In recent years, superconducting circuits have become a promising architecture for quantum computing and quantum simulation. This advancing technology offers excellent scalability, long coherence times, and large photon nonlinearities, making it a versatile platform for studying non-equilibrium condensed matter physics with light. This thesis covers a series of experiments and theoretical developments aimed at probing strongly correlated states of interacting photons. Building upon previous efforts on nonlinear superconducting lattices, this work focuses on establishing new platforms for generating interactions between microwave photons in multi-mode circuits.
The first experiment presents a new paradigm in exploiting the nonlinearity of a Josephson junction to tailor the Hilbert space of harmonic oscillators. This allows a single microwave resonator to be addressed as a two-level system. A theoretical proposal is outlined for building a field-programmable quantum simulator using a lattice of harmonic modes defined in synthetic dimensions. The idea is to harness this dynamical nonlinearity for stimulating photon-photon interactions. Numerical studies show that the steady-state of this driven lattice develops a crystalline phase for photons.
The second experiment explores the physics of quantum impurities, where a single well-controlled qubit is coupled to the many modes of a photonic crystal waveguide. The light-matter coupling strength is pushed into the ultrastrong coupling regime, where the qubit is simultaneously hybridized with many modes and the total number of excitations is not conserved. Probing transport through the waveguide reveals that multi-photon bound states participate in the scattering dynamics of a single photon. Furthermore, the effective photon interactions induced by just this single impurity leads to inelastic emission of photons. Probing correlations in the field emission reveals signatures of multi-mode entanglement.
This work presents opportunities for exploring large-scale lattices with strongly interacting photons. These platforms are compatible with well-established techniques for generating artificial magnetic fields and stabilizing many-body states through reservoir engineering, complementing growing efforts in the quest for building synthetic quantum materials with light.