Time-delayed quantum feedback control

A theory of time-delayed coherent quantum feedback is developed. More specifically, we consider a quantum system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a fictitious series of cascaded quantum systems, where the system is driven by past versions of itself. The derivation of this model relies on a tensor network representation of the system-reservoir time-propagator. For concreteness, this general theory is applied to a driven two-level atom scattering into a coherent feedback loop. We demonstrate how delay effects can qualitatively change the dynamics of the atom, and how quantum control can be implemented in the presence of time-delays.