Levitons for electron quantum optics

This an invited contribution submitted to a special issue on "single-electron control in solid-state devices"International audienceSingle electron sources enable electron quantum optics experiments where single electrons emitted in a ballistic electronic interferometer plays the role of a single photons emitted in an optical medium in Quantum Optics. A qualitative step has been made with the recent generation of single charge levitons obtained by applying Lorentzian voltage pulse on the contact of the quantum conductor. Simple to realize and operate, the source emits electrons in the form of striking minimal excitation states called levitons. We review the striking properties of levitons and their possible applications in quantum physics to electron interferometry and entanglement. Schematic generation of time-resolved single charges calledlevitons using Lorentzian voltage pulses applied on a contact.A quantum point contact is used to partition the levitons forfurther analysis. Injecting levitons on opposite contacts with adelay $\tau$ enables us to probe electronic like Hong–Ou–Mandelcorrelations

Integer and fractional charge Lorentzian voltage pulses analyzed in the frame of Photon-assisted Shot Noise

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

Impact of Channel Mixing on the Visibility of Two-particle Interferometry in Quantum Hall Edge States

We consider a two-particle interferometer, where voltage sources applied to ohmic contacts inject electronic excitations into a pair of copropagating edge channels. We analyze the impact of channel mixing due to inter-edge tunneling on the current noise measured at the output of the interferometer. Due to this mixing, the noise suppression typically expected for synchronized injecting sources is incomplete, thereby reducing the visibility of the interference. We investigate to which extent the impact of mixing on the noise visibility depends on different shapes of the voltage drives. Furthermore, we compare a simple model involving a single mixing point between the sources and the quantum point contact to the more realistic case of a continuous distribution of weak mixing points.Comment: 7 pages, 3 figures; accepted for publication in the proceedings of the LT29 Conference (Sapporo, Japan

Influence of channel mixing in fermionic Hong-Ou-Mandel experiments

We consider an electronic Hong-Ou-Mandel interferometer in the integer quantum Hall regime, where the colliding electronic states are generated by applying voltage pulses (creating for instance levitons) to ohmic contacts. The aim of this work is to investigate possible mechanisms leading to a reduced visibility of the Pauli dip, i.e., the noise suppression expected for synchronized sources. It is known that electron-electron interactions cannot account for this effect and always lead to a full suppression of the Hong-Ou-Mandel noise. Focusing on the case of filling factor ?=2, we show instead that a reduced visibility of the Pauli dip can result from mixing of the copropagating edge channels, arising from tunneling events between them

Finite bias visibility of the electronic Mach-Zehnder interferometer

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.Comment: 4 pages, 5 figure

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-P\ue9rot 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

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

Electron quantum optics in graphene

In the last decade, graphene has become an exciting platform for electron optical experiments, in many 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

Etude de la cohérence quantique dans le régime d'effet Hall quantique entier

This work is devoted to the study of decoherence process in the integer quantum Hall regime. In this regime, the current is carried by one dimensional chiral edge channel. These electronic beams are then controlled with mesoscopic beam splitters, the quantum point contacts (QPC). A precise tuning of these QPC enables us to obtain interferences of the conductance. The study of the visibility of these oscillations probes the coherence of the system. In a first part, we have studied the visibility as a function of the bias when the inner edge state is reflected and have observed a lobe structure. We have shown that for a single side lobe, a Gaussian phase averaging can explain this lobe structure. When the inner edge state is transmitted, the visibility decreases monotonously as a function of the bias: we have shown that it resulted from coupling between the inner and outer edge state. In a second part, we have studied the temperature dependence of the visibility in MZIs of different sizes, have extracted for the first time a measurement of the coherence length in the quantum Hall regime and have shown its proportionality to 1/T. We were interested then in the origin of this finite coherence length. We have shown that thermal fluctuations of the inner edge state combined with the coupling between the inner and outer edge state were the source of decoherence. In a last experiment, we have achieved the first experimental realization of the theoretically widely used voltage probe.Ce travail est consacré à l'étude des processus de décohérence dans le régime Hall quantique entier. Le transport électronique se fait alors par un ou plusieurs canaux unidimensionnels chiraux le long du bord de l'échantillon, contrôlés par des lames séparatrices mésoscopiques ou contacts ponctuels quantiques. Un réglage fin de ces contacts ponctuels quantiques permet d'obtenir des interférences de la conductance. L'étude de la visibilité de ces oscillations nous permet de sonder la cohérence du système. Dans un premier temps, nous avons étudié la visibilité en fonction de la tension drain source lorsque le canal interne est réfléchi et avons observé une structure en lobe. Nous avons montré qu'en présence d'un seul lobe, une moyenne gaussienne de la phase permettait de comprendre cette structure en lobe. Lorsque le canal interne est transmis la visibilité en fonction de la tension devient monotone: on comprend ce résultat en tenant compte du couplage entre le canal externe et interne. Dans un deuxième temps nous avons étudié la dépendance en température de la visibilité sur des MZI de différentes tailles, avons extrait pour la première fois une mesure de la longueur de cohérence de phase en régime Hall quantique et avons montré qu'elle était proportionnelle à 1/T. Nous nous sommes ensuite intéressés à l'origine de cette longueur finie de cohérence de phase. Nous avons montré que les fluctuations thermiques du canal interne combinées au couplage entre canaux étaient la source de décohérence. Enfin dans une troisième expérience, nous avons obtenu la première réalisation expérimentale quantitative d'un objet largement utilisé en théorie: la "sonde en tension"

Quantum coherence in the in the quantum Hall regime

Ce travail est consacré à l'étude des processus de décohérence dans le régime Hall quantique entier. Le transport électronique se fait alors par un ou plusieurs canaux unidimensionnels chiraux le long du bord de l'échantillon, contrôlés par des contacts ponctuels quantiques. Un réglage fin de ces contacts ponctuels quantiques permet d'obtenir des interférences de la conductance. Dans un premier temps, nous avons étudié la visibilité de ces oscillations en fonction de la tension drain source et avons observé une structure en lobe: nous avons montré qu une moyenne gaussienne de la phase expliquait cette structure en lobe. Dans un deuxième temps nous avons étudié la dépendance en température de la visibilité, et avons extrait pour la première fois une mesure de la longueur de cohérence de phase en régime Hall. Enfin dans une troisième expérience, nous avons obtenu la première réalisation expérimentale quantitative d'un objet largement utilisé en théorie: la "sonde en tension".PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Physique recherche (751052113) / SudocSudocFranceF