Dynamics And Control Of Open Quantum Systems

In this thesis, we concern on the dynamics of open quantum systems. The general description of system dynamics under Markovian approximation is discussed. Also several non-Markovian witnesses are proposed to characterize the memory effect. We then show how to simulate a simple open quantum system using linear optics. By con-trolling the spectrum of the environment, we demonstrate a transition from Markovian to non-Markovian dynamics of system.Followed we discuss the docoherence process and introduce the idea of PR ensem-bles and pointer basis. Also, by perfectly monitoring the environment which is entan-gled with the system, we show that the system dynamics admits a stochastic pure state description, which is essentially the idea of quantum trajectory. We then discuss quan-tum dynamics using the language of linear control theory. By exploring the similarity between the quantum dynamical equations and the classical ones, it is nature to apply the control theory to the quantum systems. We show by using feedback control, one can stabilize any pure state in the linear Gaussian quantum system with high fidelity. We also illustrate our results with a model system, namely, one-dimension quantum Brownian motion.