Time-delayed quantum feedback control

TL;DR

This paper develops a theoretical framework for understanding and controlling quantum systems with time-delayed feedback, revealing how delays influence dynamics and enabling quantum control despite delays.

Contribution

It introduces a novel tensor network approach to model time-delayed quantum feedback and applies it to a two-level atom, demonstrating delay effects on quantum dynamics and control.

Findings

Delay effects qualitatively alter atomic dynamics

Quantum control can be achieved with time-delayed feedback

The tensor network method effectively models time delays in quantum systems

Abstract

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.