Light-matter interactions in a Hofstadter lattice with next-nearest-neighbor couplings

The light-matter interactions for an emitter coupling to the bulk region of a Hofstadter lattice were recently investigated by De Bernardis et al. [Phys. Rev. Lett. 126, 103603 (2021)10.1103/PhysRevLett.126.103603]. We propose light-matter interactions in an extended Hofstadter lattice with the next-nearest-neighbor (NNN) couplings. Compared with the standard Hofstadter lattice, the NNN couplings break the mirror symmetry and the energy bands are not flat, but are dispersive with nonzero group velocity. In contrast to the study by De Bernardis et al., when a two-level emitter interacts with the bulk region of the extended Hofstadter lattice, the emitter is no longer trapped by the coherent oscillations and can radiate photons unidirectionally. The chiral mechanism stems from the broken mirror symmetry. Both the radiation rate and the chirality periodically change with the emitter's coupling position. All of those particular features can be realized on the photonic lattice platform and may find potential application in chiral quantum information processing.