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.
On the elementary level, electronic current consists of individual electron tunnelling events that are separated by random time intervals. The waiting time distribution is a probability to observe the electron transfer in the detector electrode at time $t+τ$ given that an electron was detected in the same electrode at earlier time $t$. We study waiting time distribution for quantum transport in a vibrating molecular junction. By treating the electron-vibration interaction exactly and molecule-electrode coupling perturbatively, we obtain master equation and compute the distribution of waiting t…
We investigate the distribution of waiting times between electrons emitted from a periodically driven single-electron turnstile. To this end, we develop a scheme for analytic calculations of the waiting time distributions for arbitrary periodic driving protocols. We illustrate the general framework by considering a driven tunnel junction before moving on to the more involved single-electron turnstile. The waiting time distributions are evaluated at low temperatures for square-wave and harmonic driving protocols. In the adiabatic regime, the dynamics of the turnstile is synchronized with the ex…
The electron waiting time is the time that passes between two subsequent charge transfers in an electronic conductor. Recently, theories of electron waiting times have been devised for quantum transport in Coulomb-blockade structures and for mesoscopic conductors, however, so far a proper description of a detector has been missing. Here we develop a quantum theory of a waiting time clock capable of measuring the distribution of waiting times between electrons above the Fermi sea in a mesoscopic conductor. The detector consists of a mesoscopic capacitor coupled to a quantum two-level system who…
Electron waiting times are an important concept in the analysis of quantum transport in nano-scale conductors. Here we show that the statistics of electron waiting times can be used to characterize Cooper pair splitters that create spatially separated spin-entangled electrons. A short waiting time between electrons tunneling into different leads is associated with the fast emission of a split Cooper pair, while long waiting times are governed by the slow injection of Cooper pairs from a superconductor. Experimentally, the waiting time distributions can be measured using real-time single-electr…
We evaluate the joint distributions of electron waiting times in coherent conductors described by scattering theory. Successive electron waiting times in a single-channel conductor are found to be correlated due to the fermionic statistics encoded in the many-body state. Our formalism allows us also to investigate the waiting times between charge transfer events in different outgoing channels. As an application we consider a quantum point contact in a chiral setup with one or both input channels biased by either a static or a time-dependent periodic voltage described by Floquet theory. The the…
We evaluate the distribution of waiting times between electrons emitted by a driven mesoscopic capacitor. Based on a wave packet approach we obtain analytic expressions for the electronic waiting time distribution and the joint distribution of subsequent waiting times. These semi-classical results are compared to a full quantum treatment based on Floquet scattering theory and good agreement is found in the appropriate parameter ranges. Our results provide an intuitive picture of the electronic emissions from the driven mesoscopic capacitor and may be tested in future experiments.
We consider a normal-superconducting junction in order to investigate the effect of new physical ingredients on waiting times. First, we study the interplay between Andreev and specular scattering at the interface on the distribution of waiting times of electrons or holes separately. In that case the distribution is not altered dramatically compared to the case of a single quantum channel with a quantum point contact since the interface acts as an Andreev mirror for holes. We then consider a fully entangled state originating from spliting of Cooper pairs at the interface and demonstrate a sign…
In the resonant tunneling regime sequential processes dominate single electron transport through quantum dots or molecules that are weakly coupled to macroscopic electrodes. In the Coulomb blockade regime, however, cotunneling processes dominate. Cotunneling is an inherently quantum phenomenon and thus gives rise to interesting observations, such as an increase in the current shot noise. Since cotunneling processes are inherently fast compared to the sequential processes, it is of interest to examine the short time behaviour of systems where cotunneling plays a role, and whether these systems …
Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared to what can be learned from the electric current fluctuations. Existing theories, however, are restricted to either weakly coupled nanostructures or phase-coherent transport in mesoscopic conductors. Here, we consider an interacting quantum dot and develop a real-time diagrammatic theory of waiting time distributions that can treat the interesting regime, in which both interaction effects and higher-order tunneling processes are important. S…
The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterising transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which have historically been calculated in the long-time limit, waiting times are able to detect non-renewal behaviour in mesoscopic systems. They have failed, however, to correctly incorporate backtunneling events. Recently, a method has been developed that can describe unidirectional and bidirectional transport on an equal footing: the distribution of first-passag…
We discuss the electronic waiting-time distribution of a quantum-dot spin valve, i.e. a single-level quantum dot coupled to two ferromagnetic electrodes with magnetizations that can point in arbitrary directions. We demonstrate that the rich transport physics of this setup such as dynamical channel blockade and spin precession in an interaction-driven exchange field shows up in the waiting-time distribution and analyze the conditions necessary to observe the various effects.
