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 of a general quantum mechanical variable

We present a quantum mechanical framework for defining the statistics of measurements of , A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes to observe the so defined statistics experimentally.Received: 30 June 2003, Published online: 15 October 2003PACS: 73.50.Td Noise processes and phenomena - 73.23.-b Electronic transport in mesoscopic systems - 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.)     

Conditional spin counting statistics as a probe of Coulomb interaction and spin-resolved bunching

Full counting statistics is a powerful tool to characterize the noise and correlations in transport through mesoscopic systems. In this work, we propose the theory of conditional spin counting statistics, i.e., the statistical fluctuations of spin-up (down) current given the observation of the spin-down (up) current. In the context of transport through a single quantum dot, it is demonstrated that a strong Coulomb interaction leads to a conditional spin counting statistics that exhibits a substantial change in comparison to that without Coulomb repulsion. It thus can be served as an effective way to probe the Coulomb interactions in mesoscopic transport systems. In case of spin polarized transport, it is further shown that the conditional spin counting statistics offers a transparent tool to reveal the spin-resolved bunching behavior.     

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.     

Measurement of counting statistics of electron transport in a tunnel junction

We present measurements of the time-dependent fluctuations of electrical current in a voltage-biased tunnel junction. We were able to simultaneously extract the first three moments of the current counting statistics. Detailed comparison of the second and the third moments reveals that the statistics is accurately described as Poissonian, expected for spontaneous current fluctuations due to electron charge discreteness, realized in tunneling transport at negligible coupling to environment.     

Influence of a random telegraph process on the transport through a point contact

We describe the transport properties of a point contact under the influence of a classical two-level fluctuator. We employ a transfer matrix formalism allowing us to calculate arbitrary correlation functions of the stochastic process by mapping them on matrix products. The result is used to obtain the generating function of the full counting statistics of a classical point contact subject to a classical fluctuator, including extensions to a pair of two-level fluctuators as well as to a quantum point contact. We show that the noise in the quantum point contact is a sum of the (quantum) partitioning noise and the (classical) noise due to the two-level fluctuator. As a side result, we obtain the full counting statistics of a quantum point contact with time-dependent transmission probabilities.     

Charge transfer statistics and entanglement in normal-quantum dot-superconductor hybrid structures

We analyze the full counting statistics (FCS) of a single-site quantum dot coupled to multiple metallic electrodes in the normal state and a superconductor for arbitrary transmission. We present an analytical solution of the problem taking into account the full energy dependence of the transmission coefficient. We identify two transport processes as sources of entanglement between the current carriers by observing positive cross current correlations. Furthermore, we consider ferromagnetic electrodes and show how they can be used as detectors in experiments violating the Bell-Clauser-Horne-Shimony-Holt inequality.     

Full counting statistics with spin-sensitive detectors reveals spin singlets

We study the full counting statistics of electric current to several drain terminals with spin-dependent entrance conductances. We show that the statistics of charge transfers can be interpreted in terms of single electrons and spin-singlet pairs coming from the source. If the source contains transport channels of high transparency, a significant fraction of electrons comes in spin-singlet pairs.     

Nanotransformation and current fluctuations in exciton condensate junctions

We analyze the nonlinear transport properties of a bilayer exciton condensate that is contacted by four metallic leads by calculating the full counting statistics of electron transport for arbitrary system parameters. Despite its formal similarity to a superconductor the transport properties of the exciton condensate turn out to be completely different. We recover the generic features of exciton condensates such as counterpropagating currents driven by excitonic Andreev reflections and make predictions for nonlinear transconductance between the layers as well as for the current (cross)correlations and generalized Johnson-Nyquist relationships. Finally, we explore the possibility of connecting another mesoscopic system (in our case a quantum point contact) to the bottom layer of the exciton condensate and show how the excitonic Andreev reflections can be used for transforming voltage at the nanoscale.     

Full counting statistics in the self-dual interacting resonant level model

We present a general technique to obtain the zero temperature cumulant generating function of the full counting statistics of charge transfer in interacting impurity models out of equilibrium from time-dependent simulations on a lattice. We demonstrate the technique with application to the self-dual interacting resonant level model, where very good agreement between numerical simulations using the density matrix renormalization group and those obtained analytically from the thermodynamic Bethe ansatz is found. We show from the exact form of counting statistics that the quasiparticles involved in transport carry charge 2e in the low bias regime and e/2 in the high bias regime.     

Elementary Andreev processes in a driven superconductor–normal metal contact

We investigate the full counting statistics of a voltage-driven normal metal(N)–superconductor(S) contact. In the low-bias regime below the superconducting gap, the NS contact can be mapped onto a purely normal contact, albeit with doubled voltage and counting fields. Hence in this regime the transport characteristics can be obtained by the corresponding substitution of the normal metal results. The elementary processes are single Andreev transfers and electron- and hole-like Andreev transfers. Considering Lorentzian voltage pulses we find an optimal quantization for half-integer Levitons.     

Full counting statistics of transport electrons through a two-level quantum dot with spin–orbit coupling

We study the full counting statistics of transport electrons through a semiconductor two-level quantum dot with Rashba spin–orbit (SO) coupling, which acts as a nonabelian gauge field and thus induces the electron transition between two levels along with the spin flip. By means of the quantum master equation approach, shot noise and skewness are obtained at finite temperature with two-body Coulomb interaction. We particularly demonstrate the crucial effect of SO coupling on the super-Poissonian fluctuation of transport electrons, in terms of which the SO coupling can be probed by the zero-frequency cumulants. While the charge currents are not sensitive to the SO coupling.     

Quantum fluctuation theorem in an interacting setup: point contacts in fractional quantum Hall edge state devices

We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a fractional quantum Hall edge state device. This is accomplished via the development of an analytical method to calculate the full counting statistics of the problem in all the parameter regimes involving the temperature, the Hall voltage, and the gate voltage.     

Full counting statistics of multiple Andreev reflection

We derive the full counting statistics of charge transfer through a voltage biased superconducting junction. We find that, for measurement times much longer than the inverse Josephson frequency, the counting statistics describes a correlated transfer of quanta of multiple electron charges, each quantum associated with the transfer of a single quasiparticle. An expression for the counting statistics in terms of the quasiparticle scattering amplitudes is derived.     

Full counting statistics of phonon transport in disordered systems

The coherent potential approximation (CPA) within full counting statistics (FCS) formalism is shown to be a suitable method to investigate average electric conductance, shot noise as well as higher order cumulants in disordered systems. We develop a similar FCS-CPA formalism for phonon transport through disordered systems. As a byproduct, we derive relations among coefficients of different phonon current cumulants. We apply the FCS-CPA method to investigate phonon transport properties of graphene systems in the presence of disorders. For binary disorders as well as Anderson disorders, we calculate up to the 8-th phonon transmission moments and demonstrate that the numerical results of the FCS-CPA method agree very well with that of the brute force method. The benchmark shows that the FCS-CPA method achieves 20 times more speedup ratio. Collective features of phonon current cumulants are also revealed.     

Keldysh technique and non-linear σ-model: basic principles and applications

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of the underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear σ-model for disordered metals and superconductors. We discuss topics such as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equations, etc. The section devoted to disordered superconductors includes the Usadel equation, fluctuation corrections, time-dependent Ginzburg–Landau theory, proximity and Josephson effects, etc.     

Stochastic path integral formulation of full counting statistics

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the saddle-point approximation to the path integral, and fluctuations around the saddle point are suppressed in the semiclassical approximation. We use this approach to derive the current cumulants of a chaotic cavity in the hot-electron regime.     

Full counting statistics of multiple Andreev reflections

We derive the full distribution of transmitted particles through a superconducting point contact of arbitrary transparency under voltage bias. The charge transport is dominated by multiple Andreev reflections. The counting statistics is a multinomial distribution of processes, in which multiple charges ne (n=1,2,3, ...) are transferred through the contact. For zero temperature we obtain analytical expressions for the probabilities of the multiple Andreev reflections. The current, shot noise, and high current cumulants in a variety of situations can be obtained from our result.     

Superconducting proximity effect in interacting quantum dots revealed by shot noise

We study the full counting statistics of charge transport through a quantum dot tunnel coupled to one normal and one superconducting lead with a large superconducting gap. As a function of the level detuning, there is a crossover from a regime with strong superconducting correlations in the quantum dot to a regime in which the proximity effect on the quantum dot is suppressed. We analyze the current fluctuations of this crossover in the shot-noise regime. In particular, we predict that the full counting statistics changes from Poissonian with charge 2e, typical for Cooper pairs, to Poissonian with charge e, when the superconducting proximity effect is present. Thus, the onset of the superconducting proximity effect is revealed by the reduction of the Fano factor from 2 to 1.