Isolated Loops in Quantum Feedback Networks

TL;DR

This paper analyzes how isolated feedback loops in quantum networks modify the Hamiltonian interactions, enabling engineered couplings between subsystems, with theoretical derivations and illustrative examples.

Contribution

It derives the modified Hamiltonian for general SLH quantum networks with isolated loops and shows how to engineer interactions between subnetworks.

Findings

Isolated loops alter the network's Hamiltonian structure.

Modified Hamiltonians enable engineered interactions.

Examples demonstrate practical application of the theory.

Abstract

A scheme making use of an isolated feedback loop was recently proposed in \cite{GP_} for creating an arbitrary bilinear Hamiltonian interaction between two multi-mode Linear Quantum Stochastic Systems (LQSSs). In this work we examine the presence of an isolated feedback loop in a general SLH network, and derive the modified Hamiltonian of the network due to the presence of the loop. In the case of a bipartite network with an isolated loop running through both parts, this results in modified Hamiltonians for each subnetwork, as well as a Hamiltonian interaction between them. As in the LQSS case, by engineering appropriate ports in each subnetwork, we may create desired interactions between them. Examples are provided that illustrate the general theory.