  Non-Hermitian systems based on parity-time (PT) symmetry reveal rich physics
beyond the Hermitian regime. So far, realizations of PT-symmetric systems have
been limited to the spatial domain. Here we theoretically and experimentally
demonstrate PT symmetry in a synthetic spectral dimension induced by nonlinear
Brillouin scattering in a single optical microcavity, where electromagnetically
induced transparency or absorption in two spectral resonances provides the
optical gain and loss to observe a phase transition between two symmetry
regimes. This scheme provides a new paradigm towards the investigation of
non-Hermitian physics in a synthetic photonic dimension for all-optical signal
processing and quantum information science.
