A low-dimensional detector model for full counting statistics: Trajectories, Back-Action, and Fidelity

TL;DR

This paper analyzes the conditions under which a capacitively coupled transport channel can serve as an effective charge detector, even with significant back-action, by studying full counting statistics and bistability regimes.

Contribution

It introduces a method to estimate detector error from time-resolved current measurements and explores detector fidelity in bistable regimes with differing tunneling rates.

Findings

High detector fidelity achievable in bistable regimes with disparate tunneling rates

Detector error can be estimated from current measurements alone

Large back-action does not necessarily impair detection accuracy

Abstract

We study the combined counting statistics of two capacitively coupled transport channels. In particular, we examine the conditions necessary for utilizing one channel as detector sensitive to the occupation of the other. A good detector fidelity may be achieved in a bistable regime when the tunneling rates through the two channels are vastly different -- even when the physical back-action of the detector on the probed channel is large. Our methods allow to estimate the error of charge counting detectors from time-resolved current measurements -- which have been obtained in recent experiments -- alone.