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arXiv:1401.5723 · Physical Review B

Waiting time distribution for trains of quantized electron pulses

Mathias Albert, P. Devillard

Published Jul 22, 2014• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.90.035431

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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.
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.
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Abstract We apply the framework developed in the preceding paper in this series (Smilansky 2017 J. Phys. A: Math. Theor . 50 215301) to compute the time-delay distribution in the scattering of ultra short radio frequency pulses on complex networks of transmission lines which are modeled by metric (quantum) graphs. We consider wave packets which are centered at high wave number and comprise many energy levels. In the limit of pulses of very short duration we compute upper and lower bounds to the actual time-delay distribution of the radiation emerging from the network using a simplified problem where time is replaced by the discrete count of vertex-scattering events. The classical limit of the time-delay distribution is also discussed and we show that for finite networks it decays exponentially, with a decay constant which depends on the graph connectivity and the distribution of its edge lengths. We illustrate and apply our theory to a simple model graph where an algebraic decay of the quantum time-delay distribution is established.
We explore the use of waiting-time statistics in a quantum electron shuttle for electric-field sensing. Electron shuttles convert nanomechanical motion into charge transport, showing a noise-broadened crossover between stochastic tunneling and mechanically assisted charge transfer. This allows investigation of how transport fluctuations encode electromechanical parameters. Using a single-level quantum shuttle in strong-Coulomb-blockade and high-bias regimes with a Markovian quantum master equation, we analyze stationary dynamics in phase space and waiting time distributions. By estimating the electromechanical coupling, proportional to the electric field, we evaluate the classical Fisher information in waiting times and compare it with the quantum Fisher information of the stationary state. We relate the metrological response to mean waiting time, variance, and Fano factor. Our results show that the crossover from tunneling to shuttling is characterized by enhanced fluctuations and increased parameter sensitivity, leading to a pronounced enhancement of the Fisher information.