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

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.

11 pages, 4 figures

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Cited by in corpus (7)

• Short-time counting statistics of charge transfer in Coulomb-blockade systems
• Inverse counting statistics based on generalized factorial cumulants
• Random-walk topological transition revealed via electron counting
• Feedback Control of Waiting Times
• Violation of detailed balance for charge-transfer statistics in Coulomb-blockade systems
• Collisional-model quantum trajectories for entangled qubit environments
• Open quantum systems are harder to track than open classical systems