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 ${\mathbb{Z}}_{2}$ local symmetry as a result of the counter-rotating wave (pairing) terms. The topology is protected by the sublattice symmetry, represented by an antiunitary transformation. We present a method 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 toward disorder.