Emergent Haldane Model and Photon-Valley Locking in Chiral Cavities

Chirality, often connected with topology, holds significant importance in both electronic and photonic systems. In this study, we demonstrate the potential use of quantum fluctuations in a photonic chiral cavity to realize the electronic Haldane model---a model recognized for its pioneering nature yet posing formidable challenges to be realized in real materials. Through the recently developed asymptotically-decoupled framework, we derive the emergence of a staggered-flux gauge field resulting from strong light-matter coupling within the chiral cavity. We show that valley polarization can be achieved by breaking the inversion symmetry of cavity graphene under equilibrium conditions. Remarkably, the topological properties of graphene could reciprocally influence cavity photons, leading to distinct photon number locking with valley electrons, linked to the Berry curvatures at opposite valleys. Furthermore, we propose a unique way to characterize topological phase transitions by probing cavity photons during interband transitions. Our findings highlight the remarkable potential of using cavity quantum fluctuations to engineer electronic and photonic properties specific to valleys and topologies, particularly within the realm of strong light-matter coupling.