Delayed feedback control in quantum transport

TL;DR

This paper extends the master equation theory of quantum transport feedback control to include delays, analyzing their effects on state stabilization, Maxwell's daemon, and electron oscillations, with applications to detector bandwidth modeling.

Contribution

It introduces a formalism to incorporate delays in feedback control of quantum transport, enabling analysis of delay effects and new probing methods.

Findings

Delay affects quantum state stabilization and Maxwell's daemon schemes.

Delay can be used to probe coherent electron oscillations.

Formalism models finite detector bandwidth effects.

Abstract

Feedback control in quantum transport has been predicted to give rise to several interesting effects, amongst them quantum state stabilisation and the realisation of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system be affected instantaneously after the measurement of electronic jumps through it. In this contribution I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport. I investigate the consequences of delay for the state-stabilisation and Maxwell's-daemon schemes. Furthermore, I describe how delay can be used as a tool to probe coherent oscillations of electrons within a transport system and how this formalism can be used to model finite detector bandwidth.