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Frontiers in Optics

Effective Photonic Modes and Quantization Volume for Cavity Quantum Electrodynamics

Michael A. D. Taylor, Pengfei Huo

Published Jan 1, 2024• 0 citations
Publisher

Abstract

Cavity light-matter coupling strength scales inversely on quantization volume, yet strong coupling occurs in Fabry-Perot cavities with macroscopic mirrors. We demystify this apparent contradiction by transforming the Hamiltonian into effective photonic modes, showing mirror-size independence.
DOI
10.1364/fio.2024.jw5a.71

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We introduce an effective modes formalism to describe how the quasi-continuum of photonic modes in an optical cavity effectively behaves in the strong light-matter coupling regime of cavity quantum electrodynamics. By expressing these effective modes, we are able to reproduce the cavity dispersion relation while showing that the mode volumes of these effective modes are independent of the physical area of the Fabry-Pérot cavity mirrors and are instead a measure of light-matter coupling strength, dependent on cavity design parameters such as mirror reflectivity.
Quantum light-matter systems at strong coupling are notoriously challenging to analyze due to the need to include states with many excitations in every coupled mode. We propose a nonperturbative approach to analyze light-matter correlations at all interaction strengths. The key element of our approach is a unitary transformation that achieves asymptotic decoupling of light and matter degrees of freedom in the limit where light-matter interaction becomes the dominant energy scale. In the transformed frame, truncation of the matter or photon Hilbert space is increasingly well justified at larger coupling, enabling one to systematically derive low-energy effective models, such as tight-binding Hamiltonians. We demonstrate the versatility of our approach by applying it to concrete models relevant to electrons in crystal potential and electric dipoles interacting with a cavity mode. A generalization to the case of spatially varying electromagnetic modes is also discussed.
Abstract Control of light–matter coupling at the quantum level is an enabling technique for many emerging quantum technologies. This tutorial describes recent advances in achieving efficient coupling of light with a single molecule using an optical Fabry–Perot microcavity. We demonstrate that the efficient cavity-molecule coupling converts the molecule to an effective two-level system. In this regime, a single molecule can act as a nearly perfect reflecting mirror and exhibits optical nonlinearity at the ultimate level of single photons.
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