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We investigate polariton-phonon hybrid excitations, which describe the collective excitations of emitter-photon polaritons and vibrational phonons, in a periodic array of vibrating two-level emitters interacting with waveguide photons. These excitations present unexpected features in the subradiant regime, including the appearance of topological edge states and transitions between ergodic and multifractal excitations. We reveal that these features are attributed to the emergence of a phonon-induced quasiperiodic structure, where phonons can effectively create a periodic potential that is incommensurate with the emitter lattice. A possible realization consisting of an array of laser-cooled atoms trapped near an optical nanofiber is also proposed. Our results demonstrate the possibility of utilizing vibrations as a unique degree of freedom in the exploration of many-body physics with waveguide quantum electrodynamics systems.
Zhu et al. (Tue,) studied this question.