We propose a device consisting in 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 emi
tter 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.
We consider a device which allows to create and probe single Majorana fermions, in the form of Bogoliubov quasiparticles. It is composed of two counter-propagating edge channels, each put in proximity with a superconducting region where Andreev refle
ction 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 in Phys. Rev. Lett. 112, 070604 (2014) and showed non-local 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.
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-O
u-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 $mathbb{Z}_{2}$ 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.
We propose an approach allowing the computation of currents and their correlations in interacting multiterminal mesoscopic systems involving quantum dots coupled to normal and/or superconducting leads. The formalism relies on the expression of branch
ing currents and noise crossed correlations in terms of one- and two-particle Greens functions for the dots electrons, which are then evaluated self-consistently within a conserving approximation. We then apply this to the Cooper-pair beam-splitter setup recently proposed [L. Hofstetter et al. Nature (London) 461 960 (2009); Phys. Rev. Lett. 107 136801 (2011); L. G. Herrmann et al. Phys. Rev. Lett. 104 026801 (2010)], which we model as a double quantum dot with weak interactions, connected to a superconducting lead and two normal ones. Our method not only enables us to take into account a local repulsive interaction on the dots, but also to study its competition with the direct tunneling between dots. Our results suggest that even a weak Coulomb repulsion tends to favor positive current cross correlations in the antisymmetric regime (where the dots have opposite energies with respect to the superconducting chemical potential).
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 branch
ing 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.
We study the conductance of a quantum wire in the presence of weak electron-electron scattering. In a sufficiently long wire the scattering leads to full equilibration of the electron distribution function in the frame moving with the electric curren
t. At non-zero temperature this equilibrium distribution differs from the one supplied by the leads. As a result the contact resistance increases, and the quantized conductance of the wire acquires a quadratic in temperature correction. The magnitude of the correction is found by analysis of the conservation laws of the system and does not depend on the details of the interaction mechanism responsible for equilibration.
