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arXiv:1408.6100 · Physical Review B

Distributions of electron waiting times in quantum-coherent conductors

Géraldine Haack, Mathias Albert, Christian Flindt

Published Nov 21, 2014• 46 citations
arXivHTMLPDF

Abstract

The distribution of electron waiting times is useful to characterize quantum transport in mesoscopic structures. Here we consider a generic quantum-coherent conductor consisting of a mesoscopic scatterer in a two-terminal setup. We extend earlier results for single-channel conductors to setups with several (possibly spin degenerate) conduction channels and we discuss the effect of a finite electronic temperature. We present detailed investigations of the electron waiting times in a quantum point contact as well as in two mesoscopic interferometers with energy-dependent transmissions: a Fabry--P\'erot interferometer and a Mach--Zehnder interferometer. We show that the waiting time distributions allow us to determine characteristic features of the scatterers, for instance, the number of resonant levels in the Fabry--P\'erot interferometer that contribute to the electronic transport.

DOI
10.1103/physrevb.90.205429

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We consider the distribution of waiting times between noninteracting fermions on a tight-binding chain. We calculate the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off as predicted by scattering theory. In addition, we consider several quantum dot structures for which we can associate oscillations in the waiting time distributions with internal energy scales of the scatterers. A detailed comparison with scattering theory and generalized master equations is provided. We focus on mesoscopic conductors, but our tight-binding models may also be realized in cold-atomic gases.
We consider a sequence of quantized Lorentzian pulses of noninteracting electrons impinging on a quantum point contact and study the waiting time distribution (WTD), for any transmission and any number of pulses. As the degree of overlap between the electronic wave functions is tuned, the WTD reveals how the correlations between particles are modified. In the weak overlap regime, the WTD is made of several equidistant peaks, separated by the same period as the incoming pulses, contained in an almost exponentially decaying envelope. In the other limit, the WTD of a single quantum channel subjected to a constant voltage is recovered. In both cases, the WTD stresses the difference between the fluctuations induced by the scatterer and the ones encoded in the incoming quantum state. A clear crossover between these two situations is studied with numerical and analytical calculations based on scattering theory.
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A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within such an approach, counting charge without breaking the circuit is possible. As an application, we derive the counting statistics in a single channel conductor at finite temperature and bias. For a perfectly transmitting channel the counting distribution is Gaussian, both for zero-point fluctuations and at finite temperature. At constant bias and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics. Another application considered is the noise due to short current pulses that involve few electrons. We find the time-dependence of the driving potential that produces coherent noise-minimizing current pulses, and display analogies of such current states with quantum-mechanical coherent states.
Abstract Decoherence is an undesirable, but ubiquitous phenomenon in quantum systems. Here, we study the effect of partial decoherence, induced via a Büttiker probe, on two-terminal electronic transport across one-dimensional quantum wires and rings, in both the linear and non-linear regimes. We find that dephasing causes backscattering when introduced locally in a ballistic channel. Further, we find that decoherence results in rectification when inversion is broken in the two-terminal transport set-up by a combination of a local dephasing centre and a static impurity. Interestingly, the rectification strength and even its direction varies strongly with the relative distance between the probe and the scatterer. We further analyze how decoherence affects characteristic quantum effects in electronic transport, such as, Fabry-Pérot oscillations in double-barrier setups, and Aharonov–Bohm interference in one-dimensional rings, and find that the amplitude of oscillations in conductance is reduced by decoherence.
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