Self-organized quasicrystals and their excitations in dipolar Bose-Einstein condensates via optical feedback

Quasicrystals emerge from competing interactions with incommensurate characteristic length scales that inhibit translational periodicity. Here, we show that such multiscale interactions can be realized in a dipolar Bose-Einstein condensate through the interplay between intrinsic dipole-dipole interactions and photon-mediated interactions generated by coupling to an excited-state manifold together with a suitably engineered optical feedback. This interplay gives rise to two pronounced roton instabilities in the Bogoliubov excitation spectrum, leading to a rich ground-state phase diagram including dodecagonal quasicrystals with twelvefold rotational symmetry for experimentally realistic parameters. We further propose a protocol to access these quasicrystals dynamically and develop a general numerical framework for calculating their collective excitation spectra.