Non-Markovian Dynamics in Chiral Quantum Networks with Spins and Photons

TL;DR

This paper investigates non-Markovian dynamics in chiral quantum networks mediated by spin excitations, revealing effects like quantum dimer formation and enabling quantum information protocols with spintronic circuits.

Contribution

It introduces a method to analyze non-Markovian effects in spin-mediated quantum networks using time-dependent density matrix renormalization group techniques.

Findings

Non-Markovian effects influence quantum dimer formation.

Engineered spintronic elements enable quantum state transfer.

Finite spin propagation velocities cause time delays in interactions.

Abstract

We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to familiar photonic networks where driven two-level atoms exchange photons via 1D photonic nanostructures, we propose and study a setup where interactions between the atoms are mediated by spin excitations (magnons) in 1D $XX$ spin chains representing spin waveguides. While Markovian quantum network theory eliminates quantum channels as structureless reservoirs in a Born-Markov approximation to obtain a master equation for the nodes, we are interested in non-Markovian dynamics. This arises from the nonlinear character of the dispersion with band-edge effects, and from finite spin propagation velocities leading to time delays in interactions. To account for the non-Markovian dynamics we treat the quantum degrees of freedom of the nodes and connecting channels as a composite spin system with the surrounding of the quantum network as a Markovian bath, allowing for an efficient solution with time-dependent density matrix renormalization group techniques. We illustrate our approach showing non-Markovian effects in the driven-dissipative formation of quantum dimers, and we present examples for quantum information protocols involving quantum state transfer with engineered elements as basic building blocks of quantum spintronic circuits.