Canonical circuit quantization with linear nonreciprocal devices

TL;DR

This paper develops a systematic theoretical framework for incorporating ideal nonreciprocal devices like gyrators and circulators into quantum circuit quantization, enabling better analysis of nonreciprocal quantum networks.

Contribution

It introduces a general Lagrangian and Hamiltonian approach for nonreciprocal devices in quantum circuits, applicable to various circuit configurations and device models.

Findings

Unified theory for nonreciprocal device integration

Comparison with impedance and scattering matrix approaches

Application to circuits with Josephson and phase-slip junctions

Abstract

Nonreciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that they couple, and can be used to create chiral information processing networks. We study the systematic inclusion of ideal gyrators and circulators into Lagrangian and Hamiltonian descriptions of lumped-element electrical networks. The proposed theory is of wide applicability in general nonreciprocal networks on the quantum regime. We apply it to pedagogical and pathological examples of circuits containing Josephson junctions and ideal nonreciprocal elements described by admittance matrices, and compare it with the more involved treatment of circuits based on nonreciprocal devices characterized by impedance or scattering matrices. Finally, we discuss the dual quantization of circuits containing phase-slip junctions and nonreciprocal devices.