Quantum dynamics on a lossy non-Hermitian lattice

TL;DR

This paper studies quantum walker dynamics on a finite non-Hermitian lattice with loss, revealing how topologically protected edge states influence decay distributions, including counterintuitive edge localization phenomena.

Contribution

It uncovers the relationship between decay probability distributions and topological edge states in non-Hermitian lattices, highlighting novel quantum dynamical behaviors.

Findings

Decay probability distribution varies with regime, showing edge localization in one.

Edge states are topologically protected and linked to non-Bloch winding number.

Counterintuitive decay distribution occurs due to edge state properties.

Abstract

We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.