Electronic transport through nanostructures can be suppressed by coherent population trapping, in which quantum coherence leads to a dark state that decouples from the drain electrode. Finite transport, then, relies on decoherence of the dark state. An alternative scenario for reduced transport is weak coupling of a state, referred to as a blocking state, to the drain. This raises the question of whether and how these two scenarios can be distinguished in the transport features. For the example of electron transport through a carbon nanotube, we identify regimes, in which this distinction is possible by analyzing the full counting statistics in terms of Lee-Yang zeros and factorial cumulants.

Spin-electronic devices are poised to become part of mainstream microelectronic technology .Downsizing them, however, faces the intrinsic difficulty that as ferromagnets become smaller, it becomes more difficult to stabilize their magnetic moment. Antiferromagnets are much more stable, and thus research on antiferromagnetic spintronics has developed into a fast-growing field. Here, we provide proof of concept data that allows us to expand the area of antiferromagnetic spintronics to the hitherto elusive level of individual molecules. In contrast to all previous work on molecular spintronics, our detection scheme of the molecule's spin state does not rely on a magnetic moment. Instead, we use field-effect transistor devices constituting of an isolated, contacted single-wall carbon nanotube covalently bound to a limited number of molecular antiferromagnets incorporating four Mn(II) or Co(II) ions. Time-dependent quantum transport measurement along the functionalized nanotube show step-like transitions between several distinct current levels, which we attribute to transitions between different antiferromagnetic states of individual molecular complexes grafted on the nanotube. A statistical analysis of the switching events using factorial cumulants indicates that the cobalt complexes switch independently from each other, while a coherent superposition of the antiferromagnetic spin states of the molecules along the nanotube is observed for the manganese complexes. The long coherence time (several seconds at 100 mK) is made possible by the absence of spin and orbital momentum in the relevant states of the manganese complex, while the cobalt complex includes a significant orbital momentum contribution due to the pseudo-octahedral d$^7$ metal centers.

Among the best known quantities obtainable from photon correlation measurements are the g((m)) correlation functions. Here, we introduce a new procedure to evaluate these correlation functions based on higher-order factorial cumulants C-F,C-m that integrate over the time dependence of the correlation functions, that is, summarize the available information at different time spans. In a systematic manner, the information content of higher-order correlation functions as well as the distribution of photon waiting times is taken into account. Our procedure greatly enhances the sensitivity for probing correlations and, moreover, is robust against a limited counting efficiency and time resolution in experiment. It can be applied even in case g((m)) is not accessible at short time spans. We use the new evaluation scheme to analyze the photon emission of a plasmonic cavity coupled to a single quantum dot. We derive criteria that must hold if the system can be described by a generic Jaynes-Cummings model. A violation of the criteria can be explained by the presence of an additional excited quantum dot state.

Time-resolved studies of quantum systems are the key to understanding quantum dynamics at its core. The real-time measurement of individual quantum numbers as they switch between certain discrete values, well known as a "random telegraph signal," is expected to yield maximal physical insight. However, the signal suffers from both systematic errors, such as a limited time resolution and noise from the measurement apparatus, as well as statistical errors due to a limited amount of data. Here we demonstrate that an evaluation scheme based on factorial cumulants can reduce the influence of such errors by orders of magnitude. The error resilience is supported by a general theory for the detection errors as well as experimental data of single-electron tunneling through a self-assembled quantum dot. Thus, factorial cumulants push the limits in the analysis of random telegraph data, which represent a wide class of experiments in physics, chemistry, engineering, and life sciences.

Spin-electronic devices are poised to become part of mainstream microelectronic technology. Downsizing them, however, faces the intrinsic difficulty that as ferromagnets become smaller, it becomes more difficult to stabilize their magnetic moment. Antiferromagnets are much more stable, and thus research on antiferromagnetic spintronics has developed into a fast-growing field. Here, we provide proof of concept data that allows us to expand the area of antiferromagnetic spintronics to the hitherto elusive level of individual molecules. In contrast to all previous work on molecular spintronics, our detection scheme of the molecule's spin state does not rely on a magnetic moment. Instead, we use the step-like transitions between several distinct current levels caused by transitions between different antiferromagnetic states of an individual molecule grafted onto a carbon nanotube. We find that in the absence of an orbital momentum the antiferromagnetic spin states of the molecules show coherent superposition.

We study the switching behavior of two spin-crossover molecules residing in a nanojunction device consisting of two closely spaced gold electrodes. The spin states are monitored through a real-time measurement of the resistance of the junction. A statistical analysis of the resistance values, the occupation probabilities, and the lifetimes of the respective spin states shows that the two spin-crossover molecules are coupled to each other. We extract the parameters for a minimal model describing the two coupled spin-crossover molecules. Finally, we use the time dependence of factorial cumulants to study the impact of interactions between the two spin-crossover molecules on the switching dynamics.

Distributions of electron waiting times have been measured in several recent experiments and have been shown to provide complementary information compared with 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. Specifically, we find that our quantum-mechanical theory captures higher-order tunneling processes at low temperatures, which are not included in a classical description, and which dramatically affect the waiting times by allowing fast tunneling processes inside the Coulomb blockade region. Our work paves the way for systematic investigations of temporal fluctuations in interacting quantum systems, for example close to a Kondo resonance or in a Luttinger liquid.

