Detecting topological edge states with the dynamics of a qubit

TL;DR

This paper demonstrates that coupling a qubit to an SSH chain allows for the detection of topological edge states through qubit decoherence dynamics, revealing strong even-odd oscillations related to the presence of edge states.

Contribution

It introduces a method to detect topological edge states using qubit dynamics, providing a new tool for probing topological phases in quantum systems.

Findings

Qubit decoherence rate oscillates with chain length, indicating edge state presence.

Qubit acts as an efficient detector for topological edge states.

Method generalizes to other topological systems.

Abstract

We consider the Su-Schrieffer-Heeger (SSH) chain, which has 0, 1, or 2 topological edge states depending on the ratio of the hopping parameters and the parity of the chain length. We couple a qubit to one edge of the SSH chain and a semi-infinite undimerized chain to the other, and evaluate the dynamics of the qubit. By evaluating the decoherence rate of the qubit we can probe the edge states of the SSH chain. The rate shows strong even-odd oscillations with the number of sites reflecting the presence or absence of edge states. Hence, the qubit acts as an efficient detector of the topological edge states of the SSH model. This can be generalized to other topological systems.