Universal oscillations in counting statistics

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants > of the number n of passed charges to very high orders (up to m=15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.Comment: 19 pages, 4 figures, final version as published in PNA

Non-equilibrium Entanglement and Noise in Coupled Qubits

We study charge entanglement in two Coulomb-coupled double quantum dots in thermal equilibrium and under stationary non-equilibrium transport conditions. In the transport regime, the entanglement exhibits a clear switching threshold and various limits due to suppression of tunneling by Quantum Zeno localisation or by an interaction induced energy gap. We also calculate quantum noise spectra and discuss the inter-dot current correlation as an indicator of the entanglement in transport experiments.Comment: 4 pages, 4 figure

The influence of charge detection on counting statistics

We consider the counting statistics of electron transport through a double quantum dot with special emphasis on the dephasing induced by a nearby charge detector. The double dot is embedded in a dissipative enviroment, and the presence of electrons on the double dot is detected with a nearby quantum point contact. Charge transport through the double dot is governed by a non-Markovian generalized master equation. We describe how the cumulants of the current can be obtained for such problems, and investigate the difference between the dephasing mechanisms induced by the quantum point contact and the coupling to the external heat bath. Finally, we consider various open questions of relevance to future research.Comment: 15 pages, 2 figures, Contribution to 5-th International Conference on Unsolved Problems on Noise, Lyon, France, June 2-6, 200

Modelling stressors on the eelgrass recovery process in two Danish estuaries

Eelgrass (Zostera marina L.) depth limit is used as an environmental indicator in Danish coastal waters in the Water Framework Directive (WFD) to evaluate coastal waters and their ecological condition. Even after decades of reduced nutrient loadings the reestablishment of eelgrass has not yet succeeded. The mechanisms hindering/delaying eelgrass recovery were recently identified: 1) lack of sediment anchoring capacity, 2) resuspension created by drifting ephemeral macroalgae, 3) seedling uprooting created by current and wave forces, 4) ballistic stress from attached macroalgae and 5) burial of seeds and seedlings by lugworms. These processes were quantified and introduced to an ecological MIKE 3D model. The developed model was calibrated and validated on two Danish estuaries, Odense Fjord and Roskilde Fjord. Analyses of the simulations were performed on area distribution maps. The parameterized stressors impact has been investigated over a three-year period.The results indicate accumulated effects from multiple stressors weakening the capability of eelgrass to recolonize. Combining all stressors in the model decreased the total area covered by eelgrass 83.72% in Odense Fjord and 80.30% in Roskilde Fjord compared to simulation without stressors. Eelgrass peak biomass declined in both fjords from 33.4 to 4.55 ton C km-2 in Odense Fjord and from 24.42 to 5.58 ton C km-2 in Roskilde Fjord. Combining lugworm burial of seeds and seedlings with resuspension from macroalgae and wave forcing had the second strongest negative impact on eelgrass growth, area reduction of 78.31% and 73.14% in Odense and Roskilde Fjord was seen. Ballistic stress from attached macroalgae also reduced growth drastically. Light conditions, sediment organic content along with shear stress at the sediment surface impact the ability of eelgrass to cope with above mentioned stressors. The spatial resolution of the model setup made it possible to generate maps where eelgrass is exposed to lowest stress, revealing areas for potential eelgrass recovery. The developed eelgrass model is now used as a national tool to predict areas where eelgrass restoration effort may be initiated. © 2016 Elsevier B.V

Optical properties of graphene antidot lattices

Undoped graphene is semi-metallic and thus not suitable for many electronic and optoelectronic applications requiring gapped semiconductor materials. However, a periodic array of holes (antidot lattice) renders graphene semiconducting with a controllable band gap. Using atomistic modelling, we demonstrate that this artificial nanomaterial is a dipole-allowed direct gap semiconductor with a very pronounced optical absorption edge. Hence, optical infrared spectroscopy should be an ideal probe of the electronic structure. To address realistic experimental situations, we include effects due to disorder and the presence of a substrate in the analysis.Comment: 11 pages, 9 figures, accepted for publication in Phys. Rev.

Frequency-dependent counting statistics in interacting nanoscale conductors

We present a formalism to calculate finite-frequency current correlations in interacting nanoscale conductors. We work within the n-resolved density matrix approach and obtain a multi-time cumulant generating function that provides the fluctuation statistics, solely from the spectral decomposition of the Liouvillian. We apply the method to the frequency-dependent third cumulant of the current through a single resonant level and through a double quantum dot. Our results, which show that deviations from Poissonian behaviour strongly depend on frequency, demonstrate the importance of finite-frequency higher-order cumulants in fully characterizing interactions.Comment: 4 pages, 2 figures, improved figures & discussion. J-ref adde

Measurement of finite-frequency current statistics in a single-electron transistor

Electron transport in nano-scale structures is strongly influenced by the Coulomb interaction which gives rise to correlations in the stream of charges and leaves clear fingerprints in the fluctuations of the electrical current. A complete understanding of the underlying physical processes requires measurements of the electrical fluctuations on all time and frequency scales, but experiments have so far been restricted to fixed frequency ranges as broadband detection of current fluctuations is an inherently difficult experimental procedure. Here we demonstrate that the electrical fluctuations in a single electron transistor (SET) can be accurately measured on all relevant frequencies using a nearby quantum point contact for on-chip real-time detection of the current pulses in the SET. We have directly measured the frequency-dependent current statistics and hereby fully characterized the fundamental tunneling processes in the SET. Our experiment paves the way for future investigations of interaction and coherence induced correlation effects in quantum transport.Comment: 7 pages, 3 figures, published in Nature Communications (open access

Factorial cumulants reveal interactions in counting statistics

Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recently it has been shown that the charge transport statistics for non-interacting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent single-particle events and the zeros of the generating function are real and negative. Here we investigate how the zeros of the generating function move into the complex plane due to interactions and demonstrate that the positions of the zeros can be detected using high-order factorial cumulants. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot for which we show that the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. Our findings are important for understanding the influence of interactions on counting statistics and the characterization in terms of zeros of the generating function provides us with a simple interpretation of recent experiments, where high-order statistics have been measured.Comment: 12 pages, 7 figures, Editors' Suggestion in Phys. Rev.

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 cross-over 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 energy level statistics and random matrix theory.Comment: 4+ pages, 3 figure

Graphene antidot lattices: Designed defects and spin qubits

Antidot lattices, defined on a two-dimensional electron gas at a semiconductor heterostructure, are a well-studied class of man-made structures with intriguing physical properties. We point out that a closely related system, graphene sheets with regularly spaced holes ("antidots"), should display similar phenomenology, but within a much more favorable energy scale, a consequence of the Dirac fermion nature of the states around the Fermi level. Further, by leaving out some of the holes one can create defect states, or pairs of coupled defect states, which can function as hosts for electron spin qubits. We present a detailed study of the energetics of periodic graphene antidot lattices, analyze the level structure of a single defect, calculate the exchange coupling between a pair of spin qubits, and identify possible avenues for further developments.Comment: 4 pages, 5 figures, accepted for publication in Phys. Rev. Let