Stochastic feedback control of quantum transport to realize a dynamical ensemble of two nonorthogonal pure states

TL;DR

This paper explores how feedback control can be used to realize finite ensembles of pure states in quantum transport systems, revealing differences between coherent and incoherent tunneling regimes through counting statistics.

Contribution

It demonstrates the application of physically realizable ensembles to quantum transport control, identifying conditions for realizing two-state ensembles and analyzing their statistical properties.

Findings

Two-state PREs can always be realized in the control scheme.

Incoherent tunneling admits infinitely many PREs not realizable by the control.

Counting statistics distinguish between coherent and incoherent regimes.

Abstract

A Markovian open quantum system which relaxes to a unique steady state $\rho_{ss}$ of finite rank can be decomposed into a finite physically realizable ensemble (PRE) of pure states. That is, as shown by Karasik and Wiseman [Phys. Rev. Lett. 106, 020406 (2011)], in principle there is a way to monitor the environment so that in the long time limit the conditional state jumps between a finite number of possible pure states. In this paper we show how to apply this idea to the dynamics of a double quantum dot arising from the feedback control of quantum transport, as previously considered by one of us and co-workers [Phys. Rev. B 84, 085302 (2011)]. Specifically, we consider the limit where the system can be described as a qubit, and show that while the control scheme can always realize a two-state PRE, in the incoherent tunneling regime there are infinitely many PREs compatible with the dynamics that cannot be so realized. For the two-state PREs that are realized, we calculate the counting statistics and see a clear distinction between the coherent and incoherent regimes.