Environmental effects in the third moment of voltage fluctuations in a tunnel junction

Realistic Protocol to Measure Entanglement at Finite Temperatures

It is desirable to relate entanglement of many-body systems to measurable observables. In systems with a conserved charge, it was recently shown that the number entanglement entropy (NEE)-i.e., the entropy change due to an unselective subsystem charge measurement-is an entanglement monotone. Here we derive finite-temperature equilibrium relations between Rényi moments of the NEE, and multipoint charge correlations. These relations are exemplified in quantum dot systems where the desired charge correlations can be measured via a nearby quantum point contact. In quantum dots recently realizing the multichannel Kondo effect we show that the NEE has a nontrivial universal temperature dependence which is now accessible using the proposed methods.

Bounds on skewness and kurtosis of steady-state currents

Current fluctuations are a powerful tool to unravel the underlying physics of the observed transport process. This work discusses some general properties of the third and the fourth current cumulant (skewness and kurtosis) related to dynamics and thermodynamics of a transport setup. Specifically, several distinct bounds on these quantities are either analytically derived or numerically conjectured, which are applicable to (1) noninteracting fermionic systems, (2) noninteracting bosonic systems, (3) thermally driven classical Markovian systems, and (4) unicyclic Markovian networks. Finally, it is demonstrated that violation of the obtained inequalities can provide a broad spectrum of information about the physics of the analyzed system; e.g., it can enable one to infer the presence of interactions or unitary dynamics, unravel the topology of the Markovian network, or characterize the nature of thermodynamic forces driving the system. In particular, relevant information about the microscopic dynamics can be gained even at equilibrium when the current variance-a standard measure of current fluctuations-is determined mostly by the thermal noise.

Suppression of shot noise in a spin-orbit coupled quantum dot

We study theoretically the transport properties of electrons in a quantum dot system with spin-orbit coupling. By using the quantum master equation approach, the shot noise and skewness of the transport electrons are calculated. We obtain super-Poisson noise behaviour by investigating the full counting statistics of the transport system. We discover super-Poisson behaviour is more obvious with the spin polarization increasing. More importantly, we discover the suppression of shot noise induced by spin-orbit coupling. The value of shot noise is gradually decreasing when spin-orbit coupling strength increases.

Microreversibility and the statistics of currents in quantum transport

For the statistics of currents in quantum transport, microreversibility is shown to provide a way to obtain the statistical cumulants at the order n+1 from the measurement of the cumulants at the order n or lower. This fundamental result is based on relations generalizing the fluctuation-dissipation theorem and the Onsager-Casimir reciprocal relations from linear toward nonlinear transport properties, as a consequence of the time-reversal symmetry of the underlying microscopic Hamiltonian dynamics. The method is demonstrated in detail in the case of multiterminal Aharonov-Bohm rings. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is obtained from the scattering matrix of these circuits. The time-reversal symmetry relations are explicitly shown to express the cumulants at equilibrium up to the fourth order in terms of lower-order cumulants and their nonequilibrium responses in the presence of an external magnetic field.

Non-Gaussian Current Fluctuations in a Short Diffusive Conductor

We report the measurement of the third moment of current fluctuations in a short metallic wire at low temperature. The data are deduced from the statistics of voltage fluctuations across the conductor using a careful determination of environmental contributions. Our results at low bias agree very well with theoretical predictions for coherent transport with no fitting parameter. By increasing the bias voltage we explore the crossover from elastic to inelastic transport.

Coherent control of single electrons: a review of current progress

In this report we review the present state of the art of the control of propagating quantum states at the single-electron level and its potential application to quantum information processing. We give an overview of the different approaches that have been developed over the last few years in order to gain full control over a propagating single-electron in a solid-state system. After a brief introduction of the basic concepts, we present experiments on flying qubit circuits for ensemble of electrons measured in the low frequency (DC) limit. We then present the basic ingredients necessary to realise such experiments at the single-electron level. This includes a review of the various single-electron sources that have been developed over the last years and which are compatible with integrated single-electron circuits. This is followed by a review of recent key experiments on electron quantum optics with single electrons. Finally we will present recent developments in the new physics that has emerged using ultrashort voltage pulses. We conclude our review with an outlook and future challenges in the field.