We study coherent oscillations in double quantum dots tunnel-coupled to metallic leads by means of full counting statistics of electron transport. If two such systems are coupled by Coulomb interaction, there are in total six (instead of only two) oscillation modes of the entangled system with interaction-dependent oscillation frequencies. By tuning the bias voltage, one can engineer decoherence such that only one of the six modes, in which the charge oscillations in both double quantum dots become synchronized in antiphase, is singled out. We suggest to use waiting-time distributions and the $g^{(2)}$-correlation function to detect the common frequency and the phase locking.

Auger recombination is a nonradiative process, where the recombination energy of an electron-hole pair is transferred to a third charge carrier. It is a common effect in colloidal quantum dots that quenches the radiative emission with an Auger recombination time below nanoseconds. In self-assembled QDs, the Auger recombination has been observed with a much longer recombination time on the order of microseconds. Here, we use two-color laser excitation on the exciton and trion transition in resonance fluorescence on a single self-assembled quantum dot to monitor in real-time single quantum events of the Auger process. Full counting statistics on the random telegraph signal give access to the cumulants and demonstrate the tunability of the Fano factor from a Poissonian to a sub-Poissonian distribution by Auger-mediated electron emission from the dot. Therefore, the Auger process can be used to tune optically the charge carrier occupation of the dot by the incident laser intensity, independently from the electron tunneling from the reservoir by the gate voltage. Our findings are not only highly relevant for the understanding of the Auger process but also demonstrate the perspective of the Auger effect for controlling precisely the charge state in a quantum system by optical means.

We consider the relaxation dynamics of two spins coupled to a common bosonic bath. The time evolution is simulated by a generalized master equation derived within a real-time diagrammatic approach. Interference effects due to the coherent coupling to the common bath give rise to characteristic features in the relaxation dynamics after a quench or during a periodic external driving. In particular, we find that the long-time behavior during periodic driving depends sensitively on the initial state as well as on system parameters such as coupling asymmetries. When coupled to more than a single reservoir, the interference effects can lead to a cooling mechanism for one of the bosonic reservoirs.

We develop a real-time diagrammatic theory of electron waiting time distributions for quantum transport in strongly interacting nanostructures. While existing methods address either weakly coupled systems with strong Coulomb interactions or coherent transport in mesoscopic conductors without interactions, our approach makes it possible to treat the interesting intermediate regime where both interaction effects and higher-order tunneling processes are important. As an illustration of experimental relevance, we consider a quantum dot coupled to electronic reservoirs and find that the distribution of waiting times between transferred electrons is drastically affected by virtual charge fluctuations and higher-order tunneling processes such as cotunneling that lead to non-Markovian dynamics on the quantum dot, and which can now be accounted for by our theoretical framework.

We report on the importance of resonant-tunneling processes on quantum transport through interacting quantum-dot spin valves. To include Coulomb interaction in the calculation of the tunneling magnetoresistance (TMR), we reformulate and generalize the recently developed, numerically exact method of iterative summation of path integrals (ISPI) to account for spin-dependent tunneling. The ISPI scheme allows us to investigate weak to intermediate Coulomb interaction in a wide range of gate and bias voltage and down to temperatures at which a perturbative treatment of tunneling severely fails.

The unpredictability of a single quantum event lies at the very core of quantum mechanics. Physical information is therefore drawn from a statistical evaluation of many such processes. Nevertheless, recording each single quantum event in a time trace the "random telegraph signal" is of great value, as it allows insight into the underlying physical system. Here, quantum dots have proven to be well suited systems, as they exhibit both single photon emission and single electron charge transport. While single photon emission is generally studied on self-assembled quantum dots, single electron transport studies are focused on gate-defined structures. We investigate, on a single self-assembled quantum dot, the single electron transport in the optical telegraph signal with high bandwidth and observe in the full counting statistics the interplay between charge and spin dynamics in a noninvasive way. In particular, we are able to identify the spin relaxation of the Zeeman-split quantum-dot level in the charge statistics.

Stochastic systems feature, in general, both coherent dynamics and incoherent transitions between different states. We propose a method to identify the coherent part in the full counting statistics for the transitions. The proposal is illustrated for electron transfer through a quantum-dot spin valve, which combines quantum-coherent spin precession with electron tunneling. We show that by counting the number of transferred electrons as a function of time, it is possible to distill out the coherent dynamics from the counting statistics even in transport regimes, in which other tools such as the frequency-dependent current noise and the waiting-time distribution fail.

Recent experiments (2015 Nature 521 196; 2017 Nat. Commun. 8 395) have presented evidence for electron pairing in a quantum dot beyond the superconducting regime. Here, we show that the impact of an attractive electron–electron interaction on the full counting statistics of electron transfer through a quantum dot is qualitatively different from the case of a repulsive interaction. In particular, the sign of higher-order (generalized) factorial cumulants reveals more pronounced correlations, which even survive in the limit of fast spin relaxation.

