Collective scattering in hybrid nanostructures with many atomic oscillators coupled to an electromagnetic resonance

Abstract

There is considerable interest in collective effects in hybrid systems formed by molecular or atomic ensembles strongly coupled by an electromagnetic resonance. For analyzing such collective effects, we develop an efficient and general theoretical formalism based on the natural modes of the resonator. The main strength of our approach is its generality and the high level of analyticity enabled by modal analysis, which allows one to model complex hybrid systems without any restriction on the resonator shapes or material properties, and to perform statistical computations to predict general properties that are robust to spatial and polarization disorders. Most notably, we establish that superradiant modes remain even after ensemble averaging and act as an "invisibility cloak" with a spectral bandwidth that scales with the number of oscillators and the spatially-averaged Purcell factor. INTRODUCTIONCooperative scattering by large collections of quantum emitters has become increasingly important in modern science and technology, 1-3 an emblematic example being Dicke superradiance. 4 Of particular interest are high cooperativity regimes, which are promoted by long-range interactions and quantum cavity-electrodynamic effects with electromagnetic resonances. Recent exemplary advances encompass the generation of coherent visible radiation by many emitters placed near plasmonic nanoparticles 5-6 or hybrid quantum systems combining coldatom clouds with photonic-crystal resonances. [7][8] Even for steady-state cases, the theoretical analysis of quantum hybrids represents a major challenge in computational electrodynamics, requiring the repeated calculation of the full-photon Green's functions of the resonator for different frequencies and atomic positions. [9][10][11] The challenge worsens when studying the dynamics by iteratively solving coupled equations for the Maxwell's fields and carrier-population operators, [12][13] or when computing ensemble-averaged responses [14][15] to interpret experiments for which the exact location and orientation of atoms are unknown. [16][17][18] Here, we provide a powerful computational "toolkit" based on the natural modes of the resonator for analyzing collective effects in large ensembles of atoms or molecules coupled by an electromagnetic resonator, which could be a high-Q or low-Q micro-nanoresonator, possibly with a spectral overlap of several resonances. The main strength of our approach is the high level of analyticity brought on by the modal analysis of the emitterresonator interaction, which enables one to perform statistical treatments and to predict general properties that are robust to spatial and polarization disorders. We adopt a classical polarizability model for the quantum emitters. Classical-oscillator treatments cannot describe all aspects of quantum hybrids, but in return provide a rudimentary and intuitive tool, which is general enough to predict many important features of quantum systems and is reusable in quantum formalisms. [19][20][21][22]10 Additionally, cooperati...

Light Interaction with Photonic and Plasmonic Resonances

“…As a consequence, a direct computation of all sub/super‐radiant states of the hybrid system becomes feasible in a small timescale by solving a generalized eigenproblem and some essential properties of hybrids, which are robust to spatial and polarization disorders, become predictable. For instance, it can be shown that the mean decay rate of the superradiant states, where denotes an ensemble average, scales linearly with the mean Purcell Factor , evidencing that ultra‐bright hybrid states in large ensembles of emitters coupled via an electromagnetic resonance arise from the combination of Dicke and Purcell effects, and not from direct dipole‐dipole interactions like in the classical Dicke effect …”

“…The present period is marked by a deployment of QNM concepts in various applications, quantum plasmonics, spectral filtering with diffraction gratings, energy loss spectroscopy in plasmonic nanostructures, second‐harmonic generation in metal nanoparticles, coupled cavity‐waveguide systems, single‐photon antennas, ultrafast‐dynamics nanooptics, scattering‐matrix reconstruction in complex systems, spontaneous emission at exceptional points, wave transport in disordered media, spatial coherence in complex media, mode hybridization and exceptional points in complex photonic structures, random lasing, light localization and cooperative phenomena in cold atomic clouds, spatially nonlocal response in plasmonic nanoresonators, and thermal emission . We discuss some of these numerous applications of QNM concepts in this Review and Figure summarizes a few.…”

“…The left inset shows the superradiant state of the hybrid, with a large cooperativity involving more than one half of the molecules. Reproduced with permission . Copyright 2017, American Physical Society.…”

Electromagnetic interactions of dye molecules surrounding a nanosphere

“…Molecule-nanoparticle electromagnetic interactions are central to many current research topics, beyond the illustrative examples treated in this work. Of particular interest will be the study of dielectric nano-resonators 33 with high quality factors, the dependence of strong coupling 29,34 on surface coverage and molecular orientation when the core particle sustains a resonance tuned with the molecular resonance, but also the influence of a core particle on superradiance 35 , or Föster resonant energy transfer 36,37 between collections of dipole emitters. The subtle changes in the polarisation properties of the local electric field have also promising applications in the understanding of surface selection rules and surface-enhanced optical activity near nanostructures.…”

“…S1). The theoretical framework is however much more general, and could readily be applied to other types of emitters or nanoparticles 32 , to dielectric nano-resonators 33 , and also in the context of strong coupling 29,34 , superradiance 35 , Föster resonant energy transfer 36,37 , and related effects involving near-field electromagnetic coupling between emitters in the vicinity of a nanoparticle 38 .…”