Dynamical Scheme for Interferometric Measurements of Full-Counting Statistics

We propose a dynamical scheme for measuring the full-counting statistics in a mesoscopic conductor using an electronic Mach-Zehnder interferometer. The conductor couples capacitively to one arm of the interferometer and causes a phase shift which is proportional to the number of transferred charges. Importantly, the full-counting statistics can be obtained from average current measurements at the outputs of the interferometer. The counting field can be controlled by varying the time delay between two separate voltage signals applied to the conductor and the interferometer, respectively. As a specific application, we consider measuring the entanglement entropy generated by partitioning electrons on a quantum point contact. Our scheme is robust against moderate environmental dephasing and may be realized thanks to recent advances in gigahertz quantum electronics.

Overbias light emission due to higher-order quantum noise in a tunnel junction

Understanding tunneling from an atomically sharp tip to a metallic surface requires us to account for interactions on a nanoscopic scale. Inelastic tunneling of electrons generates emission of photons, whose energies intuitively should be limited by the applied bias voltage. However, experiments [G. Schull et al., Phys. Rev. Lett. 102, 057401 (2009) indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission characterized by overbias energies. We propose a model of this observation in analogy to the dynamical Coulomb blockade, originally developed for treating the electronic environment in mesoscopic circuits. We explain the experimental finding quantitatively by the correlated tunneling of two electrons interacting with a LRC circuit modeling the local plasmon-polariton mode. To explain the overbias emission, the non-Gaussian statistics of the tunneling dynamics of the electrons is essential.

Emission of microwave photon pairs by a tunnel junction

We report the observation of photon pairs in the photoassisted shot noise of a tunnel junction in the quantum regime at very high frequency and very low temperature. We have measured the fluctuations of the noise power generated by the junction at two different frequencies, f(1) = 4.4 and f(2) = 7.2 GHz, while driving the junction with a microwave excitation of frequency f(0) = f(1) + f(2). We observe clear correlations between the fluctuations of the two noise powers even when the mean photon number per measurement is much smaller than one. This is strong evidence for photons being emitted in pairs. We also demonstrate that the electromagnetic field generated by the junction exhibits two-mode amplitude squeezing, a proof of its nonclassicality. The data agree very well with predictions based on the fourth cumulant of the current fluctuations generated by the junction.

Exactly solvable counting statistics in open weakly coupled interacting spin systems

We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling, we derive exact spin current statistics for a large class of parity symmetric spin-1/2 systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading-order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of a symmetrically boundary driven anisotropic Heisenberg (XXZ) spin-1/2 chain, we explicitly derive the third-order nonlinear corrections to the current statistics.

Full counting statistics of Andreev tunneling

We employ a single-charge counting technique to measure the full counting statistics of Andreev events in which Cooper pairs are either produced from electrons that are reflected as holes at a superconductor-normal-metal interface or annihilated in the reverse process. The full counting statistics consists of quiet periods with no Andreev processes, interrupted by the tunneling of a single electron that triggers an avalanche of Andreev events giving rise to strongly super-Poissonian distributions.

Fundamental quantum noise mapping with tunnelling microscopes tested at surface structures of subatomic lateral size

We present a measurement scheme that enables quantitative detection of the shot noise in a scanning tunnelling microscope while scanning the sample. As test objects we study defect structures produced on an iridium single crystal at low temperatures. The defect structures appear in the constant current images as protrusions with curvature radii well below the atomic diameter. The measured power spectral density of the noise is very near to the quantum limit with Fano factor F = 1. While the constant current images show detailed structures expected for tunnelling involving d-atomic orbitals of Ir, we find the current noise to be without pronounced spatial variation as expected for shot noise arising from statistically independent events.

Noise intensity-intensity correlations and the fourth cumulant of photo-assisted shot noise

We report the measurement of the fourth cumulant of current fluctuations in a tunnel junction under both dc and ac (microwave) excitation. This probes the non-Gaussian character of photo-assisted shot noise. Our measurement reveals the existence of correlations between noise power measured at two different frequencies, which corresponds to two-mode intensity correlations in optics. We observe positive correlations, i.e. photon bunching, which exist only for certain relations between the excitation frequency and the two detection frequencies, depending on the dc bias of the sample.

