# Electron waiting times of a periodically driven single-electron turnstile

## TL;DR

This paper develops an analytical framework to study the distribution of electron waiting times in a periodically driven single-electron turnstile, revealing how driving protocols and temperature affect emission dynamics.

## Contribution

It introduces a general scheme for calculating waiting time distributions for arbitrary periodic drives in single-electron devices, including non-adiabatic effects and finite temperature influences.

## Key findings

- Waiting time distributions depend on driving protocol and temperature.
- Cycle-missing events dominate in non-adiabatic regimes.
- The framework offers insights beyond conventional current measurements.

## Abstract

We investigate the distribution of waiting times between electrons emitted from a periodically driven single-electron turnstile. To this end, we develop a scheme for analytic calculations of the waiting time distributions for arbitrary periodic driving protocols. We illustrate the general framework by considering a driven tunnel junction before moving on to the more involved single-electron turnstile. The waiting time distributions are evaluated at low temperatures for square-wave and harmonic driving protocols. In the adiabatic regime, the dynamics of the turnstile is synchronized with the external drive. As the non-adiabatic regime is approached, the waiting time distribution becomes dominated by cycle-missing events in which the turnstile fails to emit within one or several periods. We also discuss the influence of finite electronic temperatures. The waiting time distributions provide a useful characterization of the driven single-electron turnstile with complementary information compared to what can be learned from conventional current measurements.