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. 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 towards disorder.Topological Bloch bands are characterized by a topological number which is manifested in the appearance of protected edge states. For non-interacting fermions this results in the celebrated integer quantum Hall effect [1], conducting surface states of topological insulators [2,3] and semimetals [2,4]. Topological properties can also be accessed with bosonic systems such as cold atoms [5], photons [6][7][8] and polaritons [9].The Su-Schrieffer-Heeger (SSH) model defined on the dimerized one-dimensional lattice with two sites per unit cell is one of the simplest models demonstrating topological properties [10,11]. The edge states are protected by the bipartite nature of the system (particles can hop only between the two sublattices). Arbitrary long range interaction which respect the bipartite nature of the SSH model may change the topological number but not the robustness of the edge states to disorder [12]. The topology of the SSH model is described by the Zak phase [13], which was measured in cold atoms by introducing an artificial gauge field and mimicking Bloch oscillations [5], in photonic quantum walk [14] and in photonic crystals [15]. The midgap edge stated were observed in dielectric resonators [16], polariton systems [17] and classical LC chains [18], and their wave function was explored in Ref. [18,19]. A two-leg ladder of SSH chains supports fractional excitations and shows a rich topology with two types of corner edge states [20,21]. The ladder is a onedimensional version of a two-dimensional quadrupole insulator [22] realized in Refs. [23][24][25]. In the non-linear regime a dimerized chain shows topologically enforced bifurcations [26].Here, we study topology in the strong coupling regime of quantum circuits in which the rotating wave approximation (RWA) is not applicable, leading to the appearance of counter rotating (pairing) terms. Such strong coupling limit also leads to the evolution of the JaynesCummings model towards the Rabi model when describing the qubit-cavity interaction [7,27], and to the super radiant phase in Dicke model with a macroscopic number of photons in the ground state [28,29] but has not been studied in the framework of topological systems. We start by showing that the counter rotating terms do not change the topology of the system although they modify the nature of the excitations from pure particles to Bogoliubov...
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