Quantum theory of an electron waiting time clock

TL;DR

This paper develops a quantum theory for an electron waiting time clock that measures the distribution of waiting times between electrons in mesoscopic conductors, addressing the lack of a proper detector model in previous theories.

Contribution

It introduces a quantum detector model for electron waiting times, enabling measurement of waiting time distributions in mesoscopic conductors, and analyzes deviations from ideal conditions.

Findings

The waiting time clock recovers earlier theoretical results in ideal conditions.

Deviations due to imperfect detection are analyzed.

Applications include quantum point contacts with voltage pulses.

Abstract

The electron waiting time is the time that passes between two subsequent charge transfers in an electronic conductor. Recently, theories of electron waiting times have been devised for quantum transport in Coulomb-blockade structures and for mesoscopic conductors, however, so far a proper description of a detector has been missing. Here we develop a quantum theory of a waiting time clock capable of measuring the distribution of waiting times between electrons above the Fermi sea in a mesoscopic conductor. The detector consists of a mesoscopic capacitor coupled to a quantum two-level system whose coherent precession we monitor. Under ideal operating conditions our waiting time clock recovers the results of earlier theories without a detector. We investigate possible deviations due to an imperfect waiting time clock. As specific applications we consider a quantum point contact with a constant voltage and lorentzian voltage pulses applied to an electrode.