Quantum metamaterials with complete graph interfaces in the ultrastrong coupling regime

This work studies the ultrastrong coupling (USC) regime for quantized electromagnetic (EM) fields interacting with two-level systems (qubits) arranged within the complete graph nodes of photonic networks beyond the rotating wave approximation. We show the nontrivial behavior of Bloch–Siegert (BS) phase inherent to the field is established in the structure. The collective BS phase dominates under the strong matter-field coupling condition. The network complete graph interface significantly improves the cooperativity parameter to achieve this condition. However, increasing the coupling parameter essentially beyond the strong coupling condition causes saturation effects that suppress the collective photonic phase. We demonstrate that in the USC regime the EM field exhibits the features of a single qubit BS phase enhanced by the network connectivity. Our findings open new perspectives in quantum information processing with superconductor metamaterials.