Mathias Albert

Tomonaga–Luttinger physics in electronic quantum circuits

In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga–Luttinger liquids is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances are suppressed at low energy, a phenomenon called dynamical Coulomb blockade. Here we investigate the conductance of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance, and demonstrate a proposed link to Tomonaga–Luttinger physics. We reformulate and establish experimentally a recently derived phenomenological expression for the conductance using a wide range of circuits, including carbon nanotube data obtained elsewhere. By confronting both conductance data and phenomenological expression with the universal Tomonaga–Luttinger conductance curve, we demonstrate experimentally the predicted mapping between dynamical Coulomb blockade and the transport across a Tomonaga–Luttinger liquid with an impurity.

Current noise spectrum of a single-particle emitter: Theory and experiment

The controlled and accurate emission of coherent electronic wave packets is of prime importance for future applications of nano-scale electronics. Here we present a theoretical and experimental analysis of the finite-frequency noise spectrum of a periodically driven single electron emitter. The electron source consists of a mesoscopic capacitor that emits single electrons and holes into a chiral edge state of a quantum Hall sample. We compare experimental results with two complementary theoretical descriptions: On one hand, the Floquet scattering theory which leads to accurate numerical results for the noise spectrum under all relevant operating conditions. On the other hand, a semi-classical model which enables us to develop an analytic description of the main sources of noise when the emitter is operated under optimal conditions. We find excellent agreement between experiment and theory. Importantly, the noise spectrum provides us with an accurate description and characterization of the mesoscopic capacitor when operated as a periodic single electron emitter.

Accuracy of the quantum capacitor as a single-electron source

A periodically driven quantum capacitor may function as an on-demand single-electron source as it has recently been demonstrated experimentally. However, the accuracy at which single electrons are emitted is not yet understood. Here we consider a conceptually simple model of a quantum capacitor and find analytically the noise spectrum as well as the counting statistics of emitted electrons. We find that the failure rate of the capacitor can be arbitrarily small when operated under favorable conditions. Our theoretical predictions may be tested in future experiments.

Distributions of waiting times of dynamic single-electron emitters

The distribution of waiting times between elementary tunneling events is of fundamental importance for understanding the stochastic charge transfer processes in nanoscale conductors. Here we investigate the waiting time distributions (WTDs) of periodically driven single-electron emitters and evaluate them for the specific example of a mesoscopic capacitor. We show that the WTDs provide a particularly informative characterization of periodically driven devices and we demonstrate how the WTDs allow us to reconstruct the full counting statistics (FCS) of charges that have been transferred after a large number of periods. We find that the WTDs are capable of describing short-time physics and correlations which are not accessible via the FCS alone.

Electron waiting times in mesoscopic conductors.

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with level spacing statistics and random matrix theory.

Quantum Heat Fluctuations of Single-Particle Sources

Optimal single electron sources emit regular streams of particles, displaying no low-frequency charge current noise. Because of the wave packet nature of the emitted particles, the energy is, however, fluctuating, giving rise to heat current noise. We investigate theoretically this quantum source of heat noise for an emitter coupled to an electronic probe in the hot-electron regime. The distribution of temperature and potential fluctuations induced in the probe is shown to provide direct information on the single-particle wave function properties and display strong nonclassical features.

Localization by bichromatic potentials versus Anderson localization

The one-dimensional propagation of waves in a bichromatic potential may be modeled by the Aubry-Andre Hamiltonian. This, in turn, presents a localization transition that has been observed in recent experiments using ultracold atoms or light. It is shown here that, in contrast to the Anderson model, the localization mechanism has a classical origin, namely it is not due to a quantum suppression of a classically allowed transport process, but rather is produced by a trapping by the potential. Explicit comparisons with the Anderson model as well as with experiments are presented.

Resonant Hawking radiation in Bose-Einstein condensates

We study double-barrier interfaces separating regions of asymptotically subsonic and supersonic flow of Bose-condensed atoms. These setups contain at least one black hole sonic horizon from which the analogue of Hawking radiation should be generated and emitted against the flow in the subsonic region. Multiple coherent scattering by the double-barrier structure strongly modulates the transmission probability of phonons, rendering it very sensitive to their frequency. As a result, resonant tunneling occurs with high probability within a few narrow frequency intervals. This gives rise to highly non-thermal spectra with sharp peaks. We find that these peaks are mostly associated with decaying resonances and only occasionally with dynamical instabilities. Even at achievable non-zero temperatures, the radiation peaks can be dominated by spontaneous emission, i.e. enhanced zero-point fluctuations, and not, as is often the case in analogue models, by stimulated emission.

Dipole oscillations of a Bose-Einstein condensate in the presence of defects and disorder.

We consider dipole oscillations of a trapped dilute Bose-Einstein condensate in the presence of a scattering potential consisting either in a localized defect or in an extended disordered potential. In both cases the breaking of superfluidity and the damping of the oscillations are shown to be related to the appearance of a nonlinear dissipative flow. At supersonic velocities the flow becomes asymptotically dissipationless.

Distributions of electron waiting times in quantum-coherent conductors

The distribution of electron waiting times is useful to characterize quantum transport in meso-scopic structures. Here we consider a generic quantum-coherent conductor consisting of a mesoscopic scatterer in a two-terminal setup. We extend earlier results for single-channel conductors to setups with several (possibly spin-degenerate) conduction channels and we discuss the effect of a finite electronic temperature. We present detailed investigations of the electron waiting times in a quantum point contact as well as in two mesoscopic interferometers with energy-dependent transmissions: a Fabry-Perot interferometer and a Mach-Zehnder interferometer. We show that the waiting time distributions allow us to determine characteristic features of the scatterers, for instance the number of resonant levels in the Fabry-Perot interferometer that contribute to the electronic transport.