Quantum theory of an electron waiting time clock

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.