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arXiv:1407.1306 · Physical Review B

Coherent feedback control in quantum transport

Clive Emary, John Edward Gough

Published Nov 26, 2014• 17 citations
arXivHTMLPDF

Abstract

This paper adapts control theory to the study of quantum transport in mesoscopic systems. In particular the authors study coherent control where the system as well as the controller are quantum coherent.
DOI
10.1103/physrevb.90.205436

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Abstract We consider coherent feedback control of quantum transport and focus on the application of simple controllers and the effects of a finite bias voltage. We show that simple single-parameter controllers can give rise to a range of useful effects such as amplification of changes in plant transmission, increased resolution of energy filtration, and the detection of differences between otherwise indistinguishable plants. We explore how these effects are impacted by the phase-averaging effects associated with finite bias and identify important voltage scales for the maintenance of the functionalities achieved through feedback control.
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Feedback control in quantum transport has been predicted to give rise to several interesting effects, among them quantum state stabilization and the realization of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system are 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 stabilization 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.
Feedback is a fundamental and well-understood method of control used since ancient times; this thesis investigates coherent feedback control in a quantum Hall regime. Quantum Feedback requires a level of isolation from measurement in order to maintain the coherence of the electron wavefunction, unlike the classical variant of feedback where measurement is commonplace as information is easily duplicated. Here we build upon a Landauer Büttiker model for electrons as flying qubits in a closed feedback arrangement which uses scattering matrices to represent and connect the elements of the feedback device to better analyse the qualities that modify feedback effects in a variety of systems. Here we will also investigate the effects of finite bias at each stage of the thesis, with a focus on what effect it has on the function of the feedback system and the extent of the effect depending on how feedback is employed.