A Coherent RC Circuit

We review the first experiment on dynamic transport in a phase-coherent quantum conductor. In our discussion, we highlight the use of time-dependent transport as a means of gaining insight into charge relaxation on a mesoscopic scale. For this purpose, we studied the ac conductance of a model quantum conductor, i.e. the quantum RC circuit. Prior to our experimental work, M. B\"{u}ttiker, H. Thomas and A. Pr\^{e}tre first worked on dynamic mesoscopic transport in the 1990s. They predicted that the mesoscopic RC circuit can be described by a quantum capacitance related to the density of states in the capacitor and a constant charge relaxation resistance value equal to half of the resistance quantum h/2e^2, when a single mode is transmitted between the capacitance and a reservoir. By applying a microwave excitation to a gate located on top of a coherent submicronic quantum dot that is coupled to a reservoir, we validate this theoretical prediction on the ac conductance of the quantum RC circuit. Our study demonstrates that the ac conductance is directly related to the dwell time of electrons in the capacitor. Thereby, we observed a counterintuitive behavior of a quantum origin: as the transmission of the single conducting mode decreases, the resistance of the quantum RC circuit remains constant while the capacitance oscillates.Comment: 30 page

A high sensitivity ultra-low 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 milliKelvin temperatures. The setup relies on the combination of an interferometric ampli- fication scheme and a quarter-wave impedance transformer, allowing the mea- surement of noise power spectral densities with GHz bandwith 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 bandwith make it suitable for applications manipulating single charges at GHz frequencies.Comment: The following article has been submitted to Review of Scientific Instrument

Violation of Kirchhoff's Laws for a Coherent RC Circuit

What is the complex impedance of a fully coherent quantum resistance-capacitance (RC) circuit at GHz frequencies in which a resistor and a capacitor are connected in series? While Kirchhoff's laws predict addition of capacitor and resistor impedances, we report on observation of a different behavior. The resistance, here associated with charge relaxation, differs from the usual transport resistance given by the Landauer formula. In particular, for a single mode conductor, the charge relaxation resistance is half the resistance quantum, regardless of the transmission of the mode. The new mesoscopic effect reported here is relevant for the dynamical regime of all quantum devices

Coherence and Indistinguishability of Single Electrons Emitted by Independent Sources

The on-demand emission of coherent and indistinguishable electrons by independent synchronized sources is a challenging task of quantum electronics, in particular regarding its application for quantum information processing. Using two independent on-demand electron sources, we trigger the emission of two single-electron wavepackets at different inputs of an electronic beamsplitter. Whereas classical particles would be randomly partitioned by the splitter, we observe two-particle interferences resulting from quantum exchange. Both electrons, emitted in indistinguishable wavepackets with synchronized arrival time on the splitter, exit in different outputs as recorded by the low frequency current noise. The demonstration of two-electron interference provides the possibility to manipulate coherent and indistinguishable single-electron wavepackets in quantum conductors.Comment: Science Express of January 24 201

The relaxation time of a chiral quantum R-L circuit

We report on the GHz complex admittance of a chiral one dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission-independent. This shows that the relaxation time of a chiral R-L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the c cuit

Klein-tunneling transistor with ballistic graphene

Today the availability of high mobility graphene up to room temperature makes ballistic transport in nanodevices achievable. In particular, p-n-p transistor in the ballistic regime gives access to the Klein tunneling physics and allows the realization of devices exploiting the optics-like behavior of Dirac Fermions (DF) as in the Vesalego lens or the Fabry P\'erot cavity. Here we propose a Klein tunneling transistor based on geometrical optics of DF. We consider the case of a prismatic active region delimited by a triangular gate, where total internal reflection may occur, which leads to the tunable suppression of the transistor transmission. We calculate the transmission and the current by means of scattering theory and the finite bias properties using Non Equilibrium Green's Function(NEGF) simulation.Comment: 4 pages, 5 figure

An On-Demand Coherent Single Electron Source

We report on the electron analog of the single photon gun. On demand single electron injection in a quantum conductor was obtained using a quantum dot connected to the conductor via a tunnel barrier. Electron emission is triggered by application of a potential step which compensates the dot charging energy. Depending on the barrier transparency the quantum emission time ranges from 0.1 to 10 nanoseconds. The single electron source should prove useful for the implementation of quantum bits in ballistic conductors. Additionally periodic sequences of single electron emission and absorption generate a quantized AC-current

Hanbury-Brown Twiss correlations to probe the population statistics of GHz photons emitted by conductors

soumis le 22 mars 2004We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury-Brown and Twiss correlations. The superpoissonian and poissonian photon statistics of thermal and coherent sources respectively made of a resistor and a radiofrequency generator are measured down to the quantum regimeat milliKelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductor

Subnanosecond single electron source in the time-domain

International audienceWe describe here the realization of a single electron source similar to single photon sources in optics. On-demand single electron injection is obtained using a quantum dot connected to the conductor via a tunnel barrier of variable transmission (quantum point contact). Electron emission is triggered by a sudden change of the dot potential which brings a single energy level above the Fermi energy in the conductor. A single charge is emitted on an average time ranging from 100 ps to 10 ns ultimately determined by the barrier transparency and the dot charging energy. The average single electron emission process is recorded with a 0.5 ns time resolution using a real-time fast acquisition card. Single electron signals are compared tosimulation based on scattering theory approach adapted for finite excitation energies

Characterization of helical Luttinger liquids in microwave stepped-impedance edge resonators

Coulomb interaction has important consequences on the physics of quantum spin Hall edge states, weakening the topological protection via two-particle scattering and renormalizing both the velocity and charge of collective plasmon modes compared to that of free electrons. Despite these effects, interactions remain difficult to quantify. We propose here simple and robust edge resonator geometries to characterize Coulomb interaction by means of high-frequency measurements. They rely on a transmission line approach, and take advantage of the impedance mismatch between the edge states and their microwave environment.Comment: 8 pages, 5 figures. Accepted for publication in Phys. Rev. Researc