Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes

TL;DR

This paper provides a comprehensive pedagogical overview of non-reciprocal quantum interactions, connecting Hamiltonian, scattering, and master equation approaches, emphasizing the role of synthetic gauge fields and dissipation.

Contribution

It unifies various theoretical frameworks for non-reciprocal quantum interactions and discusses their relevance to quantum reservoir engineering and feedforward schemes.

Findings

Synthetic gauge fields combined with dissipation enable non-reciprocal interactions.

Connections established between Hamiltonian, scattering, and master equation descriptions.

Insights into quantum reservoir engineering and measurement-based feedforward techniques.

Abstract

These lecture notes from the 2019 Les Houches Summer School on Quantum Information Machines provides a pedagogical introduction to the theory of non-reciprocal quantum interactions and devices. The goal is connect various approaches and concepts, including Hamiltonians encoding synthetic gauge fields, scattering descriptions, quantum master equations, and non-Hermitian Hamiltonians. The importance of having both non-trivial synthetic gauge fields and dissipation for obtaining non-reciprocal interactions is stressed. Connections to broader topics such as quantum reservoir engineering and the quantum theory of continuous-measurement based feedforward are also discussed.