Spectra of low-lying elementary excitations are critical to characterize properties of bosonic quantum fluids. Usually these spectra are difficult to observe, due to low occupation of non-condensate states compared to the ground state. Recently, low-threshold Bose-Einstein condensation was realised in a symmetry-protected bound state in the continuum, at a saddle point, thanks to coupling of this electromagnetic resonance to semiconductor excitons. While it has opened the door to long-living polariton condensates, their intrinsic collective properties are still unexplored. Here we unveil the peculiar features of the Bogoliubov spectrum of excitations in this system. Thanks to the dark nature of the bound-in-the-continuum state, collective excitations lying directly above the condensate become observable in enhanced detail. We reveal interesting aspects, such as energy-flat parts of the dispersion characterized by two parallel stripes in photoluminescence pattern, pronounced linearization at non-zero momenta in one of the directions, and a strongly anisotropic velocity of sound.

Excitonic coupling, electronic coupling, and cooperative interactions in self-assembled lead halide perovskite nanocrystals were reported to give rise to a red-shifted collective emission peak with accelerated dynamics. Here we report that similar spectroscopic features could appear as a result of the nanocrystal reactivity within the self-assembled superlattices. This is demonstrated by studying CsPbBr₃ nanocrystal superlattices over time with room-temperature and cryogenic micro-photoluminescence spectroscopy, X-ray diffraction, and electron microscopy. It is shown that a gradual contraction of the superlattices and subsequent coalescence of the nanocrystals occurs over several days of keeping such structures under vacuum. As a result, a narrow, low-energy emission peak is observed at 4 K with a concomitant shortening of the photoluminescence lifetime due to the energy transfer between nanocrystals. When exposed to air, self-assembled CsPbBr₃ nanocrystals develop bulk-like CsPbBr₃ particles on top of the superlattices. At 4 K, these particles produce a distribution of narrow, low-energy emission peaks with short lifetimes and excitation fluence-dependent, oscillatory decays. Overall, the aging of CsPbBr₃ nanocrystal assemblies dramatically alters their emission properties and that should not be overlooked when studying collective optoelectronic phenomena nor confused with superfluorescence effects.