Quantum Feedback Delay Networks

Hannes Pichler

Hendra I. Nurdin, John Edward Gough

Quantum feedback networks with non-negligible propagation delays in the interconnecting edges have recently gained attention. Grimsmo has analysed the evolution of a Markov quantum system coupled to a single field via a doublepass interaction with a time delay and derived the evolution equation for the state (density operator) of the system (after tracing out the field) using a super-operator notion of partial tracing together with a tensor network representation. However, for the purposes of feedback control (both measurement-based and coherent feedback), the propagating output fields of the system can be used to facilitate feedback interconnections. Thus it is desirable to have an equivalent input-output description of quantum systems that incorporates time delays, without tracing out the field. Here, we first extend the analysis to the setting of a single system coupled to optical fields in multiple channels with a feedback structure in which the fields makes infinite repeated interactions with the system. Then we generalise this to the setting of quantum feedback networks with both instantaneous interconnections and uniform time delays in the interconnection.

Arne L. Grimsmo

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.

Guofeng Zhang, M. R. James

John Edward Gough, M. R. James

Sven M. Hein, Franz Schulze, Alexander Carmele +1 more

A crucial property of quantum networks is the entanglement between different network nodes. We demonstrate that entanglement in quantum networks can be created and controlled by introducing quantum-coherent time-delayed self-feedback at single nodes.