Universal features of counting statistics of thermal and quantum phase slips in nanosize superconducting circuits

We perform measurements of phase-slip-induced switching current events on different types of superconducting weak links and systematically study statistical properties of the switching current distributions. We employ two types of devices in which a weak link is formed either by a superconducting nanowire or by a graphene flake subject to proximity effect. We demonstrate that independently of the nature of the weak link, higher moments of the distribution take universal values. In particular, the third moment (skewness) of the distribution is close to -1 both in thermal and quantum regimes. The fourth moment (kurtosis) also takes a universal value close to 5. The discovered universality of skewness and kurtosis is confirmed by an analytical model. Our numerical analysis shows that introduction of extraneous noise into the system leads to significant deviations from the universal values. We suggest using the discovered universality of higher moments as a robust tool for checking against undesirable effects on noise in various types of measurements.

Full counting statistics in a propagating quantum front and random matrix spectra

One-dimensional free fermions are studied with emphasis on propagating fronts emerging from a step initial condition. The probability distribution of the number of particles at the edge of the front is determined exactly. It is found that the full counting statistics coincide with the eigenvalue statistics of the edge spectrum of matrices from the Gaussian unitary ensemble. The correspondence established between the random matrix eigenvalues and the particle positions yields the order statistics of the rightmost particles in the front and, furthermore, it implies their subdiffusive spreading.

P-wave Cooper pair splitting

BACKGROUND

Splitting of Cooper pairs has recently been realized experimentally for s-wave Cooper pairs. A split Cooper pair represents an entangled two-electron pair state, which has possible application in on-chip quantum computation. Likewise the spin-activity of interfaces in nanoscale tunnel junctions has been investigated theoretically and experimentally in recent years. However, the possible implications of spin-active interfaces in Cooper pair splitters so far have not been investigated.

RESULTS

We analyze the current and the cross correlation of currents in a superconductor-ferromagnet beam splitter, including spin-active scattering. Using the Hamiltonian formalism, we calculate the cumulant-generating function of charge transfer. As a first step, we discuss characteristics of the conductance for crossed Andreev reflection in superconductor-ferromagnet beam splitters with s-wave and p-wave superconductors and no spin-active scattering. In a second step, we consider spin-active scattering and show how to realize p-wave splitting using only an s-wave superconductor, through the process of spin-flipped crossed Andreev reflection. We present results for the conductance and cross correlations.

CONCLUSION

Spin-activity of interfaces in Cooper pair splitters allows for new features in ordinary s-wave Cooper pair splitters, that can otherwise only be realized by using p-wave superconductors. In particular, it provides access to Bell states that are different from the typical spin singlet state.

Generation of nonclassical microwave states using an artificial atom in 1D open space

We have embedded an artificial atom, a superconducting transmon qubit, in a 1D open space and investigated the scattering properties of an incident microwave coherent state. By studying the statistics of the reflected and transmitted fields, we demonstrate that the scattered states can be nonclassical. In particular, by measuring the second-order correlation function, g((2)), we show photon antibunching in the reflected field and superbunching in the transmitted field. We also compare the elastically and inelastically scattered fields using both phase-sensitive and phase-insensitive measurements.

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

Electron transport in nanoscale structures is strongly influenced by the Coulomb interaction that 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 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 single-electron device. We have directly measured the frequency-dependent current statistics and, hereby, fully characterized the fundamental tunnelling processes in the single-electron transistor. Our experiment paves the way for future investigations of interaction and coherence-induced correlation effects in quantum transport.

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.

Full counting statistics of a Luttinger liquid conductor

Nonequilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the time resolved full counting statistics of the transmitted charge is derived. It is given by the Fredholm determinant of the counting operator with a time-dependent scattering phase. The result has a form of counting statistics of noninteracting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the noninteracting leads.

Shot noise in the self-dual interacting resonant level model

By using two independent and complementary approaches, we compute exactly the shot noise in an out-of-equilibrium interacting impurity model, the interacting resonant level model at its self-dual point. An analytical approach based on the thermodynamical Bethe ansatz allows us to obtain the density matrix in the presence of a bias voltage, which in turn allows for the computation of any observable. A time-dependent density matrix renormalization group technique that has proven to yield the correct result for a free model (the resonant level model) is shown to be in perfect agreement with the former method.

