Superconducting topological metamaterial coupled to flux-tunable transmon qubit: toward analog quantum simulation with giant atoms

This report present the detailed description regarding the realization of a photonic multimode environment coupled to a flux tunable artificial atom. This represent a step toward the realization of an analog quantum simulator, allowing for the experimental study of interacting two-level systems in structured environments. The platform consist of a metamaterial made out of an array of coupled Niobium Nitride (NbN) lumped-element microwave superconducting resonators, capacitively coupled to a magnetic flux tunable transmon qubit. Thin NbN films allow to achieve extremely high kinetic inductance up to 90pH/¿ due to their intrinsic disorder; on one side the resulting high impedance allows to achieve ultra strong coupling regime, on the other it allows to realize extremely compact resonator arrays; Furthermore, such platform represent an extremely versatile device, allowing for the analog quantum simulation of a two level system interacting with an engineered non-trivial photonic dispersion relation, such as SSH states exhibiting topological properties The achievement of falling group velocity at the band edge of the photonic environment, allows for the study of atom-photon bound state; from the physical perspective, this represent a fundamental step toward the study of spin systems, device side instead, such platform’s features allows for the realization of quantum random access memory for the future realization of large scale, long distance interacting qubit based, quantum processors. Engineering the metamaterial coupling allows for the exhibition of left-handedness , fundamental for the realization of high kinetic inductance quantum limited travelling wave parametric amplifiers (K-TWPA). On the context of this thesis, the system has been modeled, designed, numerically and FEM simulated, fabricated and experimentally characterized in a cryogenic environment.