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# Upper bounds on collective light-matter coupling strength with plasmonic meta-atoms

Dec 2022

Ultrastrong coupling between optical and material excitations is a distinctregime of electromagnetic interaction that enables a variety of intriguingphysical phenomena. Traditional ways to ultrastrong light-matter couplinginvolve the use of some sorts of quantum emitters, such as organic dyes,quantum wells, superconducting artificial atoms, or transitions oftwo-dimensional electron gases. Often, reaching the ultrastrong coupling domainrequires special conditions, including high vacuum, strong magnetic fields, andextremely low temperatures. Recent report indicate that a high degree oflight-matter coupling can be attained at ambient conditions with plasmonicmeta-atoms -- artificial metallic nanostructures that replace quantum emitters.Yet, the fundamental limits on the coupling strength imposed on such systemshave not been identified. Here, using a Hamiltonian approach we theoreticallyanalyze the formation of polaritonic states and examine the upper limits of thecollective plasmon-photon coupling strength in a number of dense assemblies ofplasmonic meta-atoms. Starting off with spheres, we identify the universalupper bounds on the normalized collective coupling strength $g/\omega_0$between ensembles of plasmonic meta-atoms and free-space photons. Next, weexamine spheroidal metallic meta-atoms and show that a strongly elongatedmeta-atom is the optimal geometry for attaining the highest value of thecollective coupling strength in the array of meta-atoms. The results could bevaluable for the field of polaritonics studies, quantum technology, andmodifying material properties.

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