  The competition between staggered imaginary potentials and lattice
dimerization results in a unidirectional propagating coalescing state of a
non-Hermitian Su-Schrieffer-Heeger (SSH) ring at an exceptional point. A
segment of the SSH ring inherits the unidirectional feature and exhibits some
intriguing dynamic behaviors when it is embedded in a Hermitian chain as a
$\mathcal{PT}$-symmetric scattering center. Based on the Bethe ansatz
scattering solution for the interface between Hermitian and non-Hermitian
regions, we show that the SSH scattering center supports the following
wave-packet dynamics. (i) A left incident wave packet is allowed perfect
transmission, while a right incident wave packet stimulates an amplified
reflecting wave train with the length proportional to the size of the SSH
segment. Accordingly, a unidirectional invisibility of Bragg scatterers is
observed when a multi-SSH segment is considered. (ii) A left incident wave
packet can be well confined in a SSH segment if the right lead is removed.
(iii) In addition, a wave packet is perfectly absorbed when its size closes to
the length of the SSH segment. The underlying mechanism stems from a subtle
property of the SSH segment, which supports two quasicoalescing wave packets
but with opposite group velocities. Our findings are applicable to the schemes
of realizing quantum state storage, quantum diode, and lasing device.
