  Ultrastrong coupling between optical and material excitations is a distinct
regime of electromagnetic interaction that enables a variety of intriguing
physical phenomena. Traditional ways to ultrastrong light-matter coupling
involve the use of some sorts of quantum emitters, such as organic dyes,
quantum wells, superconducting artificial atoms, or transitions of
two-dimensional electron gases. Often, reaching the ultrastrong coupling domain
requires special conditions, including high vacuum, strong magnetic fields, and
extremely low temperatures. Recent report indicate that a high degree of
light-matter coupling can be attained at ambient conditions with plasmonic
meta-atoms -- artificial metallic nanostructures that replace quantum emitters.
Yet, the fundamental limits on the coupling strength imposed on such systems
have not been identified. Here, using a Hamiltonian approach we theoretically
analyze the formation of polaritonic states and examine the upper limits of the
collective plasmon-photon coupling strength in a number of dense assemblies of
plasmonic meta-atoms. Starting off with spheres, we identify the universal
upper bounds on the normalized collective coupling strength $g/\omega_0$
between ensembles of plasmonic meta-atoms and free-space photons. Next, we
examine spheroidal metallic meta-atoms and show that a strongly elongated
meta-atom is the optimal geometry for attaining the highest value of the
collective coupling strength in the array of meta-atoms. The results could be
valuable for the field of polaritonics studies, quantum technology, and
modifying material properties.