The distribution of electron waiting times is useful to characterize quantum transport in mesoscopic 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-P…
We consider a biased Normal-Superconducting junction with various types of superconductivity. Depending on the class of superconductivity, a Majorana bound state may appear at the interface. We show that this has important consequences on the distribution of waiting times of electrons flowing out of such an interface. Therefore, the waiting time distribution is shown to be a clear fingerprint of Majorana bound state physics and may be considered as an experimental signature of its presence.
We study the electronic waiting time distributions (WTDs) in a non-interacting quantum dot spin valve by varying spin polarization and the noncollinear angle between the magnetizations of the leads using scattering matrix approach. Since the quantum dot spin valve involves two channels (spin up and down) in both the incoming and outgoing channels, we study three different kinds of WTDs, which are two-channel WTD, spin-resolved single-channel WTD and cross-channel WTD. We analyze the behaviors of WTDs in short times, correlated with the current behaviors for different spin polarizations and non…
Field electron emission from nanometer-scale objects deviates from the predictions of the classical emission theory as both the electrostatic potential curves within the tunneling region and the image potential deviates from the planar one. This impels the inclusion of additional correction terms in the potential barrier. At the apex of a tip-like rotationally symmetric surface, these terms are proportional to the (single) local emitter curvature. The present paper generalizes this relation, showing that for any emitter geometry, the coefficient of the correction terms is given by the mean cur…
We investigate the waiting time distributions (WTDs) of superconducting hybrid junctions, considering both conventional and topologically nontrivial superconductors hosting Majorana bound states at their edges. To this end, we employ a scattering matrix formalism that allows us to evaluate the waiting times between the transmissions and reflections of electrons or holes. Specifically, we analyze normal-metal-superconductor (NIS) junctions and NISIN junctions, where Cooper pairs are spatially split into different leads. The distribution of waiting times is sensitive to the simultaneous reflecti…
Quantum transport of electrons through a molecule is a series of individual electron tunnelling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using master equation approach, we compute joint probability distribution for waiting times of two successive tunnelling events. We show that the probability distribution is completely reset after each tunnelling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics ex…
We investigate the temperature-driven quantum-to-classical crossover in a single-electron emitter. The emitter is composed of a quantum conductor and an electrode, which is coupled via an Ohmic contact. At zero temperature, it has been shown that a single electron can be injected coherently by applying an unit-charge Lorentzian pulse on the electrode. As the electrode temperature increases, we show that the electron emission approaches a time-dependence Poisson process at long times. The Poissonian character is demonstrated from the time-resolved full counting statistics. In the meantime, we s…
We study the spin-resolved subgap transport in a triple quantum-dot system coupled to one superconducting and two ferromagnetic leads. We examine the Andreev processes in the parallel and antiparallel alignments of ferromagnets magnetic moments in both the linear and nonlinear response regimes. The emphasis is put on the analysis of the current cross-correlations between the currents flowing through the left and right arms of the device and relevant electron waiting time distributions. We show that both quantities can give an important insight into the subgap transport processes and their anal…
Waiting time distribution and the zero-frequency full counting statistics of unidirectional electron transport through a double quantum dot molecule attached to spin-polarized leads are analyzed using the quantum master equation. The waiting time distribution exhibits a non-trivial dependence on the value of the exchange coupling between the dots and the gradient of the applied magnetic field, which reveals the oscillations between the spin states of the molecule. The zero-frequency full counting statistics, on the other hand, is independent of the aforementioned quantities, thus giving no ins…
We analyze charge fluctuations in a parasitic state strongly coupled to a superconducting Josephson-junction-based charge detector. The charge dynamics of the state resembles that of electron transport in a quantum dot with two charge states, and hence we refer to it as a two-level fluctuator. By constructing the distribution of waiting times from the measured detector signal and comparing it with a waiting time theory, we extract the electron in- and out-tunneling rates for the two-level fluctuator, which are severely asymmetric.