We propose a procedure to reconstruct characteristic features of an unknown stochastic system from the long-time full counting statistics of some of the system's transitions that are monitored by a detector. The full counting statistics is conveniently parametrized by so-called generalized factorial cumulants. Taking only a few of them as input information is sufficient to reconstruct important features such as the lower bound of the system dimension and the full spectrum of relaxation rates. The use of generalized factorial cumulants reveals system dimensions and rates that are hidden for ordinary cumulants. We illustrate the inverse counting-statistics procedure for two model systems: a single-level quantum dot in a Zeeman field and a single-electron box subjected to sequential and Andreev tunneling.

Tunneling of electron into or out of Coulomb-blockade devices such as semiconductor quantum dots or metallic single-electron boxes is a stochastic process that gives rise to both thermal and shot noise. Recent progress in nanotechnology has made it possible to monitor the tunneling in and tunneling out events individually. This allows one to study the full counting statistics (FCS) of electron tunneling both in equilibrium and nonequilibrium and as a function of time. In this talk, we will show how the FCS can be used to acquire information about the system that is inaccessible from measuring the average transferred charge only. In particular, we will demonstrate how so-called generalized factorial cumulants indicate the presence of interaction [1]. In the limit of short measuring intervals, the factorial cumulants directly reveal correlated tunneling events of two electrons in Andreev-reflection processes [2]. They, furthermore, are suitable tools to detect violation of detailed balance in a stochastic system [3]. We also introduce the concept of inverse counting statistics [4] which seeks at identifying a stochastic system from a few measured factorial cumulants only. Finally, we present results of recent experiments that were successfully analyzed with the help of factorial cumulants. P. Stegmann, B. Sothmann, A. Hucht, J. K’́onig, Phys. Rev. B 92, 155413 (2015). P. Stegmann and J. K’́onig, Phys. Rev. B 94, 125433 (2016). P. Stegmann and J. K’́onig, Phys. Stat. Sol. B 1-7 (2016) / DOI 10.1002/pssb.201600507. P. Stegmann and J. K’́onig, New J. Phys. 19, 023018 (2017).

Tunneling of electrons through a Coulomb-blockade system is a stochastic (i.e., random) process. The number of the transferred electrons per time interval is determined by a probability distribution. The form of this distribution can be characterized by quantities called cumulants. Recently developed electrometers allow for the observation of each electron transported through a Coulomb-blockade system in real time. Therefore, the probability distribution can be directly measured. In this thesis, we introduce generalized factorial cumulants as a new tool to analyze the information contained in the probability distribution. For any kind of Coulomb-blockade system, these cumulants can be used as follows: First, correlations between the tunneling electrons are proven by a certain sign of the cumulants. In the limit of short time intervals, additional criteria indicate correlations, respectively. The cumulants allow for the detection of correlations which cannot be noticed by commonly used quantities such as the current noise. We comment in detail on the necessary ingredients for the presence of correlations in the short-time limit and thereby explain recent experimental observations. Second, we introduce a mathematical procedure called inverse counting statistics. The procedure reconstructs, solely from a few experimentally measured cumulants, characteristic features of an otherwise unknown Coulomb-blockade system, e.g., a lower bound for the system dimension and the full spectrum of relaxation rates. Third, the cumulants reveal coherent oscillations or other processes transferring single electrons in a regular manner. The sensitivity for the oscillations increases dramatically in comparison to the commonly used quantities as the waiting times and finite-frequency current noise. The increased sensitivity is especially convenient for the detection of coherent oscillations in already existing experimental set-ups. Fourth, a violation of detailed balance is indicated by the cumulants. Detailed balance means the absence of net probability currents in the system's state space for the stationary limit. A violation of detailed balance is possible if the state space consist of more than two states connected by tunneling rates in such a way that a closed loop is formed. We illustrate the application of the generalized factorial cumulants for the transport through single metallic islands and quantum dots tunnel coupled to superconducting, ferromagnetic, or normal metallic electrodes. For all these example systems, it has been demonstrated already in experiments that electron transport can be observed in real time. Thus, our results can be applied immediately to such experimental realizations of a Coulomb-blockade system.

We discuss the possibility to generate in Coulomb-blockade systems steady states that violate detailed balance. This includes both voltage biased and non-biased scenarios. The violation of detailed balance yields that the charge-transfer statistics for electrons tunneling into an island experiencing strong Coulomb interaction is different from the statistics for tunneling out. This can be experimentally tested by time-resolved measurement of the island's charge state. We demonstrate this claim for two model systems.

We study full counting statistics of electron tunneling in Coulomb-blockade systems in the limit of short measuring-time intervals. This limit is particularly suited to identify correlations among tunneling events, but only when analyzing the charge-transfer statistics in terms of factorial cumulants CF, m (t) rather than ordinary ones commonly used in literature. In the absence of correlations, the short-time behavior of the factorial cumulants is given by C-F,C-m(t)alpha(-1) m(-1) t(m). A different sign and/or a different power law of the time dependence indicates correlations. We illustrate this for sequential and Andreev tunneling in a metallic single-electron box.