Emission and coherent control of Levitons in graphene.

Flying qubits encode quantum information in propagating modes instead of stationary discrete states. Although photonic flying qubits are available, the weak interaction between photons limits the efficiency of conditional quantum gates. Conversely, electronic flying qubits can use Coulomb interactions, but the weaker quantum coherence in conventional semiconductors has hindered their realization. In this work, we engineered on-demand injection of a single electronic flying qubit state and its manipulation over the Bloch sphere. The flying qubit is a Leviton propagating in quantum Hall edge channels of a high-mobility graphene monolayer. Although single-shot qubit readout and two-qubit operations are still needed for a viable manipulation of flying qubits, the coherent manipulation of an itinerant electronic state at the single-electron level presents a highly promising alternative to conventional 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.

Scaling behavior of electron decoherence in a graphene Mach-Zehnder interferometer.

Over the past 20 years, many efforts have been made to understand and control decoherence in 2D electron systems. In particular, several types of electronic interferometers have been considered in GaAs heterostructures, in order to protect the interfering electrons from decoherence. Nevertheless, it is now understood that several intrinsic decoherence sources fundamentally limit more advanced quantum manipulations. Here, we show that graphene offers a unique possibility to reach a regime where the decoherence is frozen and to study unexplored regimes of electron interferometry. We probe the decoherence of electron channels in a graphene quantum Hall PN junction, forming a Mach-Zehnder interferometer1,2, and unveil a scaling behavior of decay of the interference visibility with the temperature scaled by the interferometer length. It exhibits a remarkable crossover from an exponential decay at higher temperature to an algebraic decay at lower temperature where almost no decoherence occurs, a regime previously unobserved in GaAs interferometers.

Quantum Hall Valley Splitters and a Tunable Mach-Zehnder Interferometer in Graphene.

Graphene is a very promising test bed for the field of electron quantum optics. However, a fully tunable and coherent electronic beam splitter is still missing. We report the demonstration of electronic beam splitters in graphene that couple quantum Hall edge channels having opposite valley polarizations. The electronic transmission of our beam splitters can be tuned from zero to near unity. By independently setting the beam splitters at the two corners of a graphene p-n junction to intermediate transmissions, we realize a fully tunable electronic Mach-Zehnder interferometer. This tunability allows us to unambiguously identify the quantum interferences due to the Mach-Zehnder interferometer, and to study their dependence with the beam-splitter transmission and the interferometer bias voltage. The comparison with conventional semiconductor interferometers points toward universal processes driving the quantum decoherence in those two different 2D systems, with graphene being much more robust to their effect.

A Josephson relation for fractionally charged anyons.

Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the fractional quantum Hall effect (FQHE). Their dynamics are of utmost importance for topological quantum phases and possible decoherence-free quantum information approaches, but observing these dynamics experimentally is challenging. Here, we report on a dynamical property of anyons: the long-predicted Josephson relation f J = e*V/h for charges e* = e/3 and e/5, where e is the charge of the electron and h is Planck's constant. The relation manifests itself as marked signatures in the dependence of photo-assisted shot noise (PASN) on voltage V when irradiating contacts at microwaves frequency f J The validation of FQHE PASN models indicates a path toward realizing time-resolved anyon sources based on levitons.

Strongly Correlated Charge Transport in Silicon Metal-Oxide-Semiconductor Field-Effect Transistor Quantum Dots.

Quantum shot noise probes the dynamics of charge transfers through a quantum conductor, reflecting whether quasiparticles flow across the conductor in a steady stream, or in syncopated bursts. We have performed high-sensitivity shot noise measurements in a quantum dot obtained in a silicon metal-oxide-semiconductor field-effect transistor. The quality of our device allows us to precisely associate the different transport regimes and their statistics with the internal state of the quantum dot. In particular, we report on large current fluctuations in the inelastic cotunneling regime, corresponding to different highly correlated, non-Markovian charge transfer processes. We have also observed unusually large current fluctuations at low energy in the elastic cotunneling regime, the origin of which remains to be fully investigated.

Quantum Hall effect in epitaxial graphene with permanent magnets.

We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, for the first time, only commercial NdFeB permanent magnets at low temperature. The relatively large and homogeneous magnetic field generated by the magnets, together with the high quality of the epitaxial graphene films, enables the formation of well-developed quantum Hall states at Landau level filling factors v = ±2, commonly observed with superconducting electro-magnets. Furthermore, the chirality of the QHE edge channels can be changed by a top gate. These results demonstrate that basic QHE physics are experimentally accessible in graphene for a fraction of the price of conventional setups using superconducting magnets, which greatly increases the potential of the QHE in graphene for research and applications.

Photon-Assisted Shot Noise in Graphene in the Terahertz Range.

When subjected to electromagnetic radiation, the fluctuation of the electronic current across a quantum conductor increases. This additional noise, called photon-assisted shot noise, arises from the generation and subsequent partition of electron-hole pairs in the conductor. The physics of photon-assisted shot noise has been thoroughly investigated at microwave frequencies up to 20 GHz, and its robustness suggests that it could be extended to the terahertz (THz) range. Here, we present measurements of the quantum shot noise generated in a graphene nanoribbon subjected to a THz radiation. Our results show signatures of photon-assisted shot noise, further demonstrating that hallmark time-dependant quantum transport phenomena can be transposed to the THz range.

Shot noise generated by graphene p-n junctions in the quantum Hall effect regime.

Graphene offers a unique system to investigate transport of Dirac Fermions at p-n junctions. In a magnetic field, combination of quantum Hall physics and the characteristic transport across p-n junctions leads to a fractionally quantized conductance associated with the mixing of electron-like and hole-like modes and their subsequent partitioning. The mixing and partitioning suggest that a p-n junction could be used as an electronic beam splitter. Here we report the shot noise study of the mode-mixing process and demonstrate the crucial role of the p-n junction length. For short p-n junctions, the amplitude of the noise is consistent with an electronic beam-splitter behaviour, whereas, for longer p-n junctions, it is reduced by the energy relaxation. Remarkably, the relaxation length is much larger than typical size of mesoscopic devices, encouraging using graphene for electron quantum optics and quantum information processing.

Harvesting dissipated energy with a mesoscopic ratchet.

The search for new efficient thermoelectric devices converting waste heat into electrical energy is of major importance. The physics of mesoscopic electronic transport offers the possibility to develop a new generation of nanoengines with high efficiency. Here we describe an all-electrical heat engine harvesting and converting dissipated power into an electrical current. Two capacitively coupled mesoscopic conductors realized in a two-dimensional conductor form the hot source and the cold converter of our device. In the former, controlled Joule heating generated by a voltage-biased quantum point contact results in thermal voltage fluctuations. By capacitive coupling the latter creates electric potential fluctuations in a cold chaotic cavity connected to external leads by two quantum point contacts. For unequal quantum point contact transmissions, a net electrical current is observed proportional to the heat produced.

Detecting noise with shot noise using on-chip photon detector.

The high-frequency radiation emitted by a quantum conductor presents a rising interest in quantum physics and condensed matter. However, its detection with microwave circuits is challenging. Here, we propose to use the photon-assisted shot noise for on-chip radiation detection. It is based on the low-frequency current noise generated by the partitioning of photon-excited electrons and holes, which are scattered inside the conductor. For a given electromagnetic coupling to the radiation, the photon-assisted shot noise response is shown to be independent on the nature and geometry of the quantum conductor used for the detection, up to a Fano factor, characterizing the type of scattering mechanism. Ordered in temperature or frequency range, from few tens of mK or GHz to several hundred of K or THz respectively, a wide variety of conductors can be used like Quantum Point Contacts (this work), diffusive metallic or semi-conducting films, graphene, carbon nanotubes and even molecule, opening new experimental opportunities in quantum physics.

Quantum tomography of an electron.

The complete knowledge of a quantum state allows the prediction of the probability of all possible measurement outcomes, a crucial step in quantum mechanics. It can be provided by tomographic methods which have been applied to atomic, molecular, spin and photonic states. For optical or microwave photons, standard tomography is obtained by mixing the unknown state with a large-amplitude coherent photon field. However, for fermions such as electrons in condensed matter, this approach is not applicable because fermionic fields are limited to small amplitudes (at most one particle per state), and so far no determination of an electron wavefunction has been made. Recent proposals involving quantum conductors suggest that the wavefunction can be obtained by measuring the time-dependent current of electronic wave interferometers or the current noise of electronic Hanbury-Brown/Twiss interferometers. Here we show that such measurements are possible despite the extreme noise sensitivity required, and present the reconstructed wavefunction quasi-probability, or Wigner distribution function, of single electrons injected into a ballistic conductor. Many identical electrons are prepared in well-controlled quantum states called levitons by repeatedly applying Lorentzian voltage pulses to a contact on the conductor. After passing through an electron beam splitter, the levitons are mixed with a weak-amplitude fermionic field formed by a coherent superposition of electron-hole pairs generated by a small alternating current with a frequency that is a multiple of the voltage pulse frequency. Antibunching of the electrons and holes with the levitons at the beam splitter changes the leviton partition statistics, and the noise variations provide the energy density matrix elements of the levitons. This demonstration of quantum tomography makes the developing field of electron quantum optics with ballistic conductors a new test-bed for quantum information with fermions. These results may find direct application in probing the entanglement of electron flying quantum bits, electron decoherence and electron interactions. They could also be applied to cold fermionic (or spin-1/2) atoms.

