Quantum symmetry breaking of exciton/polaritons in metal-nanorod plasmonic array

We study the collective, superradiant behavior in the system of emitter-dressed Ag nanorods. Starting from the Drude model for the plasmon oscillations, we arrive at a semi-empirical Hamiltonian describing the coupling between quantized surface plasmon modes and the quantum emitters that can be controlled by manipulating their geometry, spacing, and orientation. Further, identifying the lowest polariton mode as SP-states dressed by excitons in the vicinity of $k=0$, we examine conditions allowing for the polariton quantum phase transition. While the system is formally a 1D array, we show that the polariton states of interest can undergo a quantum phase transition to form a Bose condensate at finite temperatures for physically accessible parameter ranges.