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

Full counting statistics of nano-electromechanical systems

We develop a theory for the full counting statistics (FCS) for a class of nanoelectromechanical systems (NEMS), describable by a Markovian generalized master equation. The theory is applied to two specific examples of current interest: vibrating C60 molecules and quantum shuttles. We report a numerical evaluation of the first three cumulants for the C60-setup; for the quantum shuttle we use the third cumulant to substantiate that the giant enhancement in noise observed at the shuttling transition is due to a slow switching between two competing conduction channels. Especially the last example illustrates the power of the FCS.Comment: 7 pages, 3 figures; minor changes - final version as published in Europhys. Let

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

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

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

Tunable few electron quantum dots in InAs nanowires

Quantum dots realized in InAs are versatile systems to study the effect of spin-orbit interaction on the spin coherence, as well as the possibility to manipulate single spins using an electric field. We present transport measurements on quantum dots realized in InAs nanowires. Lithographically defined top-gates are used to locally deplete the nanowire and to form tunneling barriers. By using three gates, we can form either single quantum dots, or two quantum dots in series along the nanowire. Measurements of the stability diagrams for both cases show that this method is suitable for producing high quality quantum dots in InAs.Comment: 8 pages, 4 figure

Bipartite Fluctuations as a Probe of Many-Body Entanglement

We investigate in detail the behavior of the bipartite fluctuations of particle number $\hat{N}$ and spin $\hat{S}^z$ in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the R\'{e}nyi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the R\'{e}nyi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.Comment: 30 pages + 25 pages supplementary materia

Counting statistics of collective photon transmissions

We theoretically study cooperative effects in the steady-state transmission of photons through a medium of $N$ radiators. Using methods from quantum transport, we find a cross-over in scaling from $N$ to $N^2$ in the current and even higher powers of $N$ in the higher cumulants of the photon counting statistics as a function of the tunable source occupation. The effect should be observable for atoms confined within a nano-cell with a pumped optical cavity as photon source.Comment: extended results, 9 pages, 2 figures, to appear in Annals of Physic