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Delayed feedback control in quantum transport

Trans R Soc A, Clive Emary, Clive Emary

Published Oct 28, 2015• 14 citations
OpenAlex

Abstract

‘Dynamics, control and information in delay-coupled systems’. Subject Areas: applied mathematics, quantum physics Keywords: quantum transport, feedback control, delay, quantum dots Author for correspondence:

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Delayed feedback control in quantum transport

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arXiv:1207.2910•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Aug 20, 2013•17 citations
We investigate feedback control of linear quantum systems subject to feedback-loop time delays. In particular, we examine the relation between the potentially achievable control performance and the time delays and provide theoretical guidelines for the future experimental setup in two physical systems, which are typical in this research field. The evaluation criterion for the analysis is given by the optimal control performance formula, the derivation of which is from the classical control theoretic results about the input-output delay systems.
A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a fictitious series of cascaded quantum systems, where the system is driven by past versions of itself. The derivation of this model relies on a tensor network representation of the system-reservoir time propagator. For concreteness, this general theory is applied to a driven two-level atom scattering into a coherent feedback loop. We demonstrate how delay effects can qualitatively change the dynamics of the atom and how quantum control can be implemented in the presence of time delays.
A controllable low noise current lies at the heart of high-precision measurements in quantum transport and metrology. While the previous research dealt with the suppression of noise in transport through a tunneling junction or a single quantum dot (QD) device, the present work investigates noise inhibition of a double quantum dot (DQD) transport system based on closed-loop feedback control. The unique advantage of a DQD device is that bidirectional transport at low bias can be measured by a nearby quantum point contact. However, the continuous monitoring of the DQD states inevitably leads to a measurement-induced dephasing. To appropriately characterize its transport properties in the presence of feedback action, we here develop a numerical method dubbed auxiliary density matrix approach, motivated by the hierarchical expansion of the moment-generating function in the hierarchy equations of motion [J. Cerrillo et al., Phys. Rev. B 94, 214308 (2016)]. This generic method has no restriction on the system structure and parameters and is able to evaluate the feedback current cumulants to an arbitrary order. It is revealed that the feedback control of the tunnel coupling between the two dots is the most effective to suppress the noise under various tunnel coupling configurations. The influence of interdot Coulomb interaction, measurement-induced dephasing, and finite time delay on feedback is also analyzed in detail.
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.