T. Jonckheere

Electron quantum optics in ballistic chiral conductors

The edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in an optics-like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on-demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turns to the presentation of single electron emitters and their characterization through the measurements of the average electrical current and its correlations. This is followed by a discussion of electron quantum optics experiments in the Hanbury-Brown and Twiss geometry where two-particle interferences occur. Finally, Coulomb interactions effects and their influence on single electron states are considered.

Current and noise correlations in a double-dot Cooper-pair beam splitter

We consider a double quantum dot coupled to two normal leads and one superconducting lead, modeling the Cooper pair beam splitter studied in two recent experiments. Starting from a microscopic Hamiltonian we derive a general expression for the branching current and the noise crossed correlations in terms of single and two-particle Greens function of the dot electrons. We then study numerically how these quantities depend on the energy configuration of the dots and the presence of direct tunneling between them, isolating the various processes which come into play. In absence of direct tunneling, the antisymmetric case (the two levels have opposite energies with respect to the superconducting chemical potential) optimizes the Crossed Andreev Reflection (CAR) process while the symmetric case (the two levels have the same energies) favors the Elastic Cotunneling (EC) process. Switching on the direct tunneling tends to suppress the CAR process, leading to negative noise crossed correlations over the whole voltage range for large enough direct tunneling.

Electron and hole Hong-Ou-Mandel interferometry

We consider the electronic analog of the quantum optics Hong-Ou-Mandel interferometer, in a realistic condensed matter device based on single electron emission in chiral edge states. For electron-electron collisions, we show that the measurement of the zero-frequency current correlations at the output of a quantum point contact produces a dip giving precious information on the electronic wavepackets and coherence. As a feature truly unique to Fermi statistics and condensed matter, we show that two-particle interferences between electron and hole in the Fermi sea can produce a positive peak in the current correlations, which we study for realistic experimental parameters.

Electronic Hong-Ou-Mandel interferometry in two-dimensional topological insulators

The edge states of a two-dimensional topological insulator are characterized by their helicity, a very remarkable property which is related to the time-reversal symmetry and the topology of the underlying system. We theoretically investigate a Hong-Ou-Mandel like setup as a tool to probe it. Collisions of two electrons with the same spin show a Pauli dip, analogous to the one obtained in the integer quantum Hall case. Moreover, the collisions between electrons of opposite spin also lead to a dip, known as ℤ2 dip, which is a direct consequence of the constraints imposed by time-reversal symmetry. In contrast to the integer quantum Hall case, the visibility of these dips is reduced by the presence of the additional edge channels, and crucially depends on the properties of the quantum point contact. As a unique feature of this system, we show the possibility of three-electron interference, which leads to a total suppression of the noise independently of the point contact configuration. This is assured by the peculiar interplay between Fermi statistics and topology. This work intends to extend the domain of applicability of electron quantum optics.

Single quasiparticle and electron emitter in the fractional quantum Hall regime

We propose a device consisting of an antidot periodically driven in time by a magnetic field as a fractional quantum Hall counterpart of the celebrated mesoscopic capacitor-based single-electron source. We fully characterize the setup as an ideal emitter of individual quasiparticles and electrons into fractional quantum Hall edge channels of the Laughlin sequence. Our treatment relies on a master equation approach and identifies the optimal regime of operation for both types of sources. The quasiparticle/quasihole emission regime involves in practice only two charge states of the antidot, allowing for an analytic treatment. We show the precise quantization of the emitted charge, we determine its optimal working regime, and we compute the phase-noise/shot-noise crossover as a function of the escape time from the emitter. The emission of electrons, which calls for a larger amplitude of the drive, requires a full numerical treatment of the master equations as more quasiparticle charge states are involved. Nevertheless, in this case the emission of one electron charge followed by one hole per period can also be achieved, and the overall shape of the noise spectrum is similar to that of the quasiparticle source, but the presence of additional quasiparticle processes enhances the noise amplitude.