We derive the symmetrized current-noise spectrum of a quantum dot, which is weakly tunnel-coupled to an electron reservoir and driven by a slow time-dependent gate voltage. This setup can be operated as an on-demand emitter of single electrons into a mesoscopic conductor. By extending a real-time diagrammatic technique which is perturbative in the tunnel coupling, we obtain the time-resolved finite-frequency noise as well as its decomposition into noise harmonics in the presence of both strong Coulomb interaction and slow time-dependent driving. We investigate the noise over a large range of f…
We study theoretically the nonlinear optical properties of a semiconductor quantum well (QW) irradiated by a two-mode electromagnetic wave consisting of a strong resonant dressing field and a weak off-resonant driving field. In the considered strongly coupled electron-field system, the dressing field opens dynamic Stark gaps in the electron energy spectrum of the QW, whereas the driving field induces electron oscillations in the QW plane. Since the gapped electron spectrum restricts the amplitude of the oscillations, the emission of a frequency comb from the QW appears. Therefore, the doubly-d…
We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical res…
The development of single-electron sources has paved the way for a novel type of experiments in which individual electrons are emitted into a quantum-coherent circuit. In one approach, single-electron excitations are generated by applying Lorentzian-shaped voltage pulses to a contact. Here, we propose to use such voltage pulses for electronic spectroscopy of mesoscopic devices. Specifically, we show how characteristic timescales of a quantum-coherent conductor can be extracted from the distribution of waiting times between charge pulses propagating through a mesoscopic circuit. To illustrate o…
Due to their band-structure and optical properties, InAs/InP quantum dots (QDs) constitute a promising system for single-photon generation at third telecom window of silica fibers and for applications in quantum communication networks. However, obtaining the necessary low in-plane density of emitters remains a challenge. Such structures are also still less explored than their InAs/GaAs counterparts regarding optical properties of confined carriers. Here, we report on the growth via metal-organic vapor phase epitaxy and investigation of low-density InAs/InP QD-like structures, emitting in the r…
Thermionic converters generate electricity from thermal energy in a power cycle based on vacuum emission of electrons. While thermodynamically efficient, practical implementations are limited by the extreme temperatures required for electron emission (> 1500 K). Here, we show how metal nanostructures that support resonant plasmonic absorption enable an alternative strategy. High electronic temperatures required for efficient vacuum emission can be maintained during steady-state optical absorption while the lattice temperature remains within the range of thermal stability, below 600 K. We have …
Quantum emitters based on atomic defects in layered hexagonal Boron Nitride (hBN) have emerged as promising solid state 'artificial atoms' with atom-like photophysical and quantum optoelectronic properties. Similar to other atom-like emitters, defect-phonon coupling in hBN governs the characteristic single-photon emission and provides an opportunity to investigate the atomic and electronic structure of emitters as well as the coupling of their spin- and charge-dependent electronic states to phonons. Here, we investigate these questions using photoluminescence excitation (PLE) experiments at T=…
When electric current flows through a molecular junction, the molecule constantly charges and discharges by tunnelling electrons. These charging and discharging events occur at specific but random times and separated by stochastic time intervals. These time intervals can be associated with dwelling time for a charge (electron or hole) to reside on the molecule. In this paper, the statistical properties of these time intervals are studied and general formula for their distribution is derived. The theory is based on the Markovian master equation which takes into account transitions between vibra…
We present the development of the first ultrafast transmission electron microscope (UTEM) driven by localized photoemission from a field emitter cathode. We describe the implementation of the instrument, the photoemitter concept and the quantitative electron beam parameters achieved. Establishing a new source for ultrafast TEM, the Göttingen UTEM employs nano-localized linear photoemission from a Schottky emitter, which enables operation with freely tunable temporal structure, from continuous wave to femtosecond pulsed mode. Using this emission mechanism, we achieve record pulse properties in …
Heterostructures comprising of silicon (Si), molybdenum disulfide (MoS${_2}$) and graphene are investigated with respect to the vertical current conduction mechanism. The measured current-voltage (I-V) characteristics exhibit temperature dependent asymmetric current, indicating thermally activated charge carrier transport. The data is compared and fitted to a current transport model that confirms thermionic emission as the responsible transport mechanism across the devices. Theoretical calculations in combination with the experimental data suggest that the heterojunction barrier from Si to MoS…
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 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, allo…
Solid-state single photon sources (SPSs) with narrow line width play an important role in many leading quantum technologies. Within the wide range of SPSs studied to date, single fluorescent molecules hosted in organic crystals stand out as bright, photostable SPSs with a lifetime-limited optical resonance at cryogenic temperatures. Furthermore, recent results have demonstrated that photostability and narrow line widths are still observed from single molecules hosted in a nanocrystalline environment, which paves the way for their integration with photonic circuitry. Polymers offer a compatible…