Quasiprobabilistic interpretation of weak measurements in mesoscopic junctions

The impossibility of measuring noncommuting quantum mechanical observables is one of the most fascinating consequences of the quantum mechanical postulates. Hence, to date the investigation of quantum measurement and projection is a fundamentally interesting topic. We propose to test the concept of weak measurement of noncommuting observables in mesoscopic transport experiments, using a quasiprobabilistic description. We derive an inequality for current correlators, which is satisfied by every classical probability but violated by high-frequency fourth-order cumulants in the quantum regime for experimentally feasible parameters.

Experimental determination of the statistics of photons emitted by a tunnel junction

We report on an Hanbury Brown-Twiss experiment probing the statistics of microwave photons emitted by a tunnel junction in the shot-noise regime at low temperature. By measuring the cross correlation of the fluctuations of the occupation numbers of the photon modes of both detection branches, we show that while the statistics of electrons is Poissonian, the photons obey chaotic statistics. This is observed even for low photon occupation number when the voltage across the junction is close to hν/e.

Quantum noise as an entanglement meter

Transport in a quantum point contact (QPC) can be used to generate many-body entanglement of Fermi seas in the leads. A universal relation is found between the generated entanglement entropy and the fluctuations of electric current, which is valid for any protocol of driving the QPC. This relation offers a basis for direct electric measurement of entanglement entropy. In particular, by utilizing space-time duality of 1D systems, we relate electric noise generated by opening and closing the QPC periodically in time with the seminal S=1/3logL prediction of conformal field theory.

Achieving the threshold regime with an overscreened Josephson junction

We demonstrate that by utilizing an overscreened Josephson junction as a noise detector it is possible to achieve the threshold regime, whereby the tails of the fluctuating current distribution are measured. This situation is realized by placing the Josephson junction and mesoscopic conductor in an external circuit with very low impedance. In the underdamped limit, overscreening the junction inhibits the energy diffusion in the junction, effectively creating a tunable activation barrier to the dissipative state. As a result, the activation rate is qualitatively different from the Arrhenius form.

Asymmetric noise probed with a josephson junction

Fluctuations of the current through a tunnel junction are measured using a Josephson junction. The current noise adds to the bias current of the Josephson junction and affects its switching out of the supercurrent branch. The experiment is carried out in a regime where switching is determined by thermal activation. The variance of the noise results in an elevated effective temperature, whereas the third cumulant, related to its asymmetric character, leads to a difference in the switching rates observed for opposite signs of the current through the tunnel junction. Measurements are compared quantitatively with recent theoretical predictions.

Formulation of time-resolved counting statistics based on a positive-operator-valued measure

We propose a derivation of the full counting statistics of electronic current based on a positive-operator-valued measure. Our approach justifies the Levitov-Lesovik formula in the long-time limit, but can be generalized to the detection of finite-frequency noise correlations. The combined action of the projection postulate and the quantum formula for current noise at high frequencies imply an additional white noise. Estimates for this additional noise are in accordance with known experiments. We propose an experimental test of our conjecture by a simultaneous measurement of high- and low-frequency noise.

Detection of non-Gaussian fluctuations in a quantum point contact

An experimental study of current fluctuations through a tunable transmission barrier, a quantum point contact, is reported. We measure the probability distribution function of transmitted charge with precision sufficient to extract the first three cumulants. To obtain the intrinsic quantities, corresponding to voltage-biased barrier, we employ a procedure that accounts for the response of the external circuit and the amplifier. The third cumulant, obtained with a high precision, is found to agree with the prediction for the statistics of transport in the non-Poissonian regime.

Counting statistics of non-Markovian quantum stochastic processes

We derive a general expression for the cumulant generating function (CGF) of non-Markovian quantum stochastic transport processes. The long-time limit of the CGF is determined by a single dominating pole of the resolvent of the memory kernel from which we extract the zero-frequency cumulants of the current using a recursive scheme. The finite-frequency noise is expressed not only in terms of the resolvent, but also initial system-environment correlations. As an illustrative example we consider electron transport through a dissipative double quantum dot for which we study the effects of dissipation on the zero-frequency cumulants of high orders and the finite-frequency noise.

Dynamics of quantum noise in a tunnel junction under ac excitation

We report the first measurement of the dynamical response of shot noise (measured at frequency omega) of a tunnel junction to an ac excitation at frequency omega0. The experiment is performed in the quantum regime, variant Planck's over 2piomega approximately variant Planck's over 2piomega0>>kBT at very low temperature T=35 mK and high frequency omega0/2pi=6.2 GHz. We observe that the noise responds in phase with the excitation, but not adiabatically. The results are in very good agreement with a prediction based on a new current-current correlator.

