Critical Topological Photonics in Synthetic Dimensions

Abstract

Topological states and criticality have long been regarded as incompatible ingredients: the former requires a finite spectral gap, whereas the latter demands its closure. Guided by this view, topological photonics has focused almost exclusively on gapped phases, treating gap-closing transitions as mere phase boundaries. In this work, we propose a class of topological states in which topology coexists with criticality in experimentally accessible synthetic-frequency photonic platforms. In a one-dimensional (1D) synthetic lattice, we identify such critical topological photonic states through midgap degeneracies in the single-particle entanglement spectrum, and uncover a topology-enforced multicritical point that reorganizes the topology of neighboring critical states. We further extend this framework to two dimensions (2D). Our work provides an experimentally accessible route to critical topological photonics, and may also inspire novel applications such as critical topological sensing.