Resonant edge magnetoplasmons and their decay in graphene.

We investigate resonant edge magnetoplasmons (EMPs) and their decay in graphene by high-frequency electronic measurements. From EMP resonances in disk shaped graphene, we show that the dispersion relation of EMPs is nonlinear due to interactions, giving rise to the intrinsic decay of EMP wave packets. We also identify extrinsic dissipation mechanisms due to interaction with localized states in bulk graphene from the decay time of EMP wave packets. We indicate that, owing to the linear band structure and the sharp edge potential, EMP dissipation in graphene can be lower than that in GaAs systems.

Minimal-excitation states for electron quantum optics using levitons.

The on-demand generation of pure quantum excitations is important for the operation of quantum systems, but it is particularly difficult for a system of fermions. This is because any perturbation affects all states below the Fermi energy, resulting in a complex superposition of particle and hole excitations. However, it was predicted nearly 20 years ago that a Lorentzian time-dependent potential with quantized flux generates a minimal excitation with only one particle and no hole. Here we report that such quasiparticles (hereafter termed levitons) can be generated on demand in a conductor by applying voltage pulses to a contact. Partitioning the excitations with an electronic beam splitter generates a current noise that we use to measure their number. Minimal-excitation states are observed for Lorentzian pulses, whereas for other pulse shapes there are significant contributions from holes. Further identification of levitons is provided in the energy domain with shot-noise spectroscopy, and in the time domain with electronic Hong-Ou-Mandel noise correlations. The latter, obtained by colliding synchronized levitons on a beam splitter, exemplifies the potential use of levitons for quantum information: using linear electron quantum optics in ballistic conductors, it is possible to imagine flying-qubit operation in which the Fermi statistics are exploited to entangle synchronized electrons emitted by distinct sources. Compared with electron sources based on quantum dots, the generation of levitons does not require delicate nanolithography, considerably simplifying the circuitry for scalability. Levitons are not limited to carrying a single charge, and so in a broader context n-particle levitons could find application in the study of full electron counting statistics. But they can also carry a fraction of charge if they are implemented in Luttinger liquids or in fractional quantum Hall edge channels; this allows the study of Abelian and non-Abelian quasiparticles in the time domain. Finally, the generation technique could be applied to cold atomic gases, leading to the possibility of atomic levitons.

Carrier drift velocity and edge magnetoplasmons in graphene.

We investigate electron dynamics at the graphene edge by studying the propagation of collective edge magnetoplasmon excitations. By timing the travel of narrow wave packets on picosecond time scales around exfoliated samples, we find chiral propagation with low attenuation at a velocity that is quantized on Hall plateaus. We extract the carrier drift contribution from the edge magnetoplasmon propagation and find it to be slightly less than the Fermi velocity, as expected for an abrupt edge. We also extract the characteristic length for Coulomb interaction at the edge and find it to be smaller than that for soft depletion-edge systems.

Electron quantum optics: partitioning electrons one by one.

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.

A high sensitivity ultralow temperature RF conductance and noise measurement setup.

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.

Experimental determination of the statistics of photons emitted by a tunnel junction.

We report on an Hanbury Brown-Twiss experiment probing the statistics of microwave photons emitted by a tunnel junction in the shot-noise regime at low temperature. By measuring the cross correlation of the fluctuations of the occupation numbers of the photon modes of both detection branches, we show that while the statistics of electrons is Poissonian, the photons obey chaotic statistics. This is observed even for low photon occupation number when the voltage across the junction is close to hν/e.

Single carbon nanotube transistor at GHz frequency.

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.

Shot noise in Fabry-Perot interferometers based on carbon nanotubes.

We report on shot noise measurements in carbon nanotube based Fabry-Perot electronic interferometers. As a consequence of quantum interference, the noise power spectral density oscillates as a function of the voltage applied to the gate electrode. The quantum shot noise theory accounts for the data quantitatively and allows us to determine directly the transmissions of the two channels characterizing the nanotube. In the weak backscattering regime, the dependence of the noise on the backscattering current is found weaker than expected, pointing either to electron-electron interactions or to weak decoherence.