Topological Zak Phase in Strongly-Coupled LC Circuits

TL;DR

This paper demonstrates the existence of topological Zak phases in strongly-coupled LC circuits, revealing new topological properties and measurement methods in quantum circuit systems.

Contribution

It introduces a model showing topological Bogoliubov excitations in LC circuits with a novel measurement approach for the Zak phase.

Findings

Topological edge modes are robust against disorder.

A method to measure the Zak phase via microwave reflection.

Topological properties are protected by sub-lattice symmetry.

Abstract

We show the emergence of topological Bogoliubov bosonic excitations in the relatively strong coupling limit of an LC (inductance-capacitance) one-dimensional quantum circuit. This dimerized chain model reveals a ${\cal Z}_2$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sub-lattice symmetry, represented by an anti-unitary transformation. We present a methos to measure the winding of the topological Zak phase across the Brillouin zone by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems. We study the robustness of edge modes towards disorder.