Quantum feedback control of atomic ensembles and spinor Bose-Einstein condensates

Cold atomic ensembles and spinor Bose-Einstein condensates (BECs) are potential candidates for quantum memories as they have long coherence times and can be coherently controlled. Unlike most candidates for quantum memories which are genuine or effective single particle systems, in atomic ensembles the quantum information is stored as a spin coherent state involving a very large number of atoms. A typical task with such ensembles is to drive the state towards a particular quantum state. While such quantum control methods are well-developed for qubit systems, it is a non-trivial task to extend quantum control methods to the many-particle case. The objective of this work is to deterministically steer an arbitrary state of the atomic ensemble into a desired spin coherent state. To this end, we design our control law using stochastic stability theory, the quantum filtering theorem, and phase contrast imaging. We apply our control laws to different axes and show that it is possible to manipulate the atoms into different target states.