  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.