Experimental test of the high-frequency quantum shot noise theory in a quantum point contact

We report on direct measurements of the electronic shot noise of a quantum point contact at frequencies nu in the range 4-8 GHz. The very small energy scale used ensures energy independent transmissions of the few transmitted electronic modes and their accurate knowledge. Both the thermal energy and the quantum point contact drain-source voltage V_{ds} are comparable to the photon energy hnu leading to observation of the shot noise suppression when V_{ds}<hnu/e. Our measurements provide the first complete test of the finite frequency shot noise scattering theory without adjustable parameters.

Fluctuation theorem in quantum heat conduction

We consider steady-state heat conduction across a quantum harmonic chain connected to reservoirs modeled by infinite collection of oscillators. The heat, Q, flowing across the oscillator in a time interval tau is a stochastic variable and we study the probability distribution function P(Q). We compute the exact generating function of Q at large tau and the large deviation function. The generating function has a symmetry satisfying the steady-state fluctuation theorem without any quantum corrections. The distribution P(Q) is non-Gaussian with clear exponential tails. The effect of finite tau and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain the prediction of quantum heat current fluctuations at low temperatures in clean wires.

Detection of finite-frequency current moments with a dissipative resonant circuit

We consider the measurement of higher current moments with a dissipative resonant circuit, which is coupled inductively to a mesoscopic device in the coherent regime. Information about the higher current moments is coded in the histograms of the charge on the capacitor plates of the resonant circuit. The role of dissipation is shown to be essential for the measured noise to remain finite. We also identify which combination of current correlators enters the measurement of the third moment. The results are illustrated for a quantum point contact.

Wideband detection of the third moment of shot noise by a hysteretic Josephson junction

We use a hysteretic Josephson junction as an on-chip detector of the third moment of shot noise of a tunnel junction. The detectable bandwidth is determined by the plasma frequency of the detector, which is about 50 GHz in the present experiment. The third moment of shot noise results in a measurable change of the switching rate when reversing polarity of the current through the noise source. We analyze the observed asymmetry assuming adiabatic response of the detector.

Stochastic dynamics of a Josephson junction threshold detector

We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. The activation rate dependence on the third current cumulant includes an additional term originating from the backaction of the measurement circuit.

Detecting charge noise with a Josephson junction: a problem of thermal escape in presence of non-Gaussian fluctuations

Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.

Superconductor-metal transition in an ultrasmall Josephson junction biased by a noisy voltage source

Shot noise in a voltage source changes the character of the quantum (dissipative) phase transition in an ultrasmall Josephson junction: The superconductor-insulator transition transforms into the superconductor-metal transition. In the metallic phase, the IV curve probes the voltage distribution generated by shot noise, whereas in the superconducting phase, it probes the counting statistics of electrons traversing the noise junction.

Full counting statistics for the Kondo dot in the unitary limit

We calculate the charge transfer probability distribution function chi(lambda) for the Kondo dot in the strong-coupling limit within the framework of the Nozières-Fermi-liquid theory of the Kondo effect. At zero temperature, the ratio of the moments Cn of the charge distribution to the backscattering current Ibs follows a universal law Cn/2Ibs = (-1)n(1+2n)/6. The functional form of chi(lambda) is consistent with tunneling of electrons and, possibly, electron pairs. We then discuss the crossover behavior of chi(lambda) from weak to strong Coulomb repulsion in the underlying Anderson impurity model and relate this to the existing results. Finally, we extend our analysis to the case of finite temperatures.

Bidirectional Counting of Single Electrons

A bidirectional single-electron counting device is demonstrated. Individual electrons flowing in forward and reverse directions through a double quantum dot are detected with a quantum point contact acting as a charge sensor. A comprehensive statistical analysis in the frequency and time domains and of higher order moments of noise reveals antibunching correlation in single-electron transport through the device itself. The device can also be used to investigate current flow in the attoampere range, which cannot be measured by existing current meters.

