# Topological Zak Phase in Strongly-Coupled LC Circuits

### Tal Goren 1 Kirill Plekhanov 1, 2 Félicien Appas 1 Karyn Le Hur 1

#### Physical Review B : Condensed matter and materials physics, American Physical Society, 2018

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.

• 1. CPHT - Centre de Physique Théorique [Palaiseau]
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques