Quantum state preparation of spin ensembles by continuous measurement and feedback

Beginning with a microscopic model for the interaction between atoms and the electromagnetic field, we describe how stochastic equations for the state of the atomic ensemble conditioned upon homodyne measurement of the field can be derived. We investigate the evolution of the stochastic state both in the short time scale, where a description in terms of continuous variables (spin quadratures) is possible, and in the longer time scale where this description breaks down. Next we discuss general principles of quantum feedback control, and apply them to quantum state preparation in the atomic ensemble. We consider three cases: producing spin-squeezed states, preparing Dicke states (the long-time limit), and producing twin-ensemble squeezing. Where appropriate, we emphasize relations with experiments.