  An open quantum system operated at the spectral singularities where
dimensionality reduces, known as exceptional points (EPs), demonstrates
distinguishing behavior from the Hermitian counterpart. Here, we present an
analytical description of local density of states (LDOS) for microcavity
featuring chiral EPs, and unveil the anomalous spontaneous emission dynamics
from a quantum emitter (QE) due to the non-Lorentzian response of EPs.
Specifically, we reveal that a square Lorentzian term of LDOS contributed by
chiral EPs can destructively interfere with the linear Lorentzian profile,
resulting in the null Purcell enhancement to a QE with special transition
frequency, which we call {\it{EP induced transparency}}. While for the case of
constructive interference, the square Lorentzian term can narrow the linewidth
of Rabi splitting even below that of bare components, and thus significantly
suppresses the decay of Rabi oscillation. Interestingly, we further find that
an open microcavity with chiral EPs supports atom-photon bound states for
population trapping and decay suppression in long-time dynamics. As
applications, we demonstrate the advantages of microcavity operated at chiral
EPs in achieving high-fidelity entanglement generation and high-efficiency
single-photon generation. Our work unveils the exotic cavity quantum
electrodynamics unique to chiral EPs, which opens the door for controlling
light-matter interaction at the quantum level through non-Hermiticity, and
holds great potential in building high-performance quantum-optics devices.
