Introduction

This chapter gives a brief overview of and introduction to quantum feedback control and linear quantum systems. It begins with a brief history of quantum feedback control, in particular the development of quantum analogues of ideas from stochastic control theory, and discusses the notion of closed and open quantum systems, the Markov property, and quantum Langevin equations. This chapter then proceeds with an introduction to linear quantum systems and several physical examples thereof, including optical cavities, non-degenerate and degenerate parametric amplifiers, and large atomic ensembles.