Coherent confinement and unidirectional dynamics of a wave packet induced by a non-Hermitian Su-Schrieffer-Heeger segment

Abstract: 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.