Counting statistics of non-Markovian quantum stochastic processes

Critical heat current fluctuations in Curie-Weiss model in and out of equilibrium

In some models of nonequilibrium phase transitions, fluctuations of the analyzed currents have been observed to diverge with system size. To assess whether this behavior is universal across phase transitions, we examined heat current fluctuations in the Curie-Weiss model, a paradigmatic model of the paramagnetic-ferromagnetic phase transition, coupled to two thermal baths. This model exhibits phase transitions driven by both the temperature and the magnetic field. We find that at the temperature-driven phase transition, the heat current noise consists of two contributions: the equilibrium part, which vanishes with system size, and the nonequilibrium part, which diverges with system size. For small temperature differences, this leads to nonmonotonic scaling of fluctuations with system size. In contrast, at the magnetic-field-driven phase transition, heat current fluctuations do not diverge when observed precisely at the phase transition point. Instead, out of equilibrium, the noise is enhanced at the magnetic field values away but close to the phase transition point, due to stochastic switching between two current values. The maximum value of noise increases exponentially with system size, while the position of this maximum shifts towards the phase transition point. Finally, on the methodological side, the paper demonstrates that current fluctuations in large systems can be effectively characterized by combining a path-integral approach for macroscopic fluctuations together with an effective two-state model describing subextensive transitions between the two macroscopic states involved in the phase transition.

Nonequilibrium steady state full counting statistics in the noncrossing approximation

Quantum transport is often characterized not just by mean observables like the particle or energy current but by their fluctuations and higher moments, which can act as detailed probes of the physical mechanisms at play. However, relatively few theoretical methods are able to access the full counting statistics (FCS) of transport processes through electronic junctions in strongly correlated regimes. While most experiments are concerned with steady state properties, most accurate theoretical methods rely on computationally expensive propagation from a tractable initial state. Here, we propose a simple approach for computing the FCS through a junction directly at the steady state, utilizing the propagator noncrossing approximation. Compared to time propagation, our method offers reduced computational cost at the same level of approximation, but the idea can also be used within other approximations or as a basis for numerically exact techniques. We demonstrate the method's capabilities by investigating the impact of lead dimensionality on electronic transport in the nonequilibrium Anderson impurity model at the onset of Kondo physics. Our results reveal a distinct signature of one dimensional leads in the noise and Fano factor not present for other dimensionalities, showing the potential of FCS measurements as a probe of the environment surrounding a quantum dot.

Dynamical signatures of discontinuous phase transitions: How phase coexistence determines exponential versus power-law scaling

There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior. We clarify this issue by employing large deviation theory. We distinguish two distinct classes of discontinuous phase transitions that have different dynamical properties. The first class is associated with phase coexistence, i.e., the presence of multiple stable attractors of the system dynamics (e.g., local minima of the free-energy functional) in a finite phase diagram region around the phase transition point. In that case, one observes asymptotic exponential scaling related to stochastic switching between attractors (though the onset of exponential scaling may sometimes occur for very large system sizes). In the second class, there is no phase coexistence away from the phase transition point, while at the phase transition point itself there are infinitely many attractors. In that case, one observes power-law scaling related to the diffusive nature of the system relaxation to the stationary state.

Coulomb staircase in an asymmetrically coupled quantum dot

We investigate the Coulomb blockade in quantum dots asymmetrically coupled to the leads for an arbitrary voltage bias focusing on the regime where electrons do not thermalise during their dwell time in the dot. By solving the quantum kinetic equation, we show that the current-voltage characteristics are crucially dependent on the ratio of the Fermi energy to charging energy on the dot. In the standard regime when the Fermi energy is large, there is a Coulomb staircase which is practically the same as in the thermalised regime. In the opposite case of the large charging energy, we identify a new regime in which only one step is left in the staircase, and we anticipate experimental confirmation of this finding.

Memory-effect-preserving quantum master equation approach to noise spectrum of transport current

Within the time-nonlocal quantum master equation description, we develop an efficient method for calculating the noise spectrum of transport current through interacting mesoscopic systems. By introducing proper current-related density operators, we propose a practical and very efficient time-local equation of motion implementation to compute the noise spectrum, which contains the full information of emission and absorption. We obtain an analytical expression to characterize the nonequilibrium transport including Coulomb interaction and memory effect. We demonstrate the proposed method with double quantum dots systems and find good agreement with the exact results, whenever the system-reservoir coupling is smaller than the temperature.

Dynamic Cooper Pair Splitter

Cooper pair splitters are promising candidates for generating spin-entangled electrons. However, the splitting of Cooper pairs is a random and noisy process, which hinders further synchronized operations on the entangled electrons. To circumvent this problem, we here propose and analyze a dynamic Cooper pair splitter that produces a noiseless and regular flow of spin-entangled electrons. The Cooper pair splitter is based on a superconductor coupled to quantum dots, whose energy levels are tuned in and out of resonance to control the splitting process. We identify the optimal operating conditions for which exactly one Cooper pair is split per period of the external drive and the flow of entangled electrons becomes noiseless. To characterize the regularity of the Cooper pair splitter in the time domain, we analyze the g^{(2)} function of the output currents and the distribution of waiting times between split Cooper pairs. Our proposal is feasible using current technology, and it paves the way for dynamic quantum information processing with spin-entangled electrons.

Recursive evolution of spin-wave multiplets in magnonic crystals of antidot-lattice fractals

We explored spin-wave multiplets excited in a different type of magnonic crystal composed of ferromagnetic antidot-lattice fractals, by means of micromagnetic simulations with a periodic boundary condition. The modeling of antidot-lattice fractals was designed with a series of self-similar antidot-lattices in an integer Hausdorff dimension. As the iteration level increased, multiple splits of the edge and center modes of quantized spin-waves in the antidot-lattices were excited due to the fractals’ inhomogeneous and asymmetric internal magnetic fields. It was found that a recursive development (F_n = F_n−1 + G_n−1) of geometrical fractals gives rise to the same recursive evolution of spin-wave multiplets.

Electron Waiting Times in a Strongly Interacting Quantum Dot: Interaction Effects and Higher-Order Tunneling Processes

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.

Nonequilibrium Kondo regime current noise spectrum of quantum dot systems with the single impurity Anderson model

We investigate the nonequilibrium current noise spectrum of single impurity Anderson model quantum dot systems on the basis of the accurate dissipation equation of motion evaluations. By comparing between the equilibrium and nonequilibrium cases and between the non-Kondo and Kondo regimes, we identify the current noise spectrum of the nonequilibrium Kondo features that actually appear in the entire region of ω ∈ [-eV, eV]. It is well known that the primary Kondo characteristics at ω = ±eV = ±(μ_L - μ_R) display asymmetrical upturns and remarkable peaks in S(ω) and dS(ω)/dω, respectively. These features are originated from the Rabi interference of the transport current dynamics, with the Kondo oscillation frequency of |eV|. Moreover, we also identify the minor but very distinguishable inflections, crossing over from ω = -eV to ω = +eV. This uncovered feature would be related to the interference between two Kondo resonance channels.

Spectral Properties of Stochastic Resonance in Quantum Transport

We investigate theoretically and experimentally stochastic resonance in a quantum dot coupled to electron source and drain via time-dependent tunnel barriers. A central finding is a transition visible in the current noise spectrum as a bifurcation of a dip originally at zero frequency. The transition occurs close to the stochastic resonance working point and relates to quantized pumping. For the evaluation of power spectra from measured waiting times, we generalize a result from renewal theory to the ac-driven case. Moreover, we develop a master equation method to obtain phase-averaged current noise spectra for driven quantum transport.

Effective Equilibrium in Out-of-Equilibrium Interacting Coupled Nanoconductors

In the present work, we study a mesoscopic system consisting of a double quantum dot in which both quantum dots or artificial atoms are electrostatically coupled. Each dot is additionally tunnel coupled to two electronic reservoirs and driven far from equilibrium by external voltage differences. Our objective is to find configurations of these biases such that the current through one of the dots vanishes. In this situation, the validity of the fluctuation–dissipation theorem and Onsager’s reciprocity relations has been established. In our analysis, we employ a master equation formalism for a minimum model of four charge states, and limit ourselves to the sequential tunneling regime. We numerically study those configurations far from equilibrium for which we obtain a stalling current. In this scenario, we explicitly verify the fluctuation–dissipation theorem, as well as Onsager’s reciprocity relations, which are originally formulated for systems in which quantum transport takes place in the linear regime.

Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach

We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperature difference. Results are compared to perturbative treatments and demonstrate good agreement in the appropriate limits. The challenge of converging nonequilibrium quantities, currents and high order cumulants, is discussed in detail. The iFCSPI, a numerically exact technique, naturally captures strong system-bath coupling and non-Markovian effects of the environment. As such, it is a promising tool for probing fundamental questions in quantum transport and quantum thermodynamics.

Frequency-dependent current noise in quantum heat transfer: A unified polaron calculation

To investigate frequency-dependent current noise (FDCN) in open quantum systems at steady states, we present a theory which combines Markovian quantum master equations with a finite time full counting statistics. Our formulation of the FDCN generalizes previous zero-frequency expressions and can be viewed as an application of MacDonald's formula for electron transport to heat transfer. As a demonstration, we consider the paradigmatic example of quantum heat transfer in the context of a non-equilibrium spin-boson model. We adopt a recently developed polaron-transformed Redfield equation which allows us to accurately investigate heat transfer with arbitrary system-reservoir coupling strength, arbitrary values of spin bias, and temperature differences. We observe a turn-over of FDCN in the intermediate coupling regimes, similar to the zero-frequency case. We find that the FDCN with varying coupling strengths or bias displays a universal Lorentzian-shape scaling form in the weak coupling regime, and a white noise spectrum emerges with zero bias in the strong coupling regime due to distinctive spin dynamics. We also find that the bias can suppress the FDCN in the strong coupling regime, in contrast to its zero-frequency counterpart which is insensitive to bias changes. Furthermore, we utilize the Saito-Utsumi relation as a benchmark to validate our theory and study the impact of temperature differences at finite frequencies. Together, our results provide detailed dissections of the finite time fluctuation of heat current in open quantum systems.

Finite-time full counting statistics and factorial cumulants for transport through a quantum dot with normal and superconducting leads

We study the finite-time full counting statistics for subgap transport through a single-level quantum dot tunnel-coupled to one normal and one superconducting lead. In particular, we determine the factorial and the ordinary cumulants both for finite times and in the long-time limit. We find that the factorial cumulants violate the sign criterion, indicating a non-binomial distribution, even in absence of Coulomb repulsion due to the presence of superconducting correlations. At short times the cumulants exhibit oscillations which are a signature of the coherent transfer of Cooper pairs between the dot and the superconductor.

Reconciling perturbative approaches in phonon-assisted transport junctions

We present consistent results for molecular conduction using two central-complementary approaches: the non-equilibrium Green's function technique and the quantum master equation method. Our model describes electronic conduction in a donor-acceptor junction in which electron transfer is coupled to nuclear motion, modeled by a harmonic vibrational mode. This primary mode is further coupled to secondary phonon modes, a thermal bath. Assuming weak electron-phonon coupling but an arbitrary large molecule-metal hybridization, we compute several non-equilibrium transport quantities: the mean phonon number of the primary mode, charge current statistics. We further present scaling relations for the cumulants valid in the large voltage regime. Our analysis illustrates that the non-equilibrium Green's function technique and the quantum master equation method can be worked out consistently, when taking into account corresponding scattering processes.

Bistable Photon Emission from a Solid-State Single-Atom Laser

We predict a bistability in the photon emission from a solid-state single-atom laser comprising a microwave cavity coupled to a voltage-biased double quantum dot. To demonstrate that the single-atom laser is bistable, we evaluate the photon emission statistics and show that the distribution takes the shape of a tilted ellipse. The switching rates of the bistability can be extracted from the electrical current and the shot noise in the quantum dots. This provides a means to control the photon emission statistics by modulating the electronic transport in the quantum dots. Our prediction is robust against moderate electronic decoherence and dephasing and is important for current efforts to realize single-atom lasers with gate-defined quantum dots as the gain medium.

Dispersion for two classes of random variables: general theory and application to inference of an external ligand concentration by a cell

We derive expressions for the dispersion for two classes of random variables in Markov processes. Random variables such as current and activity pertain to the first class, which is composed of random variables that change whenever a jump in the stochastic trajectory occurs. The second class corresponds to the time the trajectory spends in a state (or cluster of states). While the expression for the first class follows straightforwardly from known results in the literature, we show that a similar formalism can be used to derive an expression for the second class. As an application, we use this formalism to analyze a cellular two-component network estimating an external ligand concentration. The uncertainty related to this external concentration is calculated by monitoring different random variables related to an internal protein. We show that, inter alia, monitoring the time spent in the phosphorylated state of the protein leads to a finite uncertainty only if there is dissipation, whereas the uncertainty obtained from the activity of the transitions of the internal protein can reach the Berg-Purcell limit even in equilibrium.

Quantum Phase Coherence in Mesoscopic Transport Devices with Two-Particle Interaction

In this paper we demonstrate a new type of quantum phase coherence (QPC), which is generated by the two-body interaction. This conclusion is based on quantum master equation analysis for the full counting statistics of electron transport through two parallel quantum-dots with antiparallel magnetic fluxes in order to eliminate the Aharonov-Bohm interference of either single-particle or non-interacting two-particle wave functions. The interacting two-particle QPC is realized by the flux-dependent oscillation of the zero-frequency cumulants including the shot noise and skewness with a characteristic period. The accurately quantized peaks of cumulant spectrum may have technical applications to probe the two-body Coulomb interaction.

Non-Markovian full counting statistics in quantum dot molecules

Full counting statistics of electron transport is a powerful diagnostic tool for probing the nature of quantum transport beyond what is obtainable from the average current or conductance measurement alone. In particular, the non-Markovian dynamics of quantum dot molecule plays an important role in the nonequilibrium electron tunneling processes. It is thus necessary to understand the non-Markovian full counting statistics in a quantum dot molecule. Here we study the non-Markovian full counting statistics in two typical quantum dot molecules, namely, serially coupled and side-coupled double quantum dots with high quantum coherence in a certain parameter regime. We demonstrate that the non-Markovian effect manifests itself through the quantum coherence of the quantum dot molecule system, and has a significant impact on the full counting statistics in the high quantum-coherent quantum dot molecule system, which depends on the coupling of the quantum dot molecule system with the source and drain electrodes. The results indicated that the influence of the non-Markovian effect on the full counting statistics of electron transport, which should be considered in a high quantum-coherent quantum dot molecule system, can provide a better understanding of electron transport through quantum dot molecules.

Negative differential conductance and super-Poissonian shot noise in single-molecule magnet junctions

Molecular spintroinic device based on a single-molecule magnet is one of the ultimate goals of semiconductor nanofabrication technologies. It is thus necessary to understand the electron transport properties of a single-molecule magnet junction. Here we study the negative differential conductance and super-Poissonian shot noise properties of electron transport through a single-molecule magnet weakly coupled to two electrodes with either one or both of them being ferromagnetic. We predict that the negative differential conductance and super-Poissonian shot noise, which can be tuned by a gate voltage, depend sensitively on the spin polarization of the source and drain electrodes. In particular, the shot noise in the negative differential conductance region can be enhanced or decreased originating from the different formation mechanisms of negative differential conductance. The effective competition between fast and slow transport channels is responsible for the observed negative differential conductance and super-Poissonian shot noise. In addition, we further discuss the skewness and kurtosis properties of transport current in the super-Poissonian shot noise regions. Our findings suggest a tunable negative differential conductance molecular device, and the predicted properties of high-order current cumulants are very interesting for a better understanding of electron transport through single-molecule magnet junctions.

Thermoelectric energy harvesting with quantum dots

We review recent theoretical work on thermoelectric energy harvesting in multi-terminal quantum-dot setups. We first discuss several examples of nanoscale heat engines based on Coulomb-coupled conductors. In particular, we focus on quantum dots in the Coulomb-blockade regime, chaotic cavities and resonant tunneling through quantum dots and wells. We then turn toward quantum-dot heat engines that are driven by bosonic degrees of freedom such as phonons, magnons and microwave photons. These systems provide interesting connections to spin caloritronics and circuit quantum electrodynamics.

Intermittency and dynamical Lee-Yang zeros of open quantum systems

We use high-order cumulants to investigate the Lee-Yang zeros of generating functions of dynamical observables in open quantum systems. At long times the generating functions take on a large-deviation form with singularities of the associated cumulant generating functions-or dynamical free energies-signifying phase transitions in the ensemble of dynamical trajectories. We consider a driven three-level system as well as the dissipative Ising model. Both systems exhibit dynamical intermittency in the statistics of quantum jumps. From the short-time behavior of the dynamical Lee-Yang zeros, we identify critical values of the counting field which we attribute to the observed intermittency and dynamical phase coexistence. Furthermore, for the dissipative Ising model we construct a trajectory phase diagram and estimate the value of the transverse field where the stationary state changes from being ferromagnetic (inactive) to paramagnetic (active).

Perturbative approach to Markovian open quantum systems

The exact treatment of Markovian open quantum systems, when based on numerical diagonalization of the Liouville super-operator or averaging over quantum trajectories, is severely limited by Hilbert space size. Perturbation theory, standard in the investigation of closed quantum systems, has remained much less developed for open quantum systems where a direct application to the Lindblad master equation is desirable. We present such a perturbative treatment which will be useful for an analytical understanding of open quantum systems and for numerical calculation of system observables which would otherwise be impractical.

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.

Full-counting statistics of random transition-rate matrices

We study the full-counting statistics of current of large open systems through the application of random-matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating functions based on an expansion in terms of the inverse system size. We investigate how different symmetry properties and different counting schemes affect the results.

Detector-induced backaction on the counting statistics of a double quantum dot

Full counting statistics of electron transport is of fundamental importance for a deeper understanding of the underlying physical processes in quantum transport in nanoscale devices. The backaction effect from a detector on the nanoscale devices is also essential due to its inevitable presence in experiments. Here we investigate the backaction of a charge detector in the form of a quantum point contact (QPC) on the counting statistics of a biased double quantum dot (DQD). We show that this inevitable QPC-induced backaction can have profound effects on the counting statistics under certain conditions, e.g., changing the shot noise from being sub-Poissonian to super-Poissonian, and changing the skewness from being positive to negative. Also, we show that both Fano factor and skewness can be either enhanced or suppressed by increasing the energy difference between two single-dot levels of the DQD under the detector-induced backaction.

Delayed feedback control in quantum transport

Feedback control in quantum transport has been predicted to give rise to several interesting effects, among them quantum state stabilization and the realization of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system are affected instantaneously after the measurement of electronic jumps through it. In this contribution, I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport. I investigate the consequences of delay for the state stabilization and Maxwell's daemon schemes. Furthermore, I describe how delay can be used as a tool to probe coherent oscillations of electrons within a transport system and how this formalism can be used to model finite detector bandwidth.

Waiting time distributions for the transport through a quantum-dot tunnel coupled to one normal and one superconducting lead

We have studied the waiting time distributions (WTDs) for subgap transport through a single-level quantum-dot tunnel coupled to one normal and one superconducting lead. The WTDs reveal the internal dynamics of the system, in particular, the coherent transfer of Cooper pairs between the dot and the superconductor. The WTDs exhibit oscillations that can be directly associated to the coherent oscillation between the empty and doubly occupied dot. The oscillation frequency is equal to the energy splitting between the Andreev bound states. These effects are more pronounced when the empty state and double-occupied state are in resonance.

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state

We describe how to characterize dynamical phase transitions in open quantum systems from a purely dynamical perspective, namely, through the statistical behavior of quantum jump trajectories. This approach goes beyond considering only properties of the steady state. While in small quantum systems dynamical transitions can only occur trivially at limiting values of the controlling parameters, in many-body systems they arise as collective phenomena and within this perspective they are reminiscent of thermodynamic phase transitions. We illustrate this in open models of increasing complexity: a three-level system, the micromaser, and a dissipative version of the quantum Ising model. In these examples dynamical transitions are accompanied by clear changes in static behavior. This is however not always the case, and, in general, dynamical phases need to be uncovered by observables which are strictly dynamical, e.g., dynamical counting fields. We demonstrate this via the example of a class of models of dissipative quantum glasses, whose dynamics can vary widely despite having identical (and trivial) stationary states.

Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics

We investigate Lee-Yang zeros of generating functions of dynamical observables and establish a general relation between phase transitions in ensembles of trajectories of stochastic many-body systems and the time evolution of high-order cumulants of such observables. This connects dynamical free energies for full counting statistics in the long-time limit, which can be obtained via large-deviation methods and whose singularities indicate dynamical phase transitions, to observables that are directly accessible in simulation and experiment. As an illustration, we consider facilitated spin models of glasses and show that from the short-time behavior of high-order cumulants, it is possible to infer the existence and location of dynamical or "space-time" transitions in these systems.

Minimal model for short-time diffusion in periodic potentials

We investigate the dynamics of a single, overdamped colloidal particle, which is driven by a constant force through a one-dimensional periodic potential. We focus on systems with large barrier heights where the lowest-order cumulants of the density field, that is, average position and the mean-squared displacement, show nontrivial (nondiffusive) short-time behavior characterized by the appearance of plateaus. We demonstrate that this "cage-like" dynamics can be well described by a discretized master equation model involving two states (related to two positions) within each potential valley. Nontrivial predictions of our approach include analytic expressions for the plateau heights and an estimate of the "de-caging time" obtained from the study of deviations from Gaussian behavior. The simplicity of our approach means that it offers a minimal model to describe the short-time behavior of systems with hindered dynamics.

Strong quantum memory at resonant Fermi edges revealed by shot noise

Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.

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.

Large deviations of ergodic counting processes: a statistical mechanics approach

The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic nonstationary statistical properties of its fluctuations. Here we study this formalism through a statistical mechanics approach, that is, with an auxiliary counting process that maximizes an entropy function associated with the thermodynamic potential. We show that the realizations of this auxiliary process can be obtained after applying a conditional measurement scheme to the original ones, providing is this way an alternative measurement interpretation of the thermodynamic approach. General results are obtained for renewal counting processes, that is, those where the time intervals between consecutive events are independent and defined by a unique waiting time distribution. The underlying statistical mechanics is controlled by the same waiting time distribution, rescaled by an exponential decay measured by the free energy function. A scale invariance, shift closure, and intermittence phenomena are obtained and interpreted in this context. Similar conclusions apply for nonrenewal processes when the memory between successive events is induced by a stochastic waiting time distribution.

Self-consistent electron counting statistics

We develop a self-consistent version of perturbation theory in Liouville space which seeks to combine the advantages of master equation approaches in quantum transport with the nonperturbative features that a self-consistent treatment brings. We describe how counting fields may be included in a self-consistent manner in this formalism such that the full counting statistics can be calculated. Non-Markovian effects are also incorporated. Several different self-consistent approximations are introduced and we discuss their relative strengths with a simple example.

Feedback control of quantum transport

The current through nanostructures like quantum dots can be stabilized by a classical feedback loop that continuously adjusts system parameters as a function of the number of tunnelled particles n. At large times, the feedback loop freezes the fluctuations of n, which leads to highly accurate, continuous single particle transfers. For the simplest case of feedback acting simultaneously on all system parameters, we show how to reconstruct the original full counting statistics from the frozen distribution.

Mesoscopic Coulomb drag, broken detailed balance, and fluctuation relations

When a biased conductor is put in proximity with an unbiased conductor a drag current can be induced in the absence of detailed balance. This is known as the Coulomb drag effect. However, even in this situation far away from equilibrium where detailed balance is explicitly broken, theory predicts that fluctuation relations are satisfied. This surprising effect has, to date, not been confirmed experimentally. Here we propose a system consisting of a capacitively coupled double quantum dot where the nonlinear fluctuation relations are verified in the absence of detailed balance.

Non-Markovian theory for the waiting time distributions of single electron transfers

We derive a non-Markovian theory for waiting time distributions of consecutive single electron transfer events. The presented microscopic Pauli rate equation formalism couples the open electrodes to the many-body system, allowing to take finite bias and temperature into consideration. Numerical results reveal transient oscillations of distinct system frequencies due to memory in the waiting time distributions. Memory effects can be approximated by an expansion in non-Markovian corrections. This method is employed to calculate memory landscapes displaying preservation of memory over multiple consecutive electron transfers.

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 n(m) 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.

Shot noise properties of electron transport through an interacting multi-terminal quantum dots system

We study the correlations of tunneling currents through an interacting quantum dots (QDs) system composed of a top single QD and a bottom qubit with purely capacitive coupling within a quantum master approach. We find that the super-Poissonian current noise of the qubit near resonance, which is a signature of coherent tunneling within the transport qubit for asymmetrical contact couplings, is strongly dependent on non-equilibrium transport through the top QD with different coupling configurations. For pure-dephasing coupling, such a super-Poissonian feature is asymmetrically washed out by increasing coupling strength showing obvious qubit level position dependence with finite bias and temperature, while for orthogonal coupling we can almost symmetrically lower the double peak to a double minimum by increasing coupling strength or adjusting the ratio of the top QD contact couplings in the large bias limit, indicating the transition from coherent tunneling to sequential tunneling.