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.

We present an original statistical method to measure the visibility of interferences in an electronic Mach-Zehnder interferometer in the presence of low frequency fluctuations. The visibility presents a single side lobe structure shown to result from a gaussian phase averaging whose variance is quadratic with the bias. To reinforce our approach and validate our statistical method, the same experiment is also realized with a stable sample. It exhibits the same visibility behavior as the fluctuating one, indicating the intrinsic character of finite bias phase averaging. In both samples, the dilution of the impinging current reduces the variance of the gaussian distribution. Nowadays quantum conductors can be used to perform experiments usually done in optics, where electron beams replace photon beams. A beamlike electron motion can be obtained in the Integer Quantum Hall Effect (IQHE) regime using a high mobility two dimensional electron gas in a high magnetic field at low temperature. In the IQHE regime, one-dimensional gapless excitation modes form, which correspond to electrons drifting along the edge of the sample. The number of these so-called edge channels corresponds to the number of filled Landau levels in the bulk. The chirality of the excitations yields long collision times between quasi-particles, making edge states very suitable for quantum interferences experiments like the electronic Mach-Zehnder interferometer (MZI) [1,2,3]. Surprisingly, despite some experiments which show that equilibrium length in chiral wires is rather long [4], very little is known about the coherence length or the phase averaging in these "perfect" chiral uni-dimensional wires. In particular, while in the very first interference MZI experiment the interference visibility showed a monotonic decrease with voltage bias, which was attributed to phase noise [1], in a more recent paper, a surprising non-monotonic decrease with a lobe structure was observed [5]. A satisfactory explanation has not yet been found, and the experiment has so far not been reported by other groups to confirm these results.We report here on an original method to measure the visibility of interferences in a MZI, when low frequency phase fluctuations prevent direct observation of the periodic interference pattern obtained by changing the magnetic flux through the MZI. We studied the visibility at finite energy and observed a single side lobe structure, which can be explained by a gaussian phase averaging whose variance is proportional to V 2 , where V is the bias voltage. To reinforce our result and check if low frequency fluctuation may be responsible for that behavior, we realized the same experiment on a stable sample : we also observed a single side lobe structure which can be fitted with our approach of gaussian phase averaging. This proves the validity of the results, which cannot be an artefact due to the low frequency phase fluctuations in the first sample. In both samples, the dilution of the impinging current has an unexpected effect : it decreases ...

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.

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

We have determined the finite temperature coherence length of edge states in the Integer Quantum Hall Effect (IQHE) regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at filling factor 2. The visibility shows an exponential decay with the temperature. The characteristic temperature scale is found inversely proportional to the length of the interferometer arm, allowing to define a coherence length lϕ. The variations of lϕ with magnetic field are the same for all samples, with a maximum located at the upper end of the quantum hall plateau. Our results provide the first accurate determination of lϕ in the quantum Hall regime.PACS numbers: 03.65. Yz, 73.43.Fj, 73.23.Ad The understanding of the decoherence process is a major issue in solid state physics, especially in view of controlling entangled states for quantum information purposes. The edge states of the quantum Hall effect are known to present an extremely long coherence length l ϕ at low temperature [1], providing a useful tool for quantum interference experiments [2,3,4,5,6]. Surprisingly, very little is known on the exact value of this length and the mechanisms which reduce the coherence of edge states. This is in strong contrast with diffusive conductors, where weak localisation gives a powerful way to probe l ϕ . It has been shown, in this case, that electronelectron interactions are responsible for the finite coherence length at low temperatures. In the IQHE regime, the presence of a high magnetic field destroys any time reversal symmetry needed for weak localisation corrections, making such an investigation difficult. Furthermore, due to the uni-dimensionality of the edge states, electron-electron interactions may strongly modify the single particle picture and one can ask wether the notion of phase coherence length is still relevant and how it depends on temperature. In this letter, we show for the first time that one can define a phase coherence length, and that it is inversely proportional to the temperature. Though the energy redistribution length has been studied in the past [7,8],these scattering experiments do not measure the phase coherence, which requires observation of electron interference effects. So far, experiments have only been able to put a lower bound on l ϕ at low temperatures [2, 9, 10, 11]. The electronic Fabry-Pérot interferences occurring in ballistic quantum dots have been used since the early days of mesoscopic physics [9]. These first studies showed an exponential decay of the amplitude of the Aharonov-Bohm (AB) oscillations with temperature [10]. However, this decay was attributed to thermal smearing due to the contribution of thermally activated one particle energy levels of the dot. Furthermore, the size of the interferometers was not varied, nor was a Fourier analysis performed of the AB oscillations that could yield an estimation of l ϕ [12]. Quantum dot systems also implicate the possible interplay of Coulomb Blockade effects [13]. The Mach-Zender interf...

We present an experiment where we tune the decoherence in a quantum interferometer using one of the simplest objects available in the physics of quantum conductors: an Ohmic contact. For that purpose, we designed an electronic Mach-Zehnder interferometer which has one of its two arms connected to an Ohmic contact through a quantum point contact. At low temperature, we observe quantum interference patterns with a visibility up to 57%. Increasing the connection between one arm of the interferometer to the floating Ohmic contact, the voltage probe, reduces quantum interference as it probes the electron trajectory. This unique experimental realization of a voltage probe works as a trivial which-path detector whose efficiency can be simply tuned by a gate voltage.

The periodic injection n of electrons in a quantum conductor using periodic voltage pulses applied on a contact is studied in the energy and time-domain using shot noise computation in order to make comparison with experiments. We particularly consider the case of periodic Lorentzian voltage pulses. When carrying integer charge, they are known to provide electronic states with a minimal number of excitations, while other type of pulses are all accompanied by an extra neutral cloud of electron and hole excitations. This paper focuses on the low frequency shot noise which arises when the pulse excitations are partitioned by a single scatterer in the framework of the Photo Assisted Shot Noise (PASN) theory. As a unique tool to count the number of excitations carried per pulse, shot noise reveals that pulses of arbitrary shape and arbitrary charge show a marked minimum when the charge is integer. Shot noise spectroscopy is also considered to perform energy-domain characterization of the charge pulses. In particular it reveals the striking asymmetrical spectrum of Lorentzian pulses. Finally, time-domain information is obtained from Hong Ou Mandel like noise correlations when two trains of pulses generated on opposite contacts collide on the scatterer. As a function of the time delay between pulse trains, the noise is shown to measure the electron wavepacket autocorrelation function for integer Lorentzian thanks to electron antibunching. In order to make contact with recent experiments all the calculations are made at zero and finite temperature. This paper addresses the noiseless injection of a small finite number of electrons in a quantum conductor. Indeed, quantum effects become more and more accessible when only few degrees of freedom are controlled. During the last thirty years, research in this direction has lead to the possibility to manipulate quantum states with several degrees of freedom and to entangle particles making possible simple quantum information processing. Up to now most advances have been obtained in quantum optics with the manipulation of single photons emitted by atoms or semiconductor quantum dots, and in atomic physics with optical arrays of trapped cold atoms or ions More recently the manipulation of quantum states has become available in condensed matter systems using superconducting circuits and semiconductor quantum dots.A recent approach is the manipulation of single charges injected in a quantum ballistic conductors. Realizations of time controlled single charge sources have been reported in [1][2][3][4][5] and considered theoretically in [6-13] with a particular focus on the energy resolved single electron source based on a quantum dot [1]. Injecting more than one electron requires a different practical approach which is the subject of this paper. We will consider the more general case of coherent trains of few undistinguishable electrons [14,15] which opens the way to entangle several quasi-particles but also to probe the full counting statistics [16] with a finite number of electrons...

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.