  Room temperature strong coupling from CdSeS/Zn quantum-dots embedded into a
tunable porous-silicon Fibonacci-conjugated array could be observed when
exciton's energy was tuned either to the photonic-edge or the defect in the
middle of the pseudo-bandgap region of the 1D cavity. Both, the photonic-edge
and the defect could be identified as topological edge modes and
quasi-bound-states-in-the-continuum, where large density of states and field
localization over a wider bandwidth produce a broadband Purcell enhancement,
helping to optimize the coupling among the exciton and the 1D photonic
quasi-crystal despite the natural difficulty to make the quantum dots to
penetrate the cavity pores. A clear repulsion among polaritons, amounting to
almost 8 meV for in-plane k values when the cavity energy is larger than the
exciton one (blue k-detuning), was measured when increasing the incident light
fluence, marking the potential of this non-trivial topological array for
achieving polariton quantum blockade. Evidence for ultra-strong coupling, where
a shift as large as 20 meV, could be found when the defect of the
pseudo-bandgap region of the cavity was tuned to the exciton.
