Master equation approach to study Non-Markovian dynamics of open quantum systems

A full understanding of the decoherence dynamics of an open quantum system is of crucial importance for quantum information theory and quantum computing. In the last two decades, most theoretical and experimental research is replied on the Born-Markov approximation, a no-memory and quasi-static process. The associated Lindblad master equation has the great success in explaining some phenomena, e.g. the long-time limit steady state, quantum-classical transition. However, the recently achieved strong coupling between system and environment in many experiments breaks the Born-Markov approximation and forces one to study the decoherence in a strong non-Markovian and non-equilibrium regime. The major difficulty is raised up by lack of the technique to deal with the large number of degrees of freedom of the colored noisy environment. Starting from stochastic Schrödinger equations, we demonstrate a systematical method to derive the exact time convolution-less master equation for various open quantum systems, e.g. qubit systems, multi-level systems, and harmonic oscillator systems. Our methods can also be extended to the optomechanical systems and other non-linear coupling systems.