Position-Resolved Resonance Quantization for Lossy Cavities

TL;DR

This paper introduces a novel position-resolved resonance quantization method for lossy cavities, extending traditional models to better handle highly open and extended quantum resonator systems.

Contribution

It develops a systematic approach to quantize resonances with position-resolved modes, unifying pseudomodes and quasi-normal modes theories for lossy cavities.

Findings

Successfully benchmarks the method on a 1D resonator example.

Provides a criterion for constructing the ansatz parameters.

Enhances modeling of open quantum resonator systems.

Abstract

Modern experiments in resonators are moving to ever more extreme quantum regimes, posing major challenges to established theoretical approaches, such as so-called few-mode models. While these models have driven major insights for traditional regimes, they are now hitting their limitations for highly open cavities and extended systems, as encountered in cavity experiments with molecules and solid-state systems. Here, we present a novel method that significantly extends the conceptual underpinning of these discrete-mode models, promoting them to a systematic treatment. We develop an ansatz which allows to quantize the resonator's resonances with position-resolved discrete modes, thus naturally incorporating losses in the formalism. Such a construction effectively unifies key ideas from pseudomodes and quantized quasi-normal modes theory. We further present a criterion for construction of the ansatz parameters at every point in space, and semi-analytically benchmark the resulting solution for a paradigmatic one-dimensional example resonator.