Models and Feedback Stabilization of Open Quantum Systems

At the quantum level, feedback-loops have to take into account measurement back-action. We present here the structure of the Markovian models including such back-action and sketch two stabilization methods: measurement-based feedback where an open quantum system is stabilized by a classical controller; coherent or autonomous feedback where a quantum system is stabilized by a quantum controller with decoherence (reservoir engineering). We begin to explain these models and methods for the photon box experiments realized in the group of Serge Haroche (Nobel Prize 2012). We present then these models and methods for general open quantum systems.Comment: Extended version of the paper attached to an invited conference for the International Congress of Mathematicians in Seoul, August 13 - 21, 201