Real-time simulation of finite frequency noise from a single electron emitter

We study the real-time emission of single electrons from a quantum dot coupled to a one dimensional conductor, using exact diagonalization on a discrete tight-binding chain. We show that from the calculation of the time-evolution of the one electron states, we have a simple access to all the relevant physical quantities in the system. In particular, we are able to compute accurately the finite frequency current autocorrelation noise. The method which we use is general and versatile, allowing to study the impact of many different parameters like the dot transparency or level position. Our results can be directly compared with existing experiments, and can also serve as a basis for future calculations including electronic interactions using the time dependent density-matrix renormalisation group and other techniques based on tight-binding models.

Current correlations in the interacting Cooper-pair beam-splitter

Using a conserving many-body treatment, we propose an approach allowing the computation of currents and their correlations in interacting multi-terminal mesoscopic systems involving quantum dots coupled to normal and/or superconducting leads. We illustrate our method with the Cooper-pair beam-splitter setup recently proposed, which we model as a double quantum dot with weak interactions, connected to a superconducting lead and two normal ones. Our results suggest that even a weak Coulomb repulsion tends to favor positive current cross-correlations.

Electronic quantum optics beyond the integer quantum Hall effect

The analogs of two seminal quantum optics experiments are considered in a condensed-matter setting with single-electron sources injecting electronic wave packets on edge states coupled through a quantum point contact. When only one electron is injected, the measurement of noise correlations at the output of the quantum point contact corresponds to the Hanbury–Brown and Twiss setup. When two electrons are injected on opposite edges, the equivalent of the Hong–Ou–Mandel collision is achieved, exhibiting a dip, as in the coincidence measurements of quantum optics. The Landauer–Buttiker scattering theory is used to first review these phenomena in the integer quantum Hall effect, next, to focus on two more exotic systems: edge states of two-dimensional topological insulators, where new physics emerges from time reversal symmetry and three-electron collisions can be achieved; and edges states of a hybrid Hall/superconducting device, which allow electron quantum optics experiments with Bogoliubov quasiparticles to be performed.

Nonlocal interference and Hong-Ou-Mandel collisions of single Bogoliubov quasiparticles

We consider a device which allows one to create and probe single Majorana fermions, in the form of Bogoliubov quasiparticles. It is composed of two counterpropagating edge channels, each put in proximity with a superconducting region where Andreev reflection operates, and which thus converts electrons into Bogoliubov quasiparticles. The edge channels then meet at a quantum point contact where collisions can be achieved. A voltage-biased version of the setup was studied [C. W. J. Beenakker, Phys. Rev. Lett. 112, 070604 (2014)] and showed nonlocal interference phenomena and signatures of Bogoliubov quasiparticle collisions in the high-frequency noise characteristics at the output, constituting an evidence of the Majorana fermion nature of these excitations. Here, voltage-biased leads are replaced by single-electron sources in order to achieve collisions of single Bogoliubov quasiparticles, with the major advantage that zero-frequency noise measurements are sufficient to access the intimate nature of Bogoliubov wave packets. We compute the injection parameters of the source, and go on to investigate the Hanbury-Brown and Twiss and Hong-Ou-Mandel signal at the output, as a function of the mixing angle which controls the electron/hole component of the Bogoliubov wave packet. In particular, information on the internal structure of the Bogoliubov quasiparticle can be recovered when such a quasiparticle collides with a pure electron. Experimental feasibility with singlet or triplet superconductors is discussed.

Cooper pair splitting and recombination in a nanoSQUID geometry at high transparency

We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, as a probe for Cooper pair splitting. In addition to sequential tunneling of electrons through each dot, an additional transport channel exists in this system: crossed Andreev reflection, where a Cooper pair from the source is split between the two dots and recombined in the drain superconductor. Unlike non-equilibrium scenarios for Cooper pair splitting which involves superconducting/normal metal forks, our proposal relies on an Aharonov-Bohm measurement of the DC Josephson current when a flux is inserted between the two dots. We provide a path integral approach to treat arbitrary transparencies, and we explore all contributions for the individual phases (