Angular momentum dependent spectral shift in chiral vacuum cavities

Based on a hybrid light-matter unitary transformation for cavity quantum electrodynamics, we investigate the spectral shift of an atom induced by quantum fluctuations in a chiral vacuum cavity. Remarkably, we find an intriguing angular momentum dependent shift in the spectra of bound states. Our approach shows promise in going beyond traditional perturbative methods and demonstrates effectiveness even in the strong-coupling limit, as evidenced by our numerical benchmarks in the case of a two-dimensional quantum harmonic oscillator. In addition, we establish a cavity-interaction picture for calculating the chiral vacuum Rabi oscillation in the strong-coupling limit for a generic central potential. The anomalous spectral shift revealed in this study possesses both fundamental and practical significance and could be readily observed in experiments.