Topological Zak Phase in Strongly-Coupled LC Circuits

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 Z2 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. The winding of the topological Zak phase across the Brillouin zone can be measured by a reflection measurement of (microwave) light. Our method probes bulk quantities and can be implemented even in small systems (∼10 unit cells). We also study the robustness of edge modes towards disorder.