  Exceptional points (EPs), at which more than one eigenvalue and eigenvector
coalesce, are unique spectral features of Non-Hermiticity (NH) systems. They
exist widely in open systems with complex energy spectra. We experimentally
demonstrate the appearance of paired EPs in a periodical driven degenerate
optical cavity along the synthetic orbital angular momentum (OAM) dimension
with a tunable parameter. The complex-energy band structures and the key
features of EPs, i.e. their Fermi arcs, parity-time symmetry breaking
transition, energy swapping, and half-integer band windings are directly
observed by detecting the cavity's transmission spectrum. Our results advance
the fundamental understanding of NH physics and demonstrate the flexibility of
using the photonic synthetic dimensions to implement NH systems.
