium electron-hole pairs beyond the super-Planckian regime. The combination of ZKT transport and hyperbolic phonon polariton cooling renders graphene on BN transistors a valuable nanotechnology for power devices and RF electronics.

We report on electron cooling power measurements in few-layer graphene excited by Joule heating by means of a new setup combining electrical and optical probes of the electron and phonon baths temperatures. At low bias, noise thermometry allows us to retrieve the well known acoustic phonon cooling regimes below and above the Bloch-Grüneisen temperature, with additional control over the phonon bath temperature. At high electrical bias, we show the relevance of direct optical investigation of the electronic temperature by means of black-body radiation measurements. In this regime, the onset of new efficient relaxation pathways involving optical modes is observed.

We report on microwave operation of top-gated single carbon nanotube transistors. From transmission measurements in the 0.1-1.6 GHz range, we deduce device transconductance gm and gate-nanotube capacitance Cg of micro- and nanometric devices. A large and frequency-independent gm approximately 20 microS is observed on short devices, which meets the best dc results. The capacitance per unit gate length of 60 aF/microm is typical of top gates on a conventional oxide with epsilon approximately 10. This value is a factor of 3-5 below the nanotube quantum capacitance which, according to recent simulations, favors high transit frequencies fT=gm/2piCg. For our smallest devices, we find a large fT approximately 50 GHz with no evidence of saturation in length dependence.

We report on the GHz complex admittance of a chiral one-dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission independent. This shows that the relaxation time of a chiral R -L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the circuit.

We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury Brown and Twiss correlations. The super-Poissonian and Poissonian photon statistics of thermal and coherent sources, respectively, made of a resistor and a radio frequency generator, are measured down to the quantum regime at milli-Kelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductors.