Electron waiting times for the mesoscopic capacitor

We evaluate the distribution of waiting times between electrons emitted by a driven mesoscopic capacitor. Based on a wave packet approach we obtain analytic expressions for the electronic waiting time distribution and the joint distribution of subsequent waiting times. These semi-classical results are compared to a full quantum treatment based on Floquet scattering theory and good agreement is found in the appropriate parameter ranges. Our results provide an intuitive picture of the electronic emissions from the driven mesoscopic capacitor and may be tested in future experiments.     

Andreev reflection eigenvalue density in mesoscopic conductors

The energy-dependent Andreev reflection eigenvalues determine the transport properties of normal-superconducting systems. We evaluate the eigenvalue density to get insight into the formation of resonant electron-hole transport channels. The circuit-theory-like method developed can be applied to any generic mesoscopic conductor or combinations thereof. We present the results for experimentally relevant cases of a diffusive wire and a double tunnel junction.     

On local and global currents in mesoscopic conductors

Using linear response theory we show that, in a quasi-stationary state, the local multiprobe conductance of a mesoscopic system of non-interacting electrons with a time reversal invariant Hamiltonian does not depend on the local shape of the driving self-consistent potential and thus is entirely determined by the asymptotic values of the potential in the leads. In the ballistic limit, the local conductance in the lateral direction exhibits oscillations depending on the occupation of channels. Scattering by a point impurity leads to softening of the quantized global conductance steps. In addition to that for an attractive scattering potential, a dip occurs in each plateau regime the shape of which is calculated for different values of the potential strength. We also investigate the local conductance for both a point scatterer and a finite scattering region.     

Charge densities and charge noise in mesoscopic conductors

We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. The partial density of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial density of states determine the degree of dephasing generated by a weakly coupled voltage probe. In addition the partial density of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. The partial density of states permit the formulation of a Friedel sum rule which can be applied locally. We introduce the off-diagonal elements of the partial density of states matrix to describe charge fluctuation processes. This generalization leads to a local Wigner-Smith life-time matrix.     

Two-particle scattering matrix of two interacting mesoscopic conductors

We consider two quantum coherent conductors interacting weakly via long range Coulomb forces. We describe the interaction in terms of two-particle collisions described by a two-particle scattering matrix. As an example we determine the transmission probability and correlations in a two-particle scattering experiment and find that the results can be expressed in terms of the density-of-states matrices of the noninteracting scatterers.     

Capacitive coupling of atomic systems to mesoscopic conductors

We describe a technique that enables a strong, coherent coupling between isolated neutral atoms and mesoscopic conductors. The coupling is achieved by exciting atoms trapped above the surface of a superconducting transmission line into Rydberg states with large electric dipole moments that induce voltage fluctuations in the transmission line. Using a mechanism analogous to cavity quantum electrodynamics, an atomic state can be transferred to a long-lived mode of the fluctuating voltage, atoms separated by millimeters can be entangled, or the quantum state of a solid-state device can be mapped onto atomic or photonic states.     

Frequency scales for current statistics of mesoscopic conductors

We calculate the third cumulant of current in a chaotic cavity with contacts of arbitrary transparency as a function of frequency. Its frequency dependence drastically differs from that of the conventional noise. In addition to a dispersion at the inverse RC time characteristic of charge relaxation, it has a low-frequency dispersion at the inverse dwell time of electrons in the cavity. This effect is suppressed if both contacts have either large or small transparencies.     

Local waiting times in critical systems

The quiet times at a fixed point in space are investigated in a system close to or at a non-equilibrium phase transition. The statistics for such first-return times follow from the universality class of the dynamics and the ensemble: for a power-law waiting time distribution the exponent depends on the dimension and the underlying model. We study the two-dimensional Manna sandpile, with both the continously driven self-organized version and the tuned one. The latter has an absorbing state or depinning phase transition at a critical value of the control parameter. The connection to a driven interface in a random medium gives the exponent of the waiting time distribution. In the open ensemble, differences ensue due to the spatial inhomogeneity and the properties of the driving signal. For both ensembles, the waiting time distributions are found to exhibit logarithmic corrections to scaling.Received: 13 September 2004, Published online: 23 December 2004PACS: 05.70.Ln Nonequilibrium and irreversible thermodynamics - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 52.25.Fi Transport properties     

Orbital entanglement and violation of Bell inequalities in mesoscopic conductors

We propose a spin-independent scheme to generate and detect two-particle entanglement in a mesoscopic normal-superconductor system. A superconductor, weakly coupled to the normal conductor, generates an orbitally entangled state by injecting pairs of electrons into different leads of the normal conductor. The entanglement is detected via violation of a Bell inequality, formulated in terms of zero-frequency current cross correlators. It is shown that the Bell inequality can be violated for arbitrary strong dephasing in the normal conductor.     

Electron transport through mesoscopic ring

The quantum transport properties of a non-interacting mesoscopic ring sandwiched between two metallic electrodes are investigated by the use of Green's function technique. Here, we introduce parametric approach, based on the tight-binding model to study these transport properties. The electronic transport properties are focused in three aspects: (a) geometry of the mesoscopic ring, (b) coupling strength of the ring with the two electrodes and (c) magnetic flux threaded by the ring.     

Electron localization in quasi-one-dimensional organic conductors

The theory of electron localization in quasi-one-dimensional organic conductors is reviewed in detail. The effective diagram technique to take into account strong scattering and commensurability effects is developed using the Berezinsky method. The singularities of the electron density of states, of the localization length and of the static dielectric constant near the middle of the electron band and near other rational points of the band are discussed. A transition similar to the Anderson transition is found near the band edge. The effects of the electron-phonon interaction are taken into account and exact results for the hopping conductivity are obtained. The experimental data on the electrical and optical properties of TCNQ salts with strong structural disorder and of other quasi-1d organic conductors are reviewed and analysed.     

Electron transport in interacting hybrid mesoscopic systems

A unified theory for the current through a mesoscopic region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific circumstances. In such a formulation, the requirement of gauge invariance is satisfied automatically. Moreover, one can judge unambiguously what quantities can be measured in the transport experiment. Received 22 August 2002 / Received in final form 14 February 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: phyzengz@nus.edu.sg     

Electron quantum optics in ballistic chiral conductors

The edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in an optics‐like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on‐demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turns to the presentation of single electron emitters and their characterization through the measurements of the average electrical current and its correlations. This is followed by a discussion of electron quantum optics experiments in the Hanbury‐Brown and Twiss geometry where two‐particle interferences occur. Finally, Coulomb interactions effects and their influence on single electron states are considered.     

Photovoltaic current response of mesoscopic conductors to quantized cavity modes

We extend the analysis of the effects of electromagnetic (EM) fields on mesoscopic conductors to include the effects of field quantization, motivated by recent experiments on circuit QED. We show that in general there is a photovoltaic (PV) current induced by quantized cavity modes at zero bias across the conductor. This current depends on the average photon occupation number and vanishes identically when it is equal to the average number of thermal electron-hole pairs. We analyze in detail the case of a chaotic quantum dot at temperature Te in contact with a thermal EM field at temperature Tf, calculating the rms size of the PV current as a function of the temperature difference, finding an effect approximately pA.     

Validity and breakdown of Onsager symmetry in mesoscopic conductors interacting with environments

We investigate magnetic-field asymmetries in the linear transport of a mesoscopic conductor interacting with its environment. Interestingly, we find that the interaction between the two systems causes an asymmetry only when the environment is out of equilibrium. We elucidate our general result with the help of a quantum dot capacitively coupled to a quantum Hall conductor and discuss the asymmetry dependence on the environment bias and induced dephasing.