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

Abstract

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.