Statistical evaluation of single nano-object fluorescence

Single nano-objects display strong fluctuations of their fluorescence signals. These random and irreproducible variations must be subject to statistical analysis to provide microscopic information. We review the main evaluation methods used so far by experimentalists in the field of single-molecule spectroscopy: time traces, correlation functions, distributions of "on" and "off" times, higher-order correlations. We compare their advantages and weaknesses from a theoretical point of view, illustrating our main conclusions with simple numerical simulations. We then review experiments on different types of single nano-objects, the phenomena which are observed and the statistical analyses applied to them.

Full counting statistics of chiral Luttinger liquids with impurities

We study the statistics of charge transfer through an impurity in a chiral Luttinger liquid (realized experimentally as a quantum point contact in a fractional quantum Hall edge state device). Taking advantage of the integrability we present a procedure for obtaining the cumulant generating function of the probability distribution to transfer a fixed amount of charge through the constriction. Using this approach we analyze in detail the behavior of the third cumulant C3 as a function of applied voltage, temperature, and barrier height. We predict that C3 can be used to measure the fractional charge at temperatures, which are several orders of magnitude higher than those needed to extract the fractional charge from the measurement of the second cumulant. Moreover, we identify the component of C3, which carries the information about the fractional charge.

Using qubits to measure fidelity in mesoscopic systems

We point out the similarities in the definition of the "fidelity" of a quantum system and the generating function determining the full counting statistics of charge transport through a quantum wire and suggest to use flux or charge qubits for their measurement. As an application we use the notion of fidelity within a first-quantized formalism in order to derive new results and insights on the generating function of the full counting statistics.

Full counting statistics for a single-electron transistor: nonequilibrium effects at intermediate conductance

We evaluate the current distribution for a single-electron transistor with intermediate strength tunnel conductance. Using the Schwinger-Keldysh approach and the drone (Majorana) fermion representation, we account for the renormalization of system parameters. Nonequilibrium effects induce a lifetime broadening of the charge-state levels, which suppress large current fluctuations.

Counting statistics of single electron transport in a quantum dot

We have measured the full counting statistics of current fluctuations in a semiconductor quantum dot (QD) by real-time detection of single electron tunneling with a quantum point contact. This method gives direct access to the distribution function of current fluctuations. Suppression of the second moment (related to the shot noise) and the third moment (related to the asymmetry of the distribution) in a tunable semiconductor QD is demonstrated experimentally. With this method we demonstrate the ability to measure very low current and noise levels.

Finite frequency quantum noise in an interacting mesoscopic conductor

We present a quantum calculation based on scattering theory of the frequency-dependent noise of current in an interacting chaotic cavity. We include interactions of the electron system via long range Coulomb forces between the conductor and a gate with capacitance C. We obtain explicit results exhibiting the two time scales of the problem, the cavity's dwell time tau(D) and the RC time tau(C) of the cavity in relation to the gate. The noise shows peculiarities at frequencies of the order and exceeding the inverse charge relaxation time tau(-1) = tau(D)(-1) + tau(C)(-1).

Multiparticle interference, Greenberger-Horne-Zeilinger entanglement, and full counting statistics

We investigate the quantum transport in a generalized N-particle Hanbury Brown-Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.

Full counting statistics in strongly interacting systems: non-Markovian effects

We present a theory of full counting statistics for electron transport through interacting electron systems with non-Markovian dynamics. We illustrate our approach for transport through a single-level quantum dot and a metallic single-electron transistor to second order in the tunnel coupling, and discuss under which circumstances non-Markovian effects appear in the transport properties.

Shot-noise-driven escape in hysteretic Josephson junctions

We have measured the influence of shot noise on hysteretic Josephson junctions initially in the macroscopic quantum tunneling regime. The escape threshold current into the resistive state decreases monotonically with increasing average current through the scattering conductor, which is another tunnel junction. Escape is predominantly determined by excitation due to the wideband shot noise. This process is equivalent to thermal activation (TA) over the barrier at effective temperatures up to about 4 times the critical temperature of the superconductor. The presented TA model is in excellent agreement with the experimental results.

How to detect the fourth-order cumulant of electrical noise

It is proposed to measure the current noise generated in a mesoscopic conductor by macroscopic quantum tunneling (MQT) in a current biased Josephson junction placed in parallel to the conductor. The theoretical description of this setup takes into account the complete dynamics of detector and noise source. Explicit results are given for the specific case of current fluctuations in an oxide layer tunnel junction, and it is shown how the device allows to extract the fourth-order cumulant of the noise from the MQT data for realistic experimental parameters.