Quantum-Optical Bound States in the Continuum

Abstract

Bound states in the continuum (BICs) are counterintuitive localized states that lie within the continuum of extended states. While extensively realized and utilized in classical wave systems, it is still unclear what a close analog of BICs would be, and how to extract their experimental signature in quantum-optical settings -- where the wave field itself is quantized into bosonic excitations. Here, we present a paradigmatic quantum-optical model consisting of a driven multi-level Jaynes-Cummings (JC) system, featuring few quantum degrees of freedom yet capable of hosting a BIC. Using the concept of a Fock-state lattice (FSL), this model can be mapped to an extended structure comprising two semi-infinite inhomogeneous Su-Schrieffer-Heeger (SSH) chains coupled to a common continuum. An appropriate quantum superposition of two topological zero modes from the separate chains forms a BIC that remains perfectly localized in the Fock-state dimension within the continuum spectrum, due to complete decoupling from the common continuum via destructive quantum interference. We further develop a method to extract the spectroscopic signature of the BIC -- a discrete peak embedded in a continuous background -- by Fourier-transforming the time-dependent dynamics of the system's chiral-symmetry operator. A highly feasible experimental proposal using a single trapped ion is provided. Our work bridges BIC physics with quantum optics, opening a pathway to harnessing such exotic states at the quantum limit.