Fluctuation-dissipation theorem and fundamental photon commutation relations in lossy nanostructures using quasinormal modes

Sebastian Franke,Marten Richter,Stephen Hughes,Juanjuan Ren

doi:10.1103/physrevresearch.2.033332

Sebastian Franke, Marten Richter + Show 2 more

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https://doi.org/10.1103/physrevresearch.2.033332

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Abstract

We provide theory and formal insight on the Green function quantization method for absorptive and dispersive spatial-inhomogeneous media in the context of dielectric media. We show that a fundamental Green function identity, which appears, e.g., in the fundamental commutation relation of the electromagnetic fields, is also valid in the limit of non-absorbing media. We also demonstrate how the zero-point field fluctuations yields a non-vanishing surface term in configurations without absorption, when using a more formal procedure of the Green function quantization method. We then apply the presented method to a recently developed theory of photon quantization using quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)] for finite nanostructures embedded in a lossless background medium. We discuss the strict dielectric limit of the commutation relations of the quasinormal mode operators and present different methods to obtain them, connected to the radiative loss for non-absorptive but open resonators. We show exemplary calculations of a fully three-dimensional photonic crystal beam cavity, including the lossless limit, which supports a single quasinormal mode and discuss the limits of the commutation relation for vanishing damping (no material loss and no radiative loss).

Highlights

In the limit α → 0, the sequence converges to the actual permittivity, allowing us to address explicitly the situation of a lossy or lossless resonator in a infinite lossless background medium
We have explicitly derived a form of the zero-point field fluctuations that includes a volume integral over the absorptive region and a surface term, connected to the radiative dissipation into the lossless background medium, which does not depend on the imaginary part of the permittivity
We have applied the method to a recent quasinormal modes (QNMs) quantization scheme and confirmed a contribution associated to the radiative loss

Summary

Introduction

Cavity-QED phenomena in photonics nanostructures and nanolasers, such as metal nanoparticles [1,2,3,4,5] or semiconductor and dielectric microvavities [6,7,8,9,10], have become an important and rising field in the research area of quantum optics and quantum plasmonics over the last few decades, since it provides a suitable platform to study, e.g., nonclassical light effects [11,12] and quantum information processes [13,14]. A rigorous quantum optics theory for these systems is of great importance to describe the underlying mechanisms and applications of light-matter interaction in these dissipative systems. The theory has already been successfully applied to many technologically interesting quantum optical scenarios, e.g., input-output in multilayered absorbing structures [19], active quantum emitters in the vicinity of a metal sphere [20,21], the vacuum Casimir effect [22], strong coupling effects in quantum plasmonics [23,24], and non-Markovian dynamics in nonreciprocal environments [25]

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