  Engineered non-Hermitian systems featuring exceptional points can lead to a
host of extraordinary phenomena in diverse fields ranging from photonics,
acoustics, opto-mechanics, electronics, to atomic physics. Here we introduce
and present non-Hermitian dynamics of coupled optical parametric oscillators
(OPOs) arising from phase-sensitive amplification and de-amplification, and
show their distinct advantages over conventional non-Hermitian systems relying
on laser gain and loss. OPO-based non-Hermitian systems can benefit from the
instantaneous nature of the parametric gain, noiseless phase-sensitive
amplification, and rich quantum and classical nonlinear dynamics. We show that
two coupled OPOs can exhibit spectral anti-PT symmetry and an exceptional point
between its degenerate and non-degenerate operation regimes. To demonstrate the
distinct potentials of the coupled OPO system compared to conventional
non-Hermitian systems, we present higher-order exceptional points with two
OPOs, tunable Floquet exceptional points in a reconfigurable dynamic
non-Hermitian system, and generation of squeezed vacuum around exceptional
points, all of which are not easy to realize in other non-Hermitian platforms.
Our results show that coupled OPOs are an outstanding non-Hermitian setting
with unprecedented opportunities in realizing nonlinear dynamical systems for
enhanced sensing and quantum information processing.
