Bringing quantum jumps under control

Held by Prof. Howard M. Wiseman (Griffith University, Brisbane, Australia)
Joint work with Dr. Raisa I. Karasik (Griffith University, Brisbane, Australia)

Abstract:
The modern understanding of quantum jumps is that it is the dynamics resulting from the typical form of evolution equation for the conditional state of an open quantum system – the typical form of a stochastic quantum filtering equation to use control theory language. If the average (unconditioned) system evolution is ergodic and Markovian then an experimenter can, in principle, monitor the bath to which the system is coupled with sufficient precision to make the conditioned system state pure in the long-time limit. In general, the quantum jumps, plus the between-jump evolution, create a trajectory which passes through infinitely many different pure states. That is, it would take, in principle, an infinite classical memory to keep track of the state of the quantum system. Here we show that we can use control to realize an adaptive monitoring scheme on the bath which brings this infinity under control. Specifically, for any finite dimensional system, one can expect to find an adaptive monitoring that confines the system state to jumping between only finitely many states [1]. That is, the adaptive tracking scheme can be realized as a finite-state machine. We show specifically for a two-level system how such a scheme can be constructed and analyse its stability [2].

[1] R. Karasik and H. M. Wiseman, “How many bits does it take to track an open quantum system?”, Phys. Rev. Lett. 106, 020406 (2011).
[2] R. Karasik and H. M. Wiseman, “Tracking an open quantum system using a finite state machine: stability analysis”, arXiv:1106.4292