A quantum optical description of losses in ring resonators based on field operator transformations

TL;DR

This paper introduces an operator-based method to model losses in quantum ring resonators, providing a more general framework than traditional approaches and ensuring quantum consistency across a wider range of conditions.

Contribution

It presents the OVPA approach for quantum loss modeling in ring resonators, extending beyond near-resonance limitations of conventional Langevin methods.

Findings

OVPA approach preserves operator commutation relations.

Results agree with Langevin approach near resonances.

OVPA remains valid far from resonances.

Abstract

In this work we examine loss in ring resonator networks from an "operator valued phasor addition" approach (or OVPA approach) which considers the multiple transmission and cross coupling paths of a quantum field traversing a ring resonator coupled to one or two external waveguide buses. We demonstrate the consistency of our approach by the preservation of the operator commutation relation of the out-coupled bus mode. We compare our results to those obtained from the conventional quantum Langevin approach which introduces noise operators in addition to the quantum Heisenberg equations in order to preserve commutation relations in the presence of loss. It is shown that the two expressions agree in the neighborhood of a cavity resonance where the Langevin approach is applicable, whereas the operator valued phasor addition expression we derive is more general, remaining valid far